What can we learn from a crumpled sheet?
Everyday experience shows that a sheet of paper will crumple when it is crushed. Crumpling is an ubiquitous phenomenon that occurs in a variety of systems, ranging from the membranes of vesicles in living cells to the shells that are used in engineering and packaging. A basic puzzle is the following: Why does a sheet of paper crumple when it is crushed, that is, why does the geometry of the sheet become rough on the scales of the applied stress? I will talk about an analysis of this question and it's generalization where in one considers the confinement of a m-dimensional sheet in a d-dimensional sphere, for general m and d. This leads to some interesting problems in Partial Differential Equations and Differential geometry. I will discuss some of these issues and talk about how the ideas that come out of the analysis of a crumpled sheet may have applications in a variety of interesting problems including String theory, and the development of small scales in fluid flows.
Quantum Annealing
Traditional simulated annealing utilizes thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. We compare thermal and quantum annealing in a model Ising magnet, LiHoxY1-xF4, where the effects of quantum mechanics can be tuned in the laboratory by varying a magnetic field applied transverse to the Ising axis. Our results indicate that quantum annealing indeed hastens convergence to the optimum state.
Order, Temperature and Stability in a Dynamically Driven System
Experiments and simulations have been carried out for a system of particles interacting by Coulomb forces, and contained in a sinusoidally varying quadrupole field, corresponding to a radiofrequency ion trap. As in the experiment, the simulated system settles into an ordered configuration. The kinetic energy of the motion imposed by the external containing field is up to 6 orders of magnitude greater than the thermal energies relevant to order (defined as displacements that are not periodic in the sinusoidally varying field). The coupling between the imposed motion and the 'temperature' is found to be remarkably small, though increasing with temperture.
Dynamics of Cardiac Arrhythmias
Cardiac arrhythmias are disturbances of the heartbeat in which there may be abnormal initiation of the heartbeat, abnormal conduction of the heartbeat or some combination of both. This talk explores how simple conceptual, computational, and experimental models are being used to help understand cardiac arrhythmias in people. A conceptual model for rapid heartbeats often employed by cardiologists assumes excitation travelling in a one dimensional ring. This model has surprisingly rich properties with regard to: instabilities of conduction, the effects of single and multiple stimuli, and the control of instabilities. I also discuss current attempts to develop practical applications of theoretical analysis to cardiology. This talk is directed to a general scientific audience and should be intelligible to cardiologists as well as physicists, mathematicians, and computer scientists.
Similarity solutions for capillary pinch-off in fluids of differing viscosity
Self-similar profiles associated with capillary instability of a fluid thread in a viscous surrounding fluid are obtained for values of viscosity ratio (thread viscosity / surrounding fluid viscosity) from 1/16 to 16 via a simplified numerical scheme. Universal similarity scaling is preserved despite an asymptotically large velocity in the pinching neck driven by nonlocal dynamics. The numerical results agree well with experimental measurements by Cohen, Brenner, Eggers & Nagel. For all viscosity ratios, the self-similar profile is asymmetric and conical far from the minimum. The steep cone slope increases monotonically with viscosity ratio. The shallow cone slope is maximised around viscosity ratio of 1/4.
Scaling Crossover in Paleolake Sediments: From turbulence to fossils
Nature is full with examples of phenomena that show extensive scale invariant behavior as a function of time (e.g. 1/f noise) or of distance (e.g. fractal geometries). Here we address the question of the effect that external disturbances have on a system, embedded in a random environment, subject to a self-organizing dynamics which we assume generates a scale invariant behavior. In particular, we study the stratification of sedimentary deposition of a Pleistocene paleolake at the State of Tlaxcala, Mexico, where diatom fossils alternate with material associated to volcanic activity. In this case the lake's internal (autocthonous) evolutionary processes were disturbed by the external (allocthonous) volcanic activity. Using a formalism developed for the study of intermittency in fluids, we give an interpretation for the scaling crossover observed in the power spectra of the sediment density variations. A Markov chain model is also presented for the underlying dynamics. The model provides some clues for a magnitude-frequency relation for volcanic events.
Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities
The Rayleigh-Taylor instability (RTI) and its shock driven analog, the Richtmyer-Meshkov instability (RMI) , affect a wide variety of important phenomena from sub-terrainian to astrophysical environments. The "fluids" are equally varied from plasmas and magnetic fields to elastic-plastic solids. In most applications, the instabilities occur with a complex acceleration history and evolve to a highly nonlinear state, making the theoretical description formidable. We will link the fluid and plasma regimes while describing the theoretical issues and basic experiments in different venues to isolate key physics issues. RMI experiments on the Nova laser investigate the affects of compressibility with strong radiatively driven shocks (Mach > 10) in near solid density plasmas of sub-millimeter scale. The growth of single sinusoidal and random 3-D perturbations are measured using backlit radiography. RTI experiments with the Linear Electric Motor (LEM) are conducted with a variety of acceleration (< 104 m/s2) histories and fluids of 10 cm scale. Turbulent RTI experiments with high Reynolds number liquids show self-similar growth which is characterized with laser induced fluorescence. LEM experiments with an elastic-plastic material (yogurt) exhibit a critical wavelength and amplitude for instability. The experimental results will be compared with nonlinear theories and hydrodynamic simulations.
Semiclassical limit of the focusing nonlinear Schrödinger equation: Instability, ill-posedness and symmetry breaking
We present some recent work on the semiclassical (geomtric optics) limit of the focusing nonlinear Schrödinger (NLS) equation, which arises as a model of many strongly nonlinear, strongly dispersive wave phenomena, including plasmas, gravity waves and optical pulse propagation. The semiclassical limits of many nonlinear wave equations, such as the Korteveg-DeVries equation, are well understood, whereas the semiclassical limit of the focusing NLS is still poorly understood. This is because formal asymptotic calculations yield an elliptic equation, where the wave speeds are complex valued, leading to an ill-posed problem. In this talk we present some recent numerical and theoretical work, as well as some recent experiments with pulses in optical fibers which confirms the theoretical predictions.
Some Particle Studies of Turbulent Diffusion
Many questions regarding the mixing of a passive scalar in the presence of a complicated fluid flow can be phrased in terms of the behavior of systems of particles. In this lecture, we focus upon two cases for which such a description has been successful. Firstly, we consider the case of a single particle to study transport by a class of periodic flow fields. The large scale, long time effective transport coefficients are predicted by a homogenization theory in which the coefficients are tabulated through solutions of an auxiliary "cell" problem. We address how a drifting particle undergoing Brownian motion experiences the effective transport through careful Monte-Carlo simulation and examine how effects of time variation in the flow field may help to control the complicated Peclet scaling existing in the effective diffusion coefficients for steady flows. Secondly, we consider the case involving many interacting particles which arises naturally in models for scalar intermittency. We review the results for the rapidly fluctuating linear shear layer model of Majda, and results on the periodic shear flow models due to Bronski and McLaughlin. In joint work with Jared Bronski, we conclude with a discussion regarding the tails of the pdf in the Majda model.
A three dimensional adaptive, coupled level set method for computing solutions to incompressible two-phase flow in general geometries
We present an effective numerical method for solving complex multi-phase flow problems in science and industry. Example applications include the model problem of a drop hanging from a faucet, ink jet printers, ship waves and oil spreading under ice in water. These problems are characterized by complex topological changes in the free surface (e.g. the merge and/or break-up of the interface), large density and viscosity jumps (e.g. air/water) and stiff, singular source terms due to the surface tension force. We use a coupled level set and volume of fluid approach for representing the free surface between the gas and liquid. This enables us to accurately compute surface tension driven flows and conserve mass to within a fraction of a percent. We represent the geometry surrounding (or embedded within) the fluids by way of a level set representation. Our computational results are compared to experiments for the model problem of a drop hanging from a faucet. We apply our algorithm to micro-scale jetting applications where it is important not only to model the motion of the free-surface, but also to accurately take into account the geometry of the jetting device.
Anomalous Diffusion in Polymers, Membranes, and Active Biomembranes.
Anomalous diffusion has been subject to various theoretical modelling, e.g., in the context of random walk on fractals. Here I shall discuss the dynamics of membrane bilayers and semi-flexible linear polymers in solutions. The effect of thermal undulations on both the transverse and longitudinal stochastic motion of a tagged "monomer" will be discussed. It will be shown that the motion is SUBDIFFUSIVE. A similar behavior is found for polymeric sol-gel clusters. I will demonstrate how the subdiffusion leads to a stretched exponential decay of the dynamic structure factor, which has been observed in experiment. Biomembranes include, however, among other additional constituents, carrier proteins that act as active transport sites, for example, the ATPase controlling the sodium-potassium pump. The action of these active ion pumps induces a force noise, in addition to the thermal noise which results from collisions of the solvent molecules with the membrane. I will show how this active noise leads to an ENHANCED diffusion of a tagged membrane "monomer". I will also briefly discuss the effect of the cytoskeleton in plasma membranes on this motion.
The elasticity of thin elastic bodies: from plates to shells
The famous solution to the Elastica problem (the bending of a vertical bar loaded on top) goes back to Euler, and the mechanics of elastic bodies is still a vivid domain of research. Recent theoritical works have concentrated on elastic plates. Because a plate has a small thickness, it is much easier to bend that to stretch; this simple remark underlies many mechanical properties of the plates, like the easy apparition of singularities (as in a crumpled sheet of paper). In this talk, we discuss the extension of the mechanics of plates to that of shells, i.e. to curved, thin elastic bodies. In particular, we address the compression of a spherical elastic body (a ping-pong ball) by a plane. For large enough compressions, a circular ridge is formed; its scaling properties differ from that of the ridge on a plate. We also consider a mathematical problem, the existence of infinitesimal bendings on a given surface. When such deformations exist, the shell is mechanically weak. We point out "rigidifying curves", which, when included in the mean surface of the shell, make it rigid.
Sand as Maxwell's demon
This talk addresses a simple experiment: A gas of small plastic particles inside a box is kept in a stationary state by shaking. A wall separates the box into two identical compartments, save for a small hole at some finite height h. As the amplitude of the shaking is reduced, a second order phase transition occurs, in which the particles preferentially occupy one side of the box. We develop a quantitative theory of this clustering phenomenon and find good agreement with numerical simulations.
Highly Optimized Tolerance: Robustness and Power Laws in Complex Systems
Highly Optimized Tolerance (HOT) is a new mechanism for generating power law distributions, which is motivated by biological organisms and advanced engineering technologies. Our focus is on systems which are optimized, either through natural selection or engineering design, to provide robust performance despite uncertain environments. Possible domain applications (e.g. ecosystems and the internet) will be discussed. We suggest that power laws in these systems are due to tradeoffs between yield, cost of resources, and tolerance to risks. These tradeoffs lead to highly optimized designs that allow for occasional large events. We investigate the mechanism in the context of percolation and sand pile models in order to emphasize the sharp contrasts between HOT and self organized criticality (SOC), which has been widely suggested as the origin for power laws in complex systems. Like SOC, HOT produces power laws. However, optimization introduces new sensitivities, not present in critical systems, and compared to SOC, HOT states exist for densities which are higher than the critical density, and the power laws are not restricted to special values of the density.
Optimisation under Uncertainty
In many problems one has to optimise a 'cost function' which, for each trial set of parameters, can only be estimated by statistical sampling over some distribution of external events or other unknowns. Examples include designing protein sequences for fast folding (where we don't know the detailed trajectory the molecule will follow), probabilistic versions of the travelling salesman problem (where the precise cities he will require to visit are not known in advance), and the exploitation of oil reservoirs (in the face of geological uncertainty). As one begins an optimisation, it is obviously not efficient to seek accurate evaluation of the cost function. I will discuss how by analogy with simulated annealing this approximation can be made a virtue.
Scaling in thermal convection: A unifying theory
A theory for the scaling of the Nusselt number Nu and of the Reynolds number Re in strong Rayleigh-Benard convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large scale convection roll (wind of turbulence) and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number Ra - Prandtl number Pr phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively, and whether the thermal or the kinetic boundary layer is thicker. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra < 1011) the leading terms are Nu ~ Ra1/4Pr1/8, Re ~ Ra1/2Pr-3/4 for Pr < 1 and Nu ~ Ra1/4Pr-1/12, Re ~ Ra1/2Pr-5/6 for Pr > 1. In most measurements these laws are modified by additive corrections from the neighboring regimes so that the impression of a slightly larger (effective) Nu vs. Ra-scaling exponent can arise.
Scaling and Crossovers in Diffusion Limited Aggregation
We discuss the scaling of characteristic lengths in diffusion limited aggregation clusters in light of recent developments using conformal maps. We are led to conjecture that apparently anomalous scaling (of the lengths) be due to one slow correction to scaling. This is supported by analytical argument for the scaling of the penetration depth of newly arrived random walkers,and by numerical evidence on the Laurent coefficients which uniquely determine each cluster. It gives a strong hint as to the correct Renormalisation Group for Diffusion Limited Aggregation.
Pattern Formation in Visual Cortex
Stimulus response properties of cells in visual cortex exhibit intriguing spatial organization. Patterns of cell preferences for oriented stimuli, ocular dominance of cell responses, and the establishment of a topographic retinotopic map may be accounted for through the Turing pattern formation mechanism. Starting from a biologically realistic model system I find reduced variables describing the pattern of synaptic weights in the visual system in which the Turing mechanism is particularly transparent. Simple Hamiltonians written in these reduced variables may readily be simulated with Monte Carlo techniques.
Numerical Simulations of Detonations: Fundamentals and Applications
Detonations are the fastest, most intense form of energy release in an energetic material. In the simplest theories, a propagating detonation front can be considered as a discontinuity moving through the material at a speed characteristic of the energetic and background materials. Closer examination reveals the importance of much more complex and dynamic structure. This presentation describes the methodology and applications of multidimensional, time-dependent numerical simulations of detonations. Because such simulations are extremely computer intensive, they require the highest performance computing tools available and every effort must be made to produce scalable code that runs on a variety of computers. Applications discussed include the fundamental structure of gas-phase chemical detonations, nuclear detonations in Type Ia supernovae, and design of a detonation incinerator for disposing of explosives, munitions, and chemical and biological agents.
When Cells Die
Saving lives of patients may depend on preventing cell death in critical tissues like the heart and brain. Yet the specific factors responsible for cell death remain a mystery and the understanding of these factors is likely to lead to major medical breakthroughs. Most cell death (following a wide range of diseases including stroke, myocardial infarction, cardiac arrest, drowning, and trauma) is primarily due to the effects of ischemia, or the lack of blood flow to the cells. During ischemia, reduced oxygen causes a fall in cellular ATP; classic physiology suggested that cells die because of this critical ATP deficit. However, a number of recent observations suggest that this simple "lack of ATP causes cell death" concept is not true. An important observation in the 80's was that while tissues seemed to be injured during ischemia - markers of irreversible cell death did not appear until reperfusion with the restoration of oxygen and nutrients. This paradoxical finding, that cells deteriorate as they are being restored to normal, has been termed "reperfusion injury". Reperfusion injury would suggest that lethal events for many cells occur not during ischemia, but rather during reperfusion. Reperfusion injury remains one of the most controversial issues in medical science with strongly divided advocates both for and against. Studies at the University of Chicago during the last five years lend strong support to the concepts of reperfusion injury. Careful studies of cells during ischemia and reperfusion confirm the majority of cell death occurs during the reperfusion phase. Further studies support an important role for free radicals during reperfusion injury. During ischemia, free radicals are produced from the mitochondria and a large (very likely lethal) burst of free radicals can be detected within the first minutes of reperfusion following ischemia - a possible explanation for reperfusion injury. Additional mechanisms suggest ways to treat reperfusion injury. For example, adaptive responses to ischemia (termed "preconditioning") reveal a novel pathway to cellular protection. Hypothermia may be another viable treatment option. Finally, a better understanding of non-linear dynamics ("chaos") may allow for enhanced resuscitation efforts and will be discussed.
Vortex Flow in Mesoscopic Channels
In type-II superconductors, magnetic fields are not shielded from the interior of the material but can enter in form of quantized flux bundles (vortices). On macroscopic scales, large ensembles of vortices respond to temperature or external forcing very much like ordinary states of matter such as liquids or solids. But how does the transition between liquid and solid take place when the flow is confined to mesoscopic channels, only a few vortices wide? What are the dynamic characteristics of such ultrathin vortex liquid layers? We have addressed this questions in experiments on model devices containing nanometer-scale, weak-pinning channels embedded in a strong-pinning host. In the solid phase, flux lines are pinned at defects along the channel walls. Caging and frustration of vortex arrangements inside the channels give rise to field history memory. We find that the driven flux line configuration is only marginally stable exhibiting novel commensurability effects and threshold dynamics.
What is the Diffusivity of a Sediment?
A sediment consists of a viscous fluid with a concentration of solid particles which are denser than the fluid, and therefore fall. This talk addresses the question of what is the effective diffusivity of the sediment. While all reasonable theoretical estimates have predicted that the diffusivity diverges with the system size (even in the limit of vanishing particle concentration), experiments have tended to claim that the diffusivity is independent of the system size, and determined by an as yet unknown dynamical process. I will describe our current research aimed at understanding this question, by developing a simple physical picture for what causes the diffusivity. Numerical simulations will be presented to illustrate the spatial and temporal evolution of the fluctuations in the sediment, and some simple scaling arguments will be given to explain them.
Patterns in Nature: The Epiphenomenology of Aggregation
One of the most striking patterns in biology is the formation of animal aggregations. Fish schools, insect swarms, ungulate herds, and bird flocks are all classic examples. Consisting of individual members acting selfishly, aggregations nevertheless function as an integrated system, displaying a complex set of behaviors not possible at the level of the organism. Because pattern is increasingly at larger scales of space and time, individual members operate without knowledge of the whole. Indeed, there are no leaders. And yet, many aggregations are architecturally arranged with resultant properties including polarity, repeated units, uniform density, distinct edges, complex shape, emergent functions and a behavioral repetoire. Complexity theory indicates that large populations of units can self-organize into aggregations that generate pattern, store information, and engage in collective decision-making. This talk will explore the patterns displayed by animal aggregates in the context of evolutionary theory dictating selfish individuality and address the question: Is the whole more than the sum of its parts?
Hierarchical Modeling in Geomorphology
Efforts to model processes and features of Earths landscape are hampered by its nonlinear, dissipative and open nature. A hierarchical modeling methodology for geomorphic systems is proposed as an alternative to the commonly applied approaches of Reductionism and Universality. Variables and processes characterizing a system are arranged temporally. Abstractions of processes at faster scales (simplifications of these processes that survive over longer time periods) determine the dynamics at any one temporal level and processes at slower scales provide a slowly varying context. Boundaries of the system are chosen to minimize coupling to the external environment. The theoretical consistency of the hierarchy is tested by comparing the predictions of models at two different temporal scales for the same phenomenon. This methodology is illustrated with a hierarchy of models for bedforms resulting from sediment transport, such as ripples or dunes.
Unsolved Problems of the Heart
The electrical behavior of heart muscle is normally periodic, but can go turbulent. This change of dynamical mode does not require a change of parameters: it is an alternative basin of attraction. The difference stems from there being two kinds of "action potential": the linearly propagating pulse of the text books, and alternative vortex-like solutions. The latter, called "rotors" have many curious properties, especially in 3 dimensions. They are better understood by computation than by analysis or by in-vivo experiments, at the moment. But experiments do confirm their existence and crucial role in starting "sudden cardiac death."
Pole Dynamics in the Dielectric Breakdown Model: From KPZ to DLA
The dielectric breakdown model (DBM) is a model of Laplacian growth in two dimensions that gives rise to fractal clusters. In this model, a cluster grows in the presence of an electrostatic potential obeying Laplace's equation, with the interface growing fastest where the electric field is highest; a parameter eta is introduced so that the interface speed is proportional to the eta'th power of the normal component of the electric field. At eta=1, this model is equivalent to the diffusion-limited aggregation model (DLA). At other values of eta, the DBM can describe the patterns of breakdown in dielectrics.
In this talk I will consider the DBM in the limit of small eta. In this limit, the fractal clusters of the DBM become compact, and we are left with a surface growth model that still includes many of the features of DLA: growth of fingers, competition between fingers, existence of a linearly stable fingering solution, and non-linear instability of that solution to an exponentially small amount of noise.
The dynamics is shown to have an interesting representation in terms of poles of an analytic function, which I use to derive a large family of solutions to the equation of motion in the absence of noise. Some results will be presented on the statistical properties of the surface in the presence of noise. This approach may be useful in understanding the DBM at finite eta in terms of perturbations to the small eta model.
The Virtues of Peace and Quiet: Noise-Exclusion and Noise-Imprinting in the Darwinian Evolution of Digital Organisms
Homeostasis, the creation of a stabilized internal milieu, is a ubiquitous phenomenon in biological evolution, despite the entropic cost of excluding noise information from a region. The advantages of stability seem self-evident, but the alternatives are not as clear. This issue was studied by means of numerical experiments on a simple evolution model: a population of boolean network organisms selected for performance of a curve-fitting task while subjected to noise inputs. During evolution, noise-sensitivity increased with fitness. Noise-exclusion evolved spontaneously, but only if the noise was sufficiently unpredictable. Noise that was limited to one or a few stereotyped patterns caused a symmetry-breaking that prevented noise-exclusion. Instead, the organisms incorporated the noise into their function, at little cost in ultimate fitness, and became totally noise-dependent. This noise-imprinting suggests caution when interpreting apparent adaptations seen in nature. If the noise was totally random from generation to generation, noise-exclusion evolved reliably and irreversibly, but if the noise was correlated over several generations, maladaptive selection of noise-dependent traits could reverse noise-exclusion, with catastrophic effect on population fitness. Noise entering the selection process rather than the organism had a different effect: adaptive evolution was totally abolished above a critical noise amplitude, in a manner resembling a thermodynamic phase transition. This effect may be explained qualitatively by a simple analytical model. Evolutionary adaptation to noise involves the creation of a sub-system screened from noise information, but increasingly vulnerable to its effects. Similar considerations may apply to information channeling in human cultural evolution.
Commensurability Effects for Vortices in Superconductors: An Application of the Time-Dependent Ginzburg-Landau Equations
It has recently become possible to manufacture superconducting films with artificial features such as channels and periodic pinning arrays. These samples are ideal for studying commensurability effects in the vortex lattice, where the physics is determined by the competition between length scales. Theoretically, the systems can be well described by the time-dependent Ginzburg-Landau equations in two dimensions, which can be simulated efficiently on parallel computers.
The talk will give an introduction to the time-dependent Ginzburg-Landau (TDGL) equations and explain why they are useful for this particular problem. We will then give a short overview of the numerical methods involved and their implementation. In particular, we are interested in the validity of a widely used simplification, the so called frozen field approximation. Finally, we will present the results from simulations of a number of different problems.
Stretching Genes: Elasticity of DNA and Chromosomes
I will review what we know about the microscopic elastic response of double-helix DNA, much of which has been the result of rapid developments in both experiment and theory for single-molecule micromanipulation. Much of what we understand can be summed up in terms of an effecive DNA Young modulus of about 300 MPa. This number implies that DNA should undergo thermal structural fluctuations of amplitude much larger than the accuracy to which DNA structural properties are usually quoted. Finally I will discuss how what we know about DNA and protein elastic responses is helping us understand microelasticity experiments on whole chromosomes.
Moving Mesh Methods
Meshes, both topologically regular and unstructured, which smoothly deform during a time-dependent simulation have been found useful in many situations. This talk presents some recent advances in the understanding of why such methods are effective. Since I don't want to mislead anyone about the content of the talk, I remark that most of the discussion will be theoretical, not computational. Much of the material presented is joint work with Yingjie Liu.
Is Quantum Mechanics Nonlocal?
Various reasons have been given for supposing that quantum mechanics - and the real world, insofar as quantum mechanics is an accurate description of it - is nonlocal. These include: instantaneous collapse of a wave function when a measurement is made; the peculiar properties of entangled states of spatially separated particles, including violations of Bell inequalities; the finite extent in space of Newton-Wigner states in relativistic quantum theory. The talk will introduce and then analyze these ideas, with particular emphasis on entangled states, to see whether they indicate that quantum theory is nonlocal, or simply non-classical.
Continuum Field Description of Crack Propagation
We develop a continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation, which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.
Solitary Adventures in Discrete Worlds
The properties of solitary nonlinear waves in some continuum Hamiltonian nonlinear systems, such as the sine Gordon, \phi^4 or non-linear Schrodinger equations, are well-known. On the other hand, it is very interesting to study (spatially) discrete versions of these models. The motivation stems not only from the natural numerical discretizations in order to study these PDE's on a computer but also because many of the applications are inherently discrete. Such applications range from simple systems such as coupled torsion pendula to very exciting technological applications in arrays of coupled Josephson junctions and can go as far as the breathing oscillations of DNA and the local denaturation of the Crick-Watson double strand.
This talk will be concerned with the dramatic modifications that discreteness may entail when present in these systems. In particular, we will see how continuum solitons rather than propagating merrily will now get decelerated, trapped and eventually pinned between two sites of the lattice (for strong discreteness). We will trace this behavior numerically as a function of the lattice spacing and getting insights from the numerical experiments we will seek the theoretical origins of this behavior. Using analytical (Evans function, asymptotics beyond all orders, singular perturbation theory) and mixed analytical/numerical techniques (discrete Evans function, linear stability, bisection/continued fraction methods) we will study the spectrum of the kink-like structures. Hamiltonian dispersive normal form theory will then permit us to analyze the mechanism of internal dissipation of the energy (albeit in a Hamiltonian system!) from the coherent structure to the extended wave excitations (i.e. from the localized modes into the modes of the essential spectrum). In this way, we will try to present the complete picture and theoretical analysis of the coherent structure behavior and to link it to the relevant applications. Possible future extensions of this work will also be highlighted.
Chaotic Mixing
We study the combined effects of chaotic advection and molecular diffusion on a region of pollutant in time periodic recirculating flows. We prove that the flux function and the width of the stochastic zone in the non-diffusive systems have a non-monotonic frequency dependence. Furthermore, these systems have an adiabatic transport mechanism which is inherently different from the moderate and fast frequency regimes (the relevant scale for the frequency will be defined). These different Lagrangian non-diffusive mechanisms of transport imply, as we demonstrate numerically, that diffusive, low frequency (high frequency) stirring leads to efficient transport on shorter (longer) time scales. This is a joint work with A.C. Poje.
Multistability in Delayed Feedback Control
Multistability readily arises in physiological delayed feedback control mechanisms. Here we show that conditions for multistability to occur in a recurrent loop comprised of a limit cycle oscillator subjected to pulsatile delayed feedback can be obtained from the measured phase resetting properties of the oscillator. Moreover, the basin of attraction can be determined for each attractor. Since the basins of attraction are known, it is possible, in principle, to use adaptive control techniques to regulate switches between attractors. The results are illustrated with experiments involving a time-delayed analog electronic circuit and with experiments involving a time-delayed recurrent loop involving an invertebrate neuron. Potential applications of these findings include the development of secure encoding-decoding devices and for the development of a `brain defibrillator' to treat human epilepsy.
Space-Time Adaptivity for Transport Applications
Hyperbolic conservation laws and advection-dominated parabolic equations model a great number of physically interesting phenomena such as shallow water and contaminant transport. Solutions to such equations often have sharp, moving fronts and other local, fine-scale features. Locally conservative methods such as upwind-mixed methods are of interest because of their ability to approximate these fine-scale features without excessive smearing or spurious oscillations. However, the standard explicit time-stepping procedures for these methods can incur a strong time step restriction in the presence of spatially varying velocity fields or local mesh refinement. In order to reduce this drawback, upwind methods which allow the time step to vary spatially yet retain a maximum principle and strict local conservation are developed. First and (formally) second order in time schemes which allow for high resolution in space will be developed, and one-dimensional numerical results demonstrating the accuracy and stability of the methods will be given. In addition, continuous time a posteriori estimates for a model convection-diffusion equation will be discussed.
Swollen Onions: Dissolution of Multi-lamellar Vesicles
When a lamellar phase of amphiphilic molecules is subjected to shear, it may transform into an array of close-packed multi-lamellar vesicles, called the `onion phase'. A theory will be presented for the behavior of the onion phase upon dilution. A unique feature of this system is the possibility to sustain a non-uniform pressure by tension in the lamellae. Tension enables the onions to remain stable beyond the unbinding point of a flat lamellar stack. The model accounts for various concentration profiles and interfaces, which develop in the onion as it dissolves. In particular, densely packed `onion cores' are shown to appear, as observed in experiments. The formation of interfaces and onion cores is an unusual example for interface stability in confined geometry.
Vortex Matter as a Soft Condensed Matter System
A variety of experimental techniques are now available for creating spatially resolved images of single vortices passing through Type-II superconductors and even for tracking their motions. This talk focuses on some of the recent progress in mining this rich vein of data. Images of vortex distributions created by Lorentz microscopy or Bitter decoration offer new qualitative and quantitative insights into the topology of the pinscape, or random pinning potential, on which the vortices are arrayed. Vortex correlations, similarly, make possible the first direct measurements of the vortex interaction potential using the characteristic energy scale for pinning as a reference. These measurements reveal a surprising analogy between vortices array on a quenched random pinscape and classical particles buffeted by random thermal forces. This analogy carries over to phase transitions in vortex ensembles revealed by recent torque magnetometry measurements. Understanding the kinetics of these phase transitions likely will require new insights into the mechanism of heat evolution and transportation through the superconducting "substrate".
Continued Fractions Hierarchy of Rotation Numbers in Planar Dynamics
Global bifurcations such as crises of attractors, explosions of chaotic saddles, and metamorphoses of basin boundaries play a crucial role in understanding the dynamical evolution of physical systems. Global bifurcations in dissipative planar maps are typically caused by collisions of invariant manifolds of periodic orbits, whose dynamical behaviors are described by rotation numbers. We show that the rotation numbers of the periodic orbits created at certain important tangencies are determined by the continued fraction expansion of the rotation number of the orbit involved in the collision.
The Time-Dependent Ginzburg-Landau Equations as a Dynamical System
In the first part of my talk, I will show that the TDGL equations of superconductivity define a dynamical system in a suitably chosen gauge. Then I will discuss the "frozen-field approximation" and its relation to the TDGL equations. I will illustrate with the results of some numerical simulations.
Some PDE Aspects of Thin Film Growth
The microscopic mechanisms of epitaxial growth have been known for 50 years, but we are still far from mastering their mesoscopic consequences. I will discuss two topics of this type: (a) The analysis of coarsening during spiral growth (joint work with Tim Schulze). The starting point is a simple, geometric model of spiral growth, which gives a Hamilton-Jacobi equation for the height of the growing film. The coarsening behavior is obtained by examining the Hopf-Lax solution formula. (b) The analysis of coarsening during step-flow growth, associated with step-bunching (PhD thesis work of Cameron Connell). The starting point is a reaction-diffusion model proposed by J. Kandel and D. Weeks. The coarsening in this setting is due to collision of traveling waves.
Numerical Simulation of Axisymmetric Free-Surface Flows
The dynamics of free surface flows, and in particular the mechanisms for singularity formation at the interface of fluids with different physical properties, constitute a problem of high theoretical and practical interest. The applications include such commonplace devices as ink-jet printers and fuel injectors, oil extraction, and fiber spinning. While considerable theoretical and computational advances have been achieved in our understanding of the problem in certain limiting cases (such as the drop pinch-off in lubrication approximation), theoretical understanding of the general case is still lacking. We present a general numerical algorithm aimed at describing the dynamics of singularity formation in axially symmetric free surface flows for arbitrary Reynolds numbers. In order to improve the spatial resolution in the vicinity of the singular point the interface is treated as a mathematical discontinuity corresponding to the abrupt change in the fluid properties, rather than being artificially smeared over a finite region, as is usually done. As a particular application, we discuss the results of the direct numerical simulation of selective fluid withdrawal and compare them with recent experiments by Sid Nagel and Itai Cohen.
Strongly coupled chaotic maps: collective behavior, universality, and models.
Adapting statistical physics to deterministic dynamical systems with a large number of degrees of freedom is an ubiquitous question in nowadays physics. Coupled map lattices (CMLs) constitute perhaps one of the simplest models of spatio-temporal chaos, hence appear as a model of choice to test our ideas. Strongly-coupled chaotic maps generically display collective behavior emerging out of extensive chaos. The rich phenomenology exhibited by these systems, although much more complex than that of single maps, is nevertheless reminiscent of the self-similar structure of asymptotic trajectories observed in low-dimensional (temporal) chaos. After presenting general properties of collective behavior, I will show how an extension of the well-known renormalization group (RG) of unimodal maps holds for coupled systems. I will then present an approximation scheme that, taking into account the dynamics of spatial correlations, reproduces strikingly well the collective behavior of strongly-interacting maps.
Renormalization Group Approach to Underresolved Computation
Often one is interested in the dynamics of a spatially extended system only down to some appropriate level of detail known in advance. In such a case, it is wasteful or perhaps impossible to compute the dynamics at scales smaller than this limit, even though the problem may be complex and nonlinear. This "under-resolved computation" is considered here from a renormalization group (RG) perspective. Assumptions about the behaviour of the ignored degrees of freedom typically mean that even deterministic problems must be modeled as stochastic differential equations. The RG provides a natural framework for coarse-graining such problems up to the scale of interest.
In this talk, I will discuss both the successes and current limitations of this method.
Work performed in collaboration with Qing Hou and Alan McKane, and supported by NSF-DMR-93-14938.
Generic Behavior of Reversible Cellular Automata
Contextual effects on orientation selectivity: beyond the ring
About 40 years ago Hubel and Wiesel discovered that neurons in the Visual Cortex (V1) of cats and primates respond selectively to oriented contrast edges and bars. They conjectured that converging axons from neurons of the Lateral Geniculate Nucleus (LGN), which themselves respond to spots of light on a contrasting background, could provide the anatomical substrate for edge detection. It has recently been shown in computational modelling studies that this mechanism cannot fully account for the selectivity of cortical neurons to more complex stimuli. Intracortical mechanisms are also necessary, in particular recurrent cortical excitation and lateral inhibition. Thus neighboring cortical neurons signalling similar orientation preferences cooperate, those signalling different preferences compete. This "Turing mechanism" was originally suggested as a cortical property by Wilson and Cowan in 1973. In the context of orientation tuning it is known as the "Ring Model".
In this talk I will show how the ring model can be analyzed mathematically using the techniques of nonlinear dynamics. I will do this both with continuous neuron models and also with spiking neurons. In so doing I will describe novel methods for analyzing networks of spiking neurons recently introduced by Bressloff and Coombes in the UK. Such methods lead to the prediction that visual cortex cells can exhibit clustered spiking patterns when responding to stimuli, in a manner consistent with recent experiment findings of Gray and Singer that there exists a 40 Hz modulation of neural spiking patterns.
I will then describe recent discoveries concerning the longer ranged architecture of the visual cortex which suggests how to extend the ring model to cover, not just one local patch, but the entire visual cortex. The mathematical problems of dealing with the visual cortex as a whole are both more difficult and more interesting than those concerning a single patch. I will describe some of these problems, and some experimental predictions of the analysis relevant to normal context dependent visual perception, and to abnormal phenomena such as visual illusions of angle and geometric visual hallucinations. In so doing I will suggest how top-down influences from extra-striate cortex, V2 and beyond may also play a role.
[This talk is based on joint work with my former graduate students G.B. Ermentrout (1976-1980), M. Wiener (1992-1994) and T. Mundel (1993-1996), and recently with P. Bressloff (1998-) and M. Golubitsky (1999-), and my current student P. Thomas.]
Protein Evolution - How far back can we see?
Today, sequence similarity searching is the most effective methodavailable for characterizing newly determined protein sequences. Similarity searching the bases of more than 80% of the gene assignments for the recently determined yeast, Haemophilus, and Methanococcus genomes. Similarity searching is popular because it is surprisingly effective. For the yeast genome, similarity searching found homologues to more than 75% of the yeast genes, and for the much more distantly related Methanococcus, homologues could be found for more than 50% of the genes.
However, finding homologues for 75% or 50% of the genes means 25% 50% of the genes were unidentified. Genes may be missed because they are novel - not present in other organisms. However, in most cases, these "non-homologous" genes may share a common ancestor with sequences in the databases, but the sequences have diverged so much that the homology cannot be detected by sequence comparison. Our goal is to develop more effective methods for protein sequence comparison, so that distant relationships that cannot be reliably inferred today can be detected.
The seminar will discuss the logical and statistical basis for the inference of homology from sequence similarity, demonstrating that inferences of homology based on sequence similarity are reliable. By comparing human proteins to the proteins in completely determined genomes (C. elegans, yeast, E. coli, M. jannaschii) we can estimate how far back in time we can look, and possibly discover "young" protein sequences. If many "young" proteins have emerged in the past 800 My, one might infer that discovering (or rediscovering) protein folds is easier than expected.
Snap, Jump, and Wiggle: Motion in Micellar Fluids
Non-Newtonian or viscoelastic fluids do many things which Newtonian fluids cannot do. Examples include rod climbing, the tubeless siphon, and cusp-like tails on rising bubbles. In this talk I will describe the even more peculiar behavior of aqueous micellar solutions in which the micelles take the form of long tubes (often called wormlike micelles). Our approach is both experimental and mathematical. By way of introduction to non-Newtonian fluid dynamics, I will present results on the spin down of a micellar fluid. I will then discuss new observations of the oscillations of bubbles (and spheres) rising (and falling) in a wormlike micellar fluid. We model these phenomena with various constitutive relations, and in particular focus on an ordinary differential equation model for the falling sphere in an infinite medium. For a Newtonian sphere this model is exact, for which we have proven that the sphere cannot oscillate. The work presented is in collaboration with Anand Jayaraman, Jon Jacobsen, and Andrea Young.
Surface Singularities and Jet Eruption
The formation of self-focusing singularities and jets due to the collapse of standing waves on a fluid surface is studied using experiments, theory, and numerical calculations. A qualitative characterization of the singularity development from experimental observations is presented along with a detailed theoretical and numerical analysis of the process. The singularities focus inertial energy in the system and produce very high-speed jets which rise vertically from the surface. A similarity solution to the equations of motion which leads to the focusing is presented and compared with observation.
Things we can do with a viscous liquid: wrinkles and singularities
When a bubble of air rises to the top of a highly viscous liquid, it forms a dome-shaped protuberance on the free surface. Unlike a soap bubble it bursts so slowly as to collapse under its own weight simultaneously, and folds into a wavy structure. This rippling effect occurs for both elastic and viscous sheets, and a theory for its onset is formulated. The growth of the corrugation is governed by the competition between gravitational and bending forces (shearing).
When the very same viscous liquid is drained out of the container a dimple is formed at the free surface and develop into a cusp. The interplay between the surface tension that tends to to keep the surface flat and the viscous forces "pinching" down the free surface, gives rise to a universal exponent of the height of the cusped interface versus the draining time elapsed before the dimple becomes a cusp.
Force distributions for Jammed and Unjammed Systems
We measure the distributions of interparticle normal forces $P(F)$near the glass transition in supercooled liquids and compare them to those obtained in recent experiments on static granular packings. We find that the distributions $P(F)$ for glasses and static granular packings are very similar, showing a plateau or small peak at small forces. We propose that the formation of this peak signals the development of a yield stress in glasses and jammed systems.
Phase Transformations in One-Dimensional Ising Model of Finite Size
The Ising lattice of interacting spins is the simplest> possible microscopic model in which second order phase transition is expected to occur.Whether such transition does occur also in one dimensional lattice and what is the Curie temperature of the system was a point of contention since the time when Lenz and Ising proposed the model.We recently reexamined this model concentrating on question how the size of the system affects its properties and how one should define characteristic temperatures of various transitions that occur spontaneously in a finite-size system.Conclusions may have an impact on how we look on the Ising lattices in higher dimensions.
Glassy models for granular relaxation and history-dependent jamming
In this talk I shall discuss two schematic models for slow or `glassy' relaxation in driven systems. The first is an attempt to reproduce the results of the granular compaction experiments performed here at Chicago from a minimal set of assumptions, principally that the relaxation is similar to thermal activation, with an effective `temperature' that is coupled to the external driving. The second model, which is not specific to any particular material, has a similar mathematical basis but includes strain degrees of freedom, and appears to allow a strain-dependent jamming/unjamming transition, perhaps in the spirit of `jamming phase diagram' recently proposed by Andrea Liu and Sid Nagel [Nature vol. 396, p. 21 (1998)]. It is hoped that simple mathematical models such as these may aid our understanding of complex physical systems.
Ionic Channels: Natural Nanotubes that Select between Ions
Protein channels conduct ions (Na+, K+, Ca++, and Cl-) through a narrow tunnel of fixed charge ('doping') thereby acting as gatekeepers or cells and cell compartments. Hundreds of types of channels are studied everyday in thousands of laboratories because of their biological and medical importance: a substantial fraction of all drugs used by physicians act directly or indirectly on channels. Channels are studied with the powerful techniques of molecular biology. The atoms of channels can be manipulated one at a time and the location of every atom can be determined within 0.3 Å. Ionic channels are 'holes in the wall' that use the simple physics of electrodiffusion to perform these important tasks. They have simple structure which is known in atomic detail in a few cases; more to come. They are ideal objects for mathematical and computational investigations. Computing the movement of spheres through a 'hole in the wall' should be easier than computing most other biological functions, yet it is nearly as important as any from a medical and technological point of view. The function of open channels can be described if the electric field and current flow are computed by the Poisson-Drift-Diffusion (called PNP, for Poisson Nernst Planck, in biology) equations and the channel protein is described as an invariant arrangement of fixed charges, not as an invariant potential of mean force or set of rate constants, as is done in the chemical and biological tradition. ThePoisson-Drift-Diffusion equations describe the flux of individual ions (each moving randomly in the Langevin trajectories of Brownian motion) in the mean electric field. They are nearly identical to the drift diffusion equations of semiconductor physics used there to describe the diffusion and migration of quasi-particles, holes and electrons. They are closely related to the Vlasov equations of plasma physics. Ionic channels form a biological system of great clinical significance and potential technological importance that can be immediately studied by the techniques of computational physics. Many of those techniques have not yet been used to analyze other biological systems. Perhaps they should be: the application of the even the lowest resolution techniques involving the Poisson-Drift-Diffusion equation has revolutionized the study of channels. An opportunity exists to apply the well established methods of computational physics to the central problems of computational biology. In my opinion, the plasmas of biology need to be analyzed like the plasmas of physics. The mathematics of semiconductors and ionized gases should be the starting point for the mathematics of ions and proteins, for the analysis of protein structure, protein folding, nucleic acids (i.e., DNA), and the binding of drugs to proteins and nucleic acids.
Image Segmentation and Energy Dissipation
In this talk I will present some work in progress in vision research. We consider the problem of recognizing what parts of an image are perceived as being in the foreground. We use a variant of the Pao-Geiger-Rubin model, which uses an energy dissipation approach to this problem. The model is surface-based, rather than contour-based. Specifically, the edges in the image are not viewed as isolated contours, but are viewed as bounding a surface. Each local edge has a local hypothesis; for example, a north-south edge might think "the region immediately to the left of me is part of the figure". The model then uses energy dissipation methods to seek assignments of local hypotheses that are mutually agreeable, yielding a segmentation of the image that might be perceived. We test the model on various images to address questions like: Does the model "perceive" smaller objects to be in the foreground (the way we do)? Convex objects to be in the foreground (the way we do)? How does it perform on optical illusions that viewers report to have two different segmentations?
This is joint work with Nava Rubin and Anita Disney of the Center for Neural Science, NYU. I thank Davi Geiger (Courant, NYU), Bob Shapley (CNS, NYU), and Dave McLaughlin (Courant, NYU) for useful discussions.
Towards Understanding Chaos in Higher Dimensional Systems
Recent advances in lasers and molecular beams make it possible to observe details of chemical reactions in even a femtosecond time scale. In these experiments, dynamical aspects of reactions are of interest such as the following. (1) How does the reaction path depend on initial conditions? (2) How does the energy distribution occur among degrees of freedom on the system? (3) To what extent is the process statistical? These questions are of fundamental importance in understanding molecular details of reactions such as intramolecular vibrational-energy redistribution (IVR), rates of reactions on a state-to-state basis, and dynamics of transition-state species.
On the other hand, dynamics of vibrationally excited molecules in gas phase is a typical example of Hamiltonian dynamics of many degrees of freedom. It is well known that generic Hamiltonian systems of many degrees of freedom exhibit chaos. Therefore, IVR is supposed to be closely related to chaotic motion of the molecules.
However, most of the studies on chaos so far have focused their attention to one-dimensional maps. In order to fill the gap between the study of chemical reactions and that of chaos, we need to investigare chaos of many degrees of freedom.
Our study is a step towards this direction. Our main results are two-fold. First, we will show that there exists a transition between lower dimensional chaos and a higher dimensional one. This transition is signalled by homoclinic (or heteroclinic) tangency between stable and unstable manifolds. Second, the symmetry of molecules plays an important role. Since the molecular systems are quantum, interference effects tend to suppress chaos. This phenomenon is revealed in the network of nonlinear resonances (Arnold web).
Cusp Flow
In free surface flows, cusps can form under a variety of circumstances. Examples are drop coalescence, or rising bubbles in a viscous fluid. A particularly simple two-dimensional model system consists of two counter-rotating cylinders, submerged below the surface of a viscous fluid. In the absence of an outer fluid a two-dimensional cusp forms, which is stable at any value of the capillary number. However an outer fluid, typically air, will be drawn into the narrow cusp pushing its walls apart. We show that as a result stationary solutions no longer exist above a critical capillary number. Instead, a sheet forms, that is unstable to three-dimensional peturbations at its lower rim.
On the Sound of Snapping Shrimp
Alpheus heterochaelis (``the snaping shrimp'') generates noise so loud that it disturbes submarine communication. It was believed that the noise is generated when the claw rapidly closes and its two sides hit each other. However, in this work we show with the help of high speed video (40000 frames/second) and parallel sound detection with a hydrophone that the origin of the noise in fact is a collapsing cavitation bubble: When rapidly closing the pair of sissors, the shrimp emits a thin water jet so fast that a cavitation bubble develops. This collapses and on collapse, it emits the sound. Our optical and acoustical measurements are supplemented through a simple theoretical model of the process.
Formation, Breakup and Stability of Nanojets
Atomistic molecular dynamics simulations reveal formation of nanojets with velocities up to 400 m/s, created via pressurized injection of fluid propane through nanoscale convergent gold nozzles with heating or coating of the nozzle exterior surface to prevent formation of thick blocking films. The atomistic description is related to continuum hydrodynamic modeling through derivation of a stochastic lubrication equation which includes thermally triggered fluctuations whose influence on the dynamical evolution increases as the jet dimensions become smaller. Emergence of double-cone neck shapes is predicted when the jet approaches nanoscale molecular dimensions, deviating from the long-thread universal similarity solution obtained in the absence of such fluctuations.
Computational Design of Peptides that Activate Genomic DNA-Derived Brain Protein Receptors that are Without Known Natural Messengers
Many of the amino acid polymeric protein products of human genome sequences have homologies with familiar transmembrane receptors, but are without either known natural messengers, "ligands," or physiological functions. The current approach to drug discovery for these "orphan receptors" is called "high throughput screening" and involves multimillion dollar factories that robotically screen up to a hundred thousand chemical candidates per day for biochemical signs of receptor activation. When an active compound is found (with successes in the 1-2 per 100,000 range) it is characterized by its 3D spatial geometry and charge distribution, generating a physical model called a "pharmacophore" which drives drug companies' programs of combinatorial substitution and biological testing in their search for more potent and specific ligands.
We asked the question, given only the DNA derived, receptor's amino acid sequence, could we computationally design new, short (15-20 mer) amino acid polymers, peptides, which could activate orphan receptors and thus shorten (and significantly cheapen) the process of new drug discovery. Our successes in this pursuit have involved the conversion of the receptors' amino acid sequences into a unified system of meaningful physical, quasi-thermodynamic quantities followed by the application of several signal processing and symbolic dynamical techniques to find one dimensional patterns which are then used as templates for peptide design. The sequences of receptors and other proteins that were transformed in these ways:
(1) Revealed diagnostic global familial patterns; for examples, Morlet wavelet transformations of protein sequences discriminated between helical, strand, mixed, poly and receptor proteins and in the latter located likely segments for ligand targeting.
(2) Led to sliding window computations of the local sequential Markovian metric entropy, which located segments of higher order and successfully marked the physiologically distinct sections of "polyproteins," those are post-translationally split up into multiple distinctive peptide messengers.
(3) Involved Karhuenen-Loeve-like orthogonal mode decomposition of receptor sequence, lagged autocovariance matrices and the construction of Broomhead-King-like eigenfunctions, which, when characterized by all poles, "maximum entropy" power spectra, demonstrated systematic matches between the modes of known peptide receptors and their ligands.
Inverting (3) for brain-related orphan receptor function by using the ligand-relevant, eigenfunction associated eigenvectors as templates, we designed 15 mer peptides. When 22 of these were synthesized and tested, 15 (68%) were statistically signficantly active in vitro and in vivo (in brain). This suggests , counterintuitively, that a one-dimensional approach to this apparently three dimensional protein folding-like problem can be useful. We think that Israelachvili's aqueous "hydrophobic long range attraction" (500 angstroms, 10-100 fold van der Waals forces) between matching segments of sequentially patterned hydrophobic amino acids lead to their hydrophobic aggregation, membrane receptor destabilization and physiological alteration.
*Major participants in this work include Karen A. Selz, Michael J. Owen and Michael F. Shlesinger.
Blow-up in parabolic problems
In this seminar, I will present an overview of several types of singularities that can occur in parabolic equations. Several of the examples that I will exhibit, will concern examples of singularities that appear in the so called Keller Segel system that has been extensively used in the study of chemotactic aggregation of biological organisms. The analogies between the type of singularities that occur in this system with the ones that take place in another systems, like the Kompaneets equation used in plasma physics and the classical Stefan problem in solidification will be also discussed during the seminar.
The Coalescence-Cascade of a Drop
When a drop is released from a nozzle very close to a liquid surface, it will sit momentarily before coalescing into the bottom layer. High-speed video imaging reveals that the coalescence process is not instantaneous, but rather takes place in a cascade where each step generates a smaller daughter drop.
This cascade is self-similar, with each step generating a new drop about one half the original diameter. We have observed up to 6 steps in this cascade, generating drops as small as 180 $\mu m$ in diameter. Using ultra-high-speed video, with frame rates as high as 40500 f/s, we have measured the time associated with each partial coalescence. This time scales very well with the surface tension time-scale.
The coalescence cascade will however not proceed ad infinitum due to viscous effects, as the Reynolds number of the process is proportional to square root of drop diameter. Viscous forces will thereby become increasingly important as the drops become smaller.
We will furthermore present some recent results from impacts using granular materials, thus eliminating the effect of surface tension. The results could be very useful in separating inertial and surface tension effects, as well as building constitutive laws for rapidly moving granular media.
Reference: Thoroddsen, S. T. and Takehara, K. ``The coalescence-cascade of a drop'', to appear in Physics of Fluids.
Stratified Kolmogorov Flow
In this study we investigate stratified Kolmogorov shear flow. We derive the amplitude equations for this system and solve them numerically to explore the effect of a weak stabilizing stratification. We then explore the non-diffusive limit of this system, and solve amplitude equations for this system to study the weakly nonlinear evolution of the internal boundary layer in the stratification. We further solve the full 2-dimensional system and investigate the different dynamics as we vary the Peclet number.
Noah's Flood; Historical Event Or Myth?
Geologic data have been interpreted to show that a catastrophic flood occurred 7600 years in the Black Sea. Was anyone there?
Last week, the discovery of remnants of human habitation under the Black Sea was announced. This is believed to be the first proof that people thrived along an ancient shoreline before it was inundated by a great flood thousands of years ago.
Was this event the source of the Noah's Flood story and other flood Myths?
Computational Fluid Dynamics: A High-LevelPerspective
The spectacular developments in computer hardware and software over the past half-century have revolutionized what can be done and what can be expected to be done via simulations of fluid dynamics. In this talk, we will review progress, try to make forecasts of future advances, and point out various pitfalls that can be encountered. A discussion will be given of the status of diverse methods, including direct simulation, large-eddy simulation, lattice methods, and the like.
Thermodynamics of Proteins: Experiments and Hierarchical Models
The thermodynamical properties of protein are very well documented experimentally. Two first order phase transitions are found: the well-known ``warm'' unfolding around 60 C and the less known ``cold'' unfolding around 0 C. To explain these data, we propose a protein model based on a hierarchy of constraints that force the protein to follow certain pathways when changing conformation [1]. The model exhibits a first order phase transition, cooperativity and is exactly solvable. The model is extended to explicitly take into account the coupling between the protein and water degrees of freedom. In a statistical mechanics treatment we obtain both the cold and the warm unfolding transitions and reproduce qualitatively the known experimental results. We argue that the two transitions ends in a critical point at a given temperature and chemical potential of the surrounding water [2]. In order to characterize the sharpness of the transition we weight multiple pathways for the folding and show that most transitions generically are two-state like in accordance with experiments on single domain proteins [3].
[1]. A. Hansen, M.H. Jensen, K. Sneppen and G. Zocchi, Eur. Journ. Phys B 6, 157 (1998).
[2]. A. Hansen, M.H. Jensen, K. Sneppen and G. Zocchi, Eur. Journ. Phys B, 10, 193 (1999); Europhys. Lett. 50, 120 (2000).
[3]. P.G. Dommersnes, A. Hansen, M.H. Jensen and K. Sneppen, ``Parametrization of Multiple Pathways in Proteins: Fast Folding versus Tight Transitions'', cond-mat/0006304 (2000).
Mathematics of Sea Ice
In the chaotic case (time-periodic velocity field), the scalar evolves to a complex recurrent pattern that subsequently decays without change of form, as first noted in a numerical simulation by Pierrehumbert. The typical path length per cycle of the forcing and the Reynolds number are shown to govern the decay rate, but the dependence is strikingly non-monotonic. The time evolution of various statistical measures of the scalar field provides a quantitative description of the interplay between stretching and molecular diffusion. It is surprising to note that diffusion does not broaden the striations of the scalar field, We have explored the effects of many flow variables including periodic and nonperiodic forcing in both space and time. Particle tracking over long perios of time is also used to study the transient mixing process. Weakly turbulent flows (obtained by reducing the viscosity) are shown to mix much more efficiently than chaotic flows in the same geometry.
Mathematics of Sea Ice
Sea ice is a composite of pure ice with brine and air inclusions. It is distinguished from many other porous media, such as sandstones or bone, in that its microstructure and bulk material properties depend strongly on temperature. Above a critical value of around -5 degrees C, sea ice is permeable, allowing transport of brine, nutrients, and heat through the ice. These processes play an important role in air-sea-ice interactions, in the life cycles of sea ice algae, and in remote sensing of the pack. Recently we have used percolation theory to model the transition in the transport properties of sea ice. We give an overview of these results, and how they explain data we took in Antarctica. We also describe recent work on inverse scattering algorithms for recovering the physical properties of sea ice via electromagnetic remote sensing, and how percolation processes come into play. At the conclusion, we will show a short video on a recent winter expedition into the Antarctic sea ice pack.
The evolution of language
I will give an overview of the recent work that has been done in an attempt to create a mathematical formulation of the evolution of language. I will speak about the two major components of the language: the lexicon and the grammar. In a sense, languages evolve like individuals in a population: the fittest ones survive and get passed down generations, the less fit get eliminated. The two driving forces of evolution, selection and mutation (i.e. the mistakes when learning a language), can be incorporated into a simple system of ODE's called the evolutionary equations. Within this framework, it is possible to get some analitical insights into the dynamics of the language. One of the questions we ask is how accurate children have to learn the language of their parents in order for the population to be able to maintain a coherent language? Another one is what are the evolutionary forces that shape the Chomskian Universal Grammar?
Fluid dynamics of bacterial suspensions: from interactions of individual organisms to collective order and quasi 2-d turbulence at Re<<1.
This presentation concerns the astonishing diversity of individual and collective dynamic phenomena exhibited by swimming bacteria ( Bacillus subtilis ), at concentrations ranging from dilute to close-packed. Topics covered will include 1) the distribution of swimming velocities, 2) binary interactions, 3) influence of bounding geometry on the velocity probability densities for speed and direction of swimming, 4) consumption/supply - driven bioconvection patterns, and 5) chaotic dynamics of populations at high volume fraction, where the trajectories of inert tracers include intermittent "trapping", long flights, and transport exponents reminiscent of the superdiffusion found in "2-d turbulence". Approaches to modelling some of these phenomena will be presented, e.g. bioconvection and some possible mechanisms for energy balance and long range coherence required for "turbulence" at low Reynolds Number. --> Videos ! <--
Construction of a Large Software System for a High Energy Particle Physics Experiment
The BaBar experiment at the Stanford Linear Accelerator Center has produced over 100 Terabytes of data and is expected to produce 300 Terabytes per year, soon. These data require extensive processing prior to and after storage. The 4-million lines-of-code system that performs this task was written, from scratch, in C++ by a group of people distributed all over the world. This talk will discuss the process of building this system and will discuss some aspects of the system architecture. The talk will not spend substantial time on database design nor hardware architecture.
Unusual ordering of hard-core particles sliding on fluctuating surfaces
We study a system of hard-core particles sliding locally downwards on a fluctuating surface. For certain surfaces, the system exhibits a novel steady state in which most strikingly, phase ordering coexists with large-scale fluctuations. The distribution of the particle cluster sizes varies as a power law, and gives rise to many of the unusual spatial properties of this ordered state. Insight into the origin of this phenomenon is obtained by studying coarse-grained depth models of the hill-valley profile of the underlying surfaces.
Patterns in extended, periodically forced systems : A Continuum coupled map approach.
This is joint work with Ed Ott. We propose that an useful approach to the modeling of periodically forced extended systems is through continuum coupled maps (CCMs). CCMs are discrete time, continuous space models, mapping a continuous spatially varying field Xi_n(x) from time n to time n+1.
The efficacy of CCM models is illustrated by application to experiments of Umbanhowar et al. on vertically vibrated granular layers. We first derive an appropriate CCM model for this system, using simple physical considerations (essentially dimensional analysis). We then present a framework for the analysis of pattern selection in CCM models using a truncated modal expansion. Through the analysis, we show how the model reproduces the observed experimental behavior. We also obtain some other results (scaling laws) that are experimentally testable predictions from our model. We conclude with a discussion of the limitations of our model for the vibrated granular layer systems, and extensions of this approach to other (non-granular) periodically forced, strongly dissipative systems.
Defect Statistics in the Two Dimensional Complex Ginsburg-Landau Model
The statistical correlations between defects in the two dimensional complex Ginsburg-Landau model are discussed in the defect coarsening regime. In particular the defect-velocity probability distribution is determined. The spiral arms of the defects lead to a very different behavior for the order parameter correlation function in the scaling regime compared to the results for the related dissipative model.
Experiments and Theory for Foam Drainage and Coarsening
The evolution of a foam is determined by the drainage flow of the continuous (liquid) phase and the coarsening (aging) of the gas bubbles. Free drainage experiments with slow and fast-coarsening gases show markedly different dynamics and elucidate the importance of the coupling of these two effects. Strong coarsening leads to accelerated drainage; however, the liquid flow also becomes self-limiting and cannot exceed a maximum drainage rate. A simple physical model incorporating foam drainage and diffusive coarsening shows quantitative agreement with experiment.
Search for jamming signatures and force chains in the simplest granular system
A very simple system that supports stress like a granular material is a pack of frictionless spheres of random sizes, deposited one at a time in a periodic box. David Head (University of Edinburgh) Alexei Tkachenko (Bell Labs) and I have been studying jamming and force chains in simulations of this system in two dimensions. First I'll describe how the simulation achieves a mechanically stable state by a simplified relaxation process that requires no translational motion. Next I'll show how forces propagate in this granular medium, corroborating previous theoretical postulates. The support for an applied small point force is concentrated along diagonal lines leading to the bottom: so-called light cones. The distribution of contact forces resembles those reported in physical jammed systems of simulated emulsions or real glass beads. We report how the force distribution evolves under various conditions of loading. We also report our search for organization of the contact forces into force chains, in which strong forces tend to occur in opposing pairs on a given particle.
Investigating The Topological Transition In The Selective Withdrawal Problem
In the selective withdrawal experiment we lower a straw so that its tip hangs above a water-oil interface. We then withdraw the oil through the straw. When the withdrawal rate is low the interface below the straw deforms into a hump with a flow stagnation point located at the hump peak. As the withdrawal rate is increased, this hump grows in height and the curvature at the hump peak becomes very large. At the transition flow rate the interface makes a topological transition from being bounded to being unbounded in the vertical direction. The water is then entrained in a thin spout along with the oil and the stagnation point moves from the interfacial boundary to the interior of the lower fluid. For two-fluid systems with different straw diameters, viscosity ratios, density differences and surface tensions, I will present data showing interesting scaling and hysteretic behavior in the transition-flow-rate dependence on the straw heights. I will then discuss the scaling behavior in the steady state hump shapes as the system approaches the transition point. Finally, I will point out some experimental problems related to selective withdrawal and will try to draw the audience into a discussion of these experimental issues.
ActiveSpaces: The Access Grid, Active Mural and Advanced Visualization Systems
At Argonne, Chicago and elsewhere work has begun to explore the concept of integrated whole room scale visual environments. These environments consist of group work rooms that have been augmented with multiple displays including: large-format whole wall displays (e.g. ActiveMural our high-resolution rear projected tiled display), driven by PC clusters, or multi-processor visualization engines, semi-immersive or immersive displays (Workbenches, ImmersaDesks, CAVEs), multiple desktop devices, and multiple front projection systems. These rooms may also have active or passive tracking systems, multiple channels of audio support, and support for multiple wireless hand-held controllers and navigation devices.
These room-sized environments can be linked via the national "Grid" to form compelling collaborative visualization environments (e.g. "The Access Grid"). We believe these systems represent a new type of visual application development target and delivery mechanism. We call these ensembles ActiveSpaces. In this talk I will explore with the audience some of the ideas we are working on to facilitate the delivery of high-end scientific visualization to groups of users and to create new types of electronically augmented spaces explicitly designed to support rapid collaborative exploration and visual analysis of complex data.
The possible physics (mechanics) of walking
Robots have motors and people have muscles. What for? To guide motions and to make up for lost mechanical energy. How much guidance is fundamentally needed for repetitive tasks? How much energy needs to be supplied for what losses? One approach to understanding the need for motors and controllers is what can be done without them.
Tad McGeer demonstrated (1988-1993) with simple computational models and with physical devices that uncontrolled human-like walking motions can be achieved with, to put it simply, sticks and hinges that walk downhill. The motions of these toy-like devices are energetically efficient (low specific transport cost) and stable (limit-cycles with linearized stability). We have found that, in principle, some of these devices can walk on arbitrarily small slopes and thus approach perfect efficiency and that Robot configurations that have this efficiency are reminiscent of the human design. These models can also limp (period 2), waltz (period 3) , and stumble (chaos). One of our devices has the unintuitive feature that it has no stable standing posture, yet can walk stably.
The basic theory is not novel: numerical search for limit cycles and numerical evaluation of their stability. However, two morals seem to be exposed: locomotion efficiency is based on avoidance of impacts, and stability comes from utilizing non-holonomic constraints.
Mean field approximation and a small parameter inturbulence theory
Numerical and physical experiments on two-dimensional (2d) turbulenceshow that the differences of transverse components of velocity field are well described by Gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume the existence of a critical space-dimensionality d=dc, at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At d<dc the flow can be described by the ``mean-field theory'', leading to the observed gaussian statistics and Kolmogorov scaling of transverse velocity differences. It is shown that in the vicinity of d=dc the ratio of the relaxation and translation characteristic times decreases to zero, thus giving rise to a small parameter of the theory.
The expressions for pressure and dissipation contributions to the exact equation for the generating function of transverse velocity differences are derived in the vicinity of d=dc. The resulting equation describes experimental data on two-dimensional turbulence and demonstrate onset of intermittency as d-dc>0 and r/L -> 0 in three-dimensional flows in close agreement with experimental data. In addition, some new exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point pdf of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a gaussian.
Asymptotic flamelets and large scale simulations of turbulent premixed flames.
[Joint work with Boualem Khouider (UdM) and Andy Majda (Courant).]
Turbulence enhances the speed of propagation of premixed flames via mixing in the preheat zone. Capturing this phenomenon is a huge computational challenge because, to do so accurately, one would need to resolve the wide range of length scales induced by turbulence, chemical reactions, and their interaction.
On the other hand, a rigorous homogenization approach to describe the turbulent flame propagation in the asymptotic limit of a very thin reaction zone has been developed by Majda and Souganidis (1994) in an idealized context. In this talk, I will describe our attempts at bridging the gap between the mathematical understanding in the asymptotic limit and practical simulations requirements.
This involves purely numerical issues (designing a novel, robust numerical solver for the effective Hamiltonian of the flame for a variety of flows); fundamental modeling issues (using the numerical database and formal asymptotics to parameterize the burning speed turbulent enhancement as a function of a flame residence time - this lead us to a new quantitative explanation for the so-called "bending" effect); large scale computational issues (possible interpretation of the homogenized limit not just as a mathematical concept by also in the practical context of the validation of large scale simulations by comparison with resolved computations at finite values of the flame thickness.)
Wax Tectonics
The floor of the earth's ocean has been created over the past 150 million years by plate tectonics. Continental plates are moving apart and new ocean floor is perpetually solidified at the mid-ocean ridges. From satellite data and ship soundings we have an excellent knowledge of the bathymetry of the ocean floors and find three distinct morphological features: transform faults and fracture zones, a spreading velocity dependent mid ocean ridge profile, and microplates. Midocean ridge dynamics combines the full complexity of fluid flow, phase transformation, and fracture. I will show in my talk that a simple table top experiment can capture the complex dynamics of earth like processes. Our experiments pose a challenge to theorists: Is it possible to develop a consistent theoretical model that captures the complexity of our table top experiments and possibly that of the earth.
Avoidance and detachment in bailout embeddings
Many interesting problems involve a combination of Hamiltonian mechanics with some dissipative dynamics. In this work, a large space contains a friction-free lower dimensional region embedded within it. A particle located in that embedded region will undergo a Hamiltonian dynamics. Particles with trajectories in some nearby regions are drawn into the space. Other nearby orbits make the particle escape, 'bail out', of this neighborbood of the Hamiltonian region and go someplace far away. Escape and reinjection into the neighborhhood permit all kinds of interesting orbital behaviors.
We can design this space so that orbits of our choosing bail out, and others stay. Specifically, we build our system so the KAM trajectories stay near the embedded region. (KAM trajectories are particularly interesting motion of the Hamiltonian system, which show marginal stability and an integrable behavior.) A particle initially on the embedded region is subjected to small amounts of noise, which then serves to move it slightly out of the embedding region. Such a particle typically bails out of the neighborhood of the embedded region after some time, except if it lies on a KAM orbit. This procedure thus allows us to "surgically" separate KAM orbits from the other Hamiltonian orbits.
We analyze this bailout in terms of the fluctuation amplitude around the stable embedding for infinitesimally small noise. We show that the bailout process consists of two distinct phases, an avoidance phase, where the fluctuations are small but whose amplitude acquire arbitrarily large prefactors, and a detachment phase, where the fluctuations become finite in size even for infinitesimally small noise.
Knowledge about What?
Quantum Mechanics and Computation
I will try to describe quantum computation to computer scientists unfamiliar with quantum mechanics, without boring quantum physicists unfamiliar with its recent application to computation. People familiar with both subjects will have to settle for the pleasure of understanding everything they hear, though they may find my point of view amusing. Or irritating.
Things That Think
The digital revolution has given us a clear distinction between hardware and software, between channels and the content they carry, between physical science and computer science, but it is right at these boundaries between the bits of the digital world and the atoms of our physical world that the most compelling opportunities and problems in information technology lay. I will discuss the science underlying the integration of information with its physical properties over length scales from atomic nuclei to planetary networks, and discuss its implications for the life of people, and their machines. Examples will be drawn from projects addressing global development, creative expression, and appropriate interfaces.
Studying protein folding with simplified and atomically detailed simulations
My research aims to elucidate how proteins attain their folded conformation within biologically relevant time scales. Proteins sample a vast number of conformations on their way to the folded state and the study of folding is best approached from a statistical standpoint. Concepts borrowed from the well-established field of statistical mechanics have provided considerable insight into the folding problem. The energy landscape of the protein may be described as a minimally rough surface, in which a strong energy bias towards the native state "funnels" the protein towards its biologically active conformation. Roughness of the surface, which hinders this funneling, can be due to both energetic factors (associated with the formation of incorrect but stabilizing interactions) and to topological factors (geometric constraints leading to the premature formation of native interactions). I will discuss the origins of topological roughness (or "frustration") and how the native state "shape" of the protein affects the folding process. My approach involves a combination of off-lattice minimalist models in which the protein is described in a coarse-grained manner and fully atomic models, which provide a detailed representation of both the protein and the solvent.
Two Problems in Internet Architecture
Most talks in this series describe how one can use computation to help answer scientific questions. This talk will instead be about using science to improve the computational infrastructure. I will discuss two design questions relating to the Internet architecture. These questions involve extending the Internet architecture to improve Quality-of-Service (QoS); one extension is to allow bandwidth reservation and the other is to use multiple priority levels for streaming media. The emphasis will be on using extremely simple models to explore qualitative aspects of these design issues. This talk will be self-contained, and no knowledge of networking or of Internet architecture is required.
Some free surface problems solved by the boundary integral method
The following free surface problems will be presented, two forpotential flow and two for Stokes flow. 1. The design of the pressure pulse for a drop-on-demand ink-jet-printer, and the associated pinch-off. 2. How cusps are rounded by surface tension in the Hele-Shaw flow of an initially circular blob of fluid withdrawn through a non-concentric sink. 3. The collision of two deformable drops in a viscous suspension undergoing shear. 4. The rheology of an emulsion at moderate concentration.
The presentation will be partly about mechanics, including some unresolved problems, and partly about numerical methods, including some recent ideas such as the use of B-splines to represent the unknown surface distributions in 2D calculations and the use of radial basis functions to calculate the curvature of a 3D surface.
Polymer brushes under shear
Motivated by experiments performed both with a surface forces apparatus and by neutron scattering, we discuss theoretically the behavior of grafted polymer layers under a hydrodynamic shear.
In the existing models, chain configurations are stationnary; we take explicitly into account the diffusion of the chain end points in the direction perpendicular to the grafting surface; this diffusive motion allows an exchange of the chain configurations. Each chain is subjected to the shear only when its end point stands in the thin region at the edge of the grafted layer where the flow penetrates.
We calculate both the extension of a chain in the direction of the flow and the tension on the grafting surface. As long as the relevant Deborah number (the dimensionless shear rate) remains small, these quantities remain small of the order of hte values that they reach by thermal fluctuations. This is in agreement with the recent neutron scattering experiments but in strong disagreement with the old surface force experiment where a strong deformation of the chains is observed. Our mean field approach also predicts a thinning of the grafted layer due to the shear.
JFI Symposium
Computational issues in object detection in images
A central problem in computer vision is the detectionof objects of a particular class in complex images containing multiple objects. Detection refers not only to computing the location, but other parameters describing the particular instantiation of the object in the image. This can have the form of a non-linear deformation defined on a `prototypical' example of the object. I will describe two continuum based variational problems for finding the deformation of a prototype to a simple image containing only one object, at more or less the scale of the prototype. These are solved using a coarse to fine gradient descent procedure. In complex images location and scale need to be identified prior to the computation of the deformation. This is impossible to do with the original continuum based cost functions. Instead a coarse and discrete approximation to these functions is formulated, allowing for very efficient identification of candidate locations and scales.
Nonlinear evolution of unstable fluid interface
Every day, whenever water flows out from an overturned cap, we observe the Rayleigh-Taylor instability. Turbulent mixing caused by this instability is a long-standing problem in many physical and technological applications (inertial confinement fusion, supernova, flames, etc.). The cascades of energy and the dynamics of large-scale coherent structure are fundamental issues. This large-scale structure is a periodic array of regular bubbles and singular spikes. To study its dynamics we propose new approach based on symmetry theory. First we analyze the local properties, and derive from the conservation laws a dynamical system governing the bubble dynamics. Due to formation of the singularities, the regular asymptotic solution to the dynamical system for a family, and we choose the fastest stable solution in the family as the physically dominant one. The dependence of the bubble motion on the acceleration history as well as on the flow symmetry is analyzed. It is shown that 3D bubbles in RTI conserve near-circular contour, and the 3D-2D dimensional crossover is discontinuous. Then we consider global properties, and study the structural stability and the transitions associated with the growth of the flow length scale. Both local and global analysis lead us to a conclusion that in RT turbulent mixing a balance between the inverse and direct cascades is required to keep isotropy of the flow. The theory eliminates discrepancies between previous approaches, explains existing experiments, predicts new ways of the bubble front evolution, and establishes control parameters to be monitored in experiments.
Continuum description of avalanches in granular media
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition between flowing and static components of the granular system. We apply this theory to several important granular problems: avalanche flow in deep and shallow inclined layers, and shear granular flows between two plates. We carry out quantitative comparisons between the theory and experiment.
High dimensional crumpling: A mathematician's apology (withapologies to G. H. Hardy).
There has been much recent activity on the problem of crumpling of elastic membranes, both here at the Univ. of Chicago, and at many other places. I will give an (elementary) overview of some of the mathematical questions that come up through the study of crumpled sheets. I will then discuss some of the tools and techniques that are used to study this problem. Finally, I will give my (very biased) perspective on some of the recent results that have been obtained, and the many questions that spring from these results.
Uses of Optimal Control in Comparisons of Experiments and Simulations
It is often the case that successful simulations of experiments result from a collaboration of the experimentalists and the modelers, because the relation between the two groups allows transfer of details about the weaknesses of the tools that each group must use. The aim of the work discussed in this talk is move part of this relationship to the experiment and the simulation by allowing the simulation to use partial and flawed experimental information, such as isolated measurements, shadow-like projections and/or qualitative information to confine simulation results. We will give TOY examples in which we have only qualitative information about initial conditions and a few isolated measurements which illustrate how we can guess initial conditions and experimental parameters that give agreement between the experiments and the simulations. Techniques that incorporate uncertainty in the measured values will be examined.
BE WARNED, this is a report on work that is quite preliminary. If you are expecting an encyclopedic view, you will be disappointed. On the other hand, since we don't know what we are doing, your insights will be much appreciated.
Clustering and anomalous diffusion in a granular gas
Granular gases spontaneously separate into dense and dilute regions. Here we experimentally and theoretically demonstrate that the cluster formation and its breakage are fundamentally different due to the lack of time reversability: For a vibro-fluidized granular gas in N connected compartments the cluster formation process is gradual, via several metastable states, whereas the collapse of the cluster is very abrupt. The observed cluster lifetime (as a function of the driving intensity) is analytically calculated within a flux model, making use of the self-similarity of the process. After collapse, the cluster diffuses out into the uniform distribution in a self-similar way, with an anomalous diffusion exponent 1/3.
From synthetic towards real fully developed turbulence -- learning from phenomenology
Turbulence is one of those notorious problems in classical and nonlinear physics, which so far has not surrendered to the cohorts of physicists. Over almost a century many tactics have been invented to derive the statistical properties of fully developed turbulence from the fundamental hydrodynamical equations, but with little success. Contrary to these theoretical top-down approaches, a bottom-up approach is presented. The emphasis is put on understanding the data and the relationship between various, apparently different data-motivated models first. From there, more sophisticated phenomenological models are developed, which are expected to bridge the gap between data and fundamental hydrodynamical equations.
Faraday Wave Patterns
Standing waves, parametrically excited on the free surface of a fluid byperiodic acceleration, are found in a wide variety of patterns: squares,hexagons, quasipatterns, superlattices, etc. The more exotic of these patterns are readily obtained in laboratory experiments by employing a periodic forcing function that has (at least) two frequency components. This introduces a number of control parameters to the problem: the amplitudes, frequencies and relative phases of the forcing components. Our aim is to understand the role of each in the pattern formation problem in a systematic fashion. We use methods of equivariant bifurcation theory to make some headway with this, focusing on the weakly inviscid situation. Our analysis identifies a subtle stabilization mechanism for superlattice patterns that involves resonant interactions of waves driven by the two frequency components. We also use general symmetry arguments to derive the form of the resonant coefficients in the relevant bifurcation problem in several cases, showing how these depend strongly on the forcing frequency ratio and on the relative phase of the two driving terms. Additional scaling laws follow from the weakly broken time reversal symmetry and an underlying Hamiltonian structure. The predicted scaling laws, etc. are confirmed by numerically calculating coefficients for the resonant triad amplitude equations from the quasipotential formulation of the gravity-capillary wave problem due to Zhang and Vinals. This talk highlights collaborative work with Jeff Porter and Chad Topaz.
Comparing simulations with the real world
Space, maps and the evolution of navigation
I am interested in the evolution of spatial representation. I present here a radical revision of how the mammalian brain sees, understands and maps its external world. This process, mediated by the hippocampus, has implications not only for the evolution of spatial navigation but for the evolution of a complex cognitive trait from simple antecedents. Based on a new model of hippocampal evolution, I propose that the hippocampus maps space with two independent representations, that are mediated by the 'old' (dentate gyrus) and the 'new' (Ammon's horn) hippocampal structures. The two maps are based on different stimuli: distributed and discrete stimuli, respectively. The coactivation of these parallel maps leads to the cognitive map, which I argue is a property that can only emerge from the collaboration of these two maps. The parallel map theory of hippocampal function has important implications: it explains paradoxes of spatial learning in rats with hippocampal lesions, patterns of sex differences in learning in rats, and why the hippocampus continues to generate new cells, even in the adult mammal. It also predicts sex differences in humans, not only in how men and women navigate the world, but also in abstract thought processes that are spatially encoded. Thus the understanding of a primitive universal, the need to navigate in space, may have important consequences for the development of higher cognitive processes.
Shedding and interaction of solitons in imperfect medium
The propagation of a soliton pattern through one-dimensional medium with weakly disordered dispersion is considered. Solitons, perturbed by this disorder, radiate. The emergence of a long-range interaction between the solitons, mediated by the radiation, is reported. Basic soliton patterns are analyzed. The interaction is triple and is extremely sensitive to the phase mismatch and relative spatial separations within the pattern. The phenomenon is a generic feature of any problem explaining adiabatic evolution of solitons through a medium with frozen disorder. This is a joint work with I. Gabitov, I. Kolokolov, and V. Lebedev to appear in October issue of JETP Lett.
Secrets of Alien Technology Revealed!-- or Chirality Transformations Propagating on Bacterial Flagella
Chemotaxis in many bacterial species is made possible by the remarkable and bizarre dynamics of their multiple, rotating, helical flagella. They bundle and de-bundle as their rotary motors episodically change rotational direction. When the flagella are bundled, the bacterium moves linearly, but the dissolution of the bundle leads to a tumbling event that effectively randomizes the cell's orientation. The motor reversal that initiates the tumbling not only torques the flagella oppositely, but also reverse the chirality of the filament, turning a left-handed helix into a right-handed helix. Hotani has performed careful experiments on helical flagella in external flows and he observed that regions within the filament periodically flip to the opposite chirality, and that those domains propagate stably downstream. I'll present a dynamical model for this phenomenon based on the existence of two competing locally stable states of opposite chirality whose interaction with the flow is through the torque they produce. The model displays a number of the key features seen in the experiments.
Tightening of Knots and Dynamics of Topological Constraints in Granular Chains
For polymer systems, it has been conjectured that entropic effects lead to a spontaneous tightening of knots. However, this cannot be directly observed, only indirectly through radius of gyration. I will instead be discussing a system for which such an observation is possible. This system is a vibrated granular chain, and combines aspect of polymer and granular systems.I will discuss the entropic reasons for tightening in equilibrium. Experimental results will be given, which show a much sharper behavior than expected for an equilibrium system, as well as a clear breakdown of detailed balance. To interpret these results, I will give a dynamical explanation for the tightening, qualitatively valid for both equilibrium and nonequilibrium processes. This approach is hoped to elucidate the role of entropy in nonequilibrium systems.
SMALL IS DIFFERENT --FROM ELECTRONS TO NANOJETS
That the properties of materials depend on size is commonly expected and often observed. At sufficiently small sizes such dependencies may go beyond mere scaling with size, manifesting themselves in physical and chemical behavior that is new and different from that found at larger sizes. Such circumstances, when small is different in an essential way , may occur when one (or more) of the physical dimensions of the material aggregate approaches a length-scale characteristic to a physical phenomenon (with different phenomena being characterized by different length-scales), and similarly in the time domain. Associated with the above is the sensitivity of sufficiently small materials aggregates to shape. Not only can one affect the properties of a confined system by varying its shape, but, most importantly, is the spontaneous shape-selection occurring in such systems, originating from the ability of finite systems to adjust their shape (and structure) in order to minimize their (free) energy. Basic research of these and related issues underlies future technologies, from nano-scale machines, nanotribological systems, cellular injections, and nanocatalysis, to miniaturization of electronic circuitry and novel information storage and retrieval systems.In this talk we discuss and illustrate the above issues through large-scale classical and quantum mechanical simulations of several nano-scale systems. Topics include: (i) Formation mechanisms, mechanical, and quantized conductance properties of metal and semiconductor nanowires and their interconnections [1]; (ii) Atomic-scale friction, control of friction, and nanotribological processes in lubricated junctions [2]; (iii) Generation, stability and breakup of nanojets [3]; (iv) Catalysis by small gold and palladium clusters [4]; (v) Spontaneous symmetry breaking leading to formation of crystallized clusters (electron molecules) in individual two-dimensional quantum dots, and quantum-dot-molecules [5], (vi) Emergence of magnetism in free and surface-supported small palladium clusters [6], and (vii) Charge Transport in DNA (Science, August 19, 2001).
References
1. U. Landman et al, Microscopic Mechanisms and Dynamics of Adhesion, Microindentation and Fracture, Science 248, 454 (1990); U. Landman et al., Metal-Semiconductor Nanocontacts: Silicon Nanowires, Phys. Rev. Lett. 85, 1958 (2000).
2. B. Bhushan, J.N. Israelachvili and U. Landman, Nanotribology: Friction, Wear and Lubrication at the Atomic Scale, Nature 374, 607 (1995); J. Gao, W.D. Luedtke, and U. Landman, Friction Control in Thin-Film Lubrication, J. Phys. Chem. Chem. B 102, 5033 (1998).
3. M. Moseler and U. Landman, Formation, Stability and Breakup of Nanojets, Science 289, 1165 (2000).
4. A. Sanchez et al., When Gold is not Noble: Nanoscale Gold Catalysts, J. Phys. Chem. A 103, 9573 (1999); S. Abbet, U. Heiz, H. Hakkinen, and U. Landman, CO Oxdidation on a Single Pd Atom Model Catalyst, Phys. Rev. Lett, 86, 5950 (2001).
5. C. Yannouleas and U. Landman, Spontaneous Symmetry Breaking in Quantum Dots and Dot-Molecules, Phys. Rev. Lett. 82, 5325 (1999); ibid., Collective and Independent-Particle Motion in Two-Electron Artificial Atoms, Phys. Rev. Lett. 85, 1726 (2000); Coupling and Dissociation in Artificial Molecules, Euor.. Phys. J D 16, 373 (2001).
6. M. Moseler, H. Hakkinen, R.N. Barnett, and U. Landman, Structural and Spin Isomers of Neutral and Anionic Palladium clusters, Phys. Rev. Lett. 86, 2545 (2001).
Expression of any single gene in a living cell is dependent upon presence of the products of other genes, known as transcription factors. This cross-regulation is essential for development and function of an organism. Mathematically, it means that the master equations for the protein concentrations are coupled in a highly non--linear manner. Interestingly, analysis of this nonlinear system can be considerably simplified in the limit when the maximum concentrations of the transcription factors are much larger than the thresholds of their catalytic (inhibiting) action. In particular, the search of the fixed points of this system is reduced to a "semi-linear" problem, somewhat analogous to electric circuit with ideal diodes. We have developed an intuitive diagrammatic representation of the problem, which allows one to find the fixed points, and to study their stability. In this framework, I will discuss the criterion for multistability of a genetic network. It will be argued that the multistability is crucial for understanding many important aspects of the problem, such as robustness, cell fate differentiation, and pattern formation. As an example, I will apply some of these ideas to early development of Drosophila embryo.
We consider two-dimensional turbulence for the case in which a drag force linear in the velocity is present. Such a drag force occurs in all cases where two dimensionality is justified. We find modifications from the dragless power law exponent of the wavenumber-energy-spectrum associated with the enstrophy cascade. The case with drag is also predicted to desplay intermittency (in contrast to the case without drag). Comparisons with numerical simulations will be given.
Elucidation of the electrostatic properties of biomolecules has become a standard practice in molecular biophysics. Foremost among the models used to evaluate the electrostatic potential is the Poisson-Boltzmann equation, however, existing solution methods have limited the scope of accurate calculations to relatively small biomolecular systems. Two new numerical techniques will be presented which enable the parallel solution of the Poisson-Boltzmann equation for supramolecular structures orders of magnitude larger in size than those accessible with traditional methods. As a demonstration of this methodology, electrostatic potentials have been calculated for large microtubule and ribosome structures. The results point to the likely role of electrostatics in a variety of activities of these structures.
We formulate a reaction-diffusion model for bacterial branching growth, and use this model to study possible scenarios during the life of a colony: The use of chemotactic signaling, the appearance of chirality, the emergence of mutations and the stress of antibiotics.
The human visual pathway comprises some 10% of the neocortex, about 1 billion nerve cells. It embodies and implements the computations underlying our ability to perceive the world as composed of three dimensional moving colored figures relative to some stationary background. In this talk we will focus on those computations implemented by the visual cortex, the first area of the neocortex which receives signals from the eyes. It comprises about 130 million nerve cells arranged in a somewhat disordered lattice of about 1300 modules, each therefore containing about 100 000 nerve cells. I will describe how one formulates equations to represent the population dynamics of nerve cell interactions within and between these modules, and how one analyzes them. I will focus on one aspect of the computations carried out by the visual cortex, how it implements a windowed two dimensional Fourier transform of visual data, and what this might mean for human visual perception.
In this talk I'll look at how ideas about natural history gave shape to museum practices not just in science museums but in many other kinds of museums as well. I'll focus on the late nineteenth and early twentieth centuries but I'll also examine how this legacy poses particular problems and challenges for science museums today.
We study numerically the effect of the feedback of gravity on flame propagation in the Boussinesq limit using a simple reaction model. The propagation speed is expected to increase due to distortion of flame front by the Rayleigh-Taylor instability. Indeed, the Rayleigh-Taylor-type instability was observed at initial stages of development; however, burning consumes the smallest scales, and after a transitional period, a travelling wave solution is established. For thin flames (flames with laminar thickness small with respect to the wavelength of the initial perturbation,) the propagation speed is proportional to the square root of the product of the gravity and the wavelength of the initial perturbation. For thick flames, the flame propagation speed also depends on the laminar flame speed. To understand the results, we looked at the flame structure, vorticity generation, growth exponents of individual modes and flame stability.
At high Reynolds number, the boundary layer is bounded by a contorted curve: fingers of fluid reach into the boundary layer and slender spires of boundary-layer fluid curl outward. This ragged edge of the boundary layer grasps fluid of high momentum and energy and draws it into the boundary layer. This transport taking place near the outer edge of the boundary layer-- by which the boundary layer invigorates its own mass, momentum and energy--has not been much studied, compared with the more intensively investigated near-wall region.
Transport across the outer edge of the boundary layer occurs by entrainment, by which the boundary layer incorporates new fluid, and detrainment, by which it looses vortical fluid into the outer region. We show that both entrainment and detrainment can be described by a simple two-dimensional inviscid flow model composed of layers of constant vorticity. It is found that an initial disturbance to the boundary-layer thickness breaks down into a wave field plus, if the initial disturbance is steep enough, a volume of entrained fluid. The entrained fluid is drawn from the outer layer and is folded into a crevice. The crevice stretches and eventually pinches off becoming completely enveloped within the boundary layer. The enveloped bolus of fluid can be drawn in deeply, nearly reaching the lower boundary. Very steep disturbances result in detrainment. The characteristics of folding and stretching make the process presented here a candidate for a mechanism by which high-Reynolds-number boundary layers commence mixing with outer-layer fluid.
When a mathematical model of a reaction/transport process is implemented in a computer program, there exist two approaches to its study. The first consists of direct simulation: setting initial conditions, setting parameter values and running forward in time. This approach performs on the computer what an experimentalist would do in the laboratory with the same system. The alternative approach is to build algorithms (based on the same physical model) that directly search for a feature of its behavior (like a steady state, or like the boundary of an operability diagram, which may be a turning point bifurcation, e.g. an ignition). This alternative approach, which encompasses tasks such as continuation, stability, numerical bifurcation, parametric sensitivity, optimization, controller design etc., we term "system level tasks". Such studies are possible for continuum process models (ordinary differential, partial differential, integrodifferential systems of equations), but in principle inaccessible to microscopic (Monte Carlo, Molecular Dynamics, Lattice Boltzmann and hybrid codes).
Over the last few years we have been developing a computer-assisted approach that enables microscopic timesteppers to perform such system level tasks, sidestepping the necessity of first constructing continuum, mesoscopic equations and then analyzing them. The approach is built on the so-called time-stepper based bifurcation calculations, and is applicable in systems for which the long-term, "coarse" dynamics are dissipative and involve a certain separation of time scales.
In this talk we will present a guided tour of the approach and some of its connections to numerical analysis and nonequilibrium statistical mechanics. We will present examples of coarse stability and bifurcation analysis for multiphase flows and for catalytic reactions. We will also demonstrate techniques for coarse integration of these problems with the recently introduced micro-Galerkin projective integrators. Finally, we will demonstrate extension of this approach to perform the analysis of effective medium equations for reaction/transport in complex media. Elements of this work constitute collaborations with a number of coworkers: D. Maroudas at UCSB, O. Runborg, K. Theodoropoulos and C. W. Gear at Princeton, P. Kevrekidis at UMass, J. M. Hyman at Los Alamos and K. Lust at Leuven.
The computational architecture of the olfactory bulb is intriguing, as it combines a relatively ordered set of inputs from the peripheral olfactory nerve with a massive array of inputs from many other brain areas. When animals are anesthetized or passively exposed to odors, the activity of the principal neurons (mitral cells) appears to be driven by a relatively ordered set of relationships dependent on similarities in chemical structure, which is suggestive of chemotopy. Neural recordings from awake animals, trained to associate a behavioral meaning with an odor stimulus, present a different picture of odor "representation." In these experiments we find that the activity of individual mitral cells is driven primarily by the behavioral requirements of the stimulus. Odor representation, when seen, is also driven by meaning. When the behavioral requirements of the stimulus changes, so does a cell's odor selectivity. These changes are most likely driven by input from other brain areas, one candidate of which we have found to be the entorhinal cortex as part of the hippocampal system. Behavioral experiments, which we have designed to test the behavioral relevance of chemotopy, also show that an animal's prior experience with odors influences to a large degree the ability to recall a learned odor from among a set of chemically similar odors. However, there is some influence of the odor's chemical class (e.g., all alcohols smell similar, even though individual alcohols can be easily distinguished). We also find that in special circumstances, the chemical structures of mixture components, combined with olfactory receptor biophysics, can determine the perceptual quality of the mixture. These results elucidate the computational structure of the olfactory system, which involves a dynamic interplay between chemistry, anatomy, meaning and behavior.
Vascular disease, including atherosclerosis, aneurysms, and plaque disruption are currently one of the leading causes of death in the United States. During the past two decades, the role of hemodynamics, or fluid mechanics of blood flow, has been implicated in the development of arterial disease and in the regulation of cellular biology in both normal and diseased arteries. Among the methods used to investigate the hemodynamic forces in the vasculature system, computational fluid dynamics (CFD) is becoming the most prevalent because of its ability to provide more detailed flow information than either in vivo or in vitro experiments. This talk will provide a brief overview of a simulation procedure for studying blood flow at transitional Reynolds numbers in subject-specific carotid arteries and arteriovenous (AV) grafts, two sites that are prone to vascular disease. We describe PDE-based procedures for translation of MR or CT scan images into high-quality hexahedral meshes and the extraction of velocity boundary conditions from Doppler ultrasound data. We illustrate that spectral element discretizations, which have minimal numerical dissipation and dispersion, are particularly effective for simulating this class of flows and discuss some of the algorithmic hurdles in their implementation. We close with a comparison between simulation results and available in vitro and in vivo data.
The question in the title was posed by David Raup in his book ``Extinction: bad genes or bad luck?'' In this talk, I will propose a model, based on a very simple (and purely terrestrial) mechanism, which attempts to answer this question, as well as a number of others, such as the origin of mass extinctions, ice ages, subdivisions of the geological time scale, etc. It may even shed light on some obscure passages from the Epic of Gilgamesh and similar sources. While the basic mechanism is simple, it is not easily observable in action, and the evidence I will provide will be, by necessity, indirect. Moreover, the mechanism appears to violate some commonly accepted geophysical notions. Thus, I expect (and welcome) a lively debate. This will be the first public presentation of the model.
We discuss various phenomena connected with individual and many bubbles in still and flowing water.
1. The dynamics of a bubble in a flow is determined by buoyancy and hydrodynamic forces. If an acoustic field is also present, the dynamics is modified, hydrodynamic and acoustic forces now compete. Understanding this competition opens the possibility of controlling the motion of bubbles subjected to a flow by means of an external sound field. We show that this competition leads to spiralling bubbles. This dynamics is modeled by expressing the balance between Bjerknes and hydrodynamic forces in terms of an ODE model, to which a separation of time scales is applied. The success of this model shows that the simple force balance approach is still meaningful when bubbles are subjected to sound fields.
2. Such a force model is also applied to bubbles in turbulent flow. Employing it, the motion and the action of microbubbles in homogeneous and isotropic turbulence are investigated through (three-dimensional) direct numerical simulations of the Navier-Stokes equations. The forces acting on the bubbles are added mass, drag, lift, and gravity. The bubbles are found to accumulate in vortices, preferably on the side with downward velocity. This effect, mainly caused by the lift force, leads to a reduced average bubble rise velocity. Once the reaction of the bubbles on the carrier flow is embodied using a point-force approximation, an attenuation of the turbulence on large scales and an extra forcing on small scales is found.
3. Finally, we address problems to overcome when trying to confirm this numerical finding in experiment, employing hot-film anemometry. One of the main problems of this method in two-phase flows is the small spiky structure of the signal given by the hot-film probe. It is caused by the abrupt change of heat transfer when the bubbles are crossing or touching the probe. In order to study the relation between the hot-film signal and the bubble dynamics, we correlated the hot-film signal with high-speed videos of the passing bubble with various diameters. In contrast to what has been suggested in literature, we find that bubbles can be considerably delayed when hitting the probe. The experiments thus reveal the limitations on the use of hot-films to obtain information about the gas fraction and the bubble velocity.
4. These results triggered an analysis of bubble shape oscillations: When a bubble rising with constant velocity hits a hot--film anemometer probe, bubble shape oscillations can be induced. As a consequence also the bubble rise velocity strongly oscillates. With the help of a force balance -- and thus coming back to above subject 1 -- we show that these velocity oscillations are an added--mass effect.
It was suggested recently that the statistical physics of turbulent transport processes can be understood in terms of Statistically Preserved Structures. In this talk I will explain the nature of the latter, and how they arise naturally in the discussion of generic systems in which the turbulent velocity field arises from the Navier-Stokes equations or from shell models. In situations with Lagrangian structures the Statistically Preserved Structures have to do with special geometries of Lagrangian trajectories. In general we always have a time-dependent (non compact) linear operator that governs the dynamics of correlation functions. I will show how to naturally discuss the dynamics in terms of an effective compact operator that displays ``zero modes" which determine the anomalous scaling of the correlation functions. In passing I will point out a bonus of the present approach, in providing analytic predictions for the time-dependent correlation functions in decaying turbulent transport.
When Lord Rayleigh and other greats of 19th century physical science were laying down the foundations of fluid dynamics of drops and jets, they could not have imagined that drops and jets would still be of great interest in the 21st century. Indeed, there is currently an explosion of interest in drops and jets because they are scientifically fascinating and technologically important. Whether a millimeter-sized drop drips from the kitchen tap once per second or a stream of micron-sized drops are ejected from the nozzle of an ink jet printer or a DNA arrayer at a rate of 10,000 drops/second, drop formation is a complex free boundary problem exhibiting interface rupture. Physicists, mathematicians, and engineers are drawn to the study of drop breakup because of formation of finite time singularities and self-similar behavior near pinch-off. Computational scientists and engineers are attracted to the problem because it entails large changes in interface topology and the creation of several disconnected liquid masses from an initially single connected liquid mass. Visualization of drop breakup is equally challenging given the micrometer and microsecond length and time scales of interest near pinch-off. This talk will describe recent computational and experimental work aimed at elucidating several interesting situations involving drops and jets. First, the talk will describe analysis of interface rupture during dripping of a liquid from a nozzle into air using computational algorithms of unprecedented accuracy that accord with scaling theories and ultra high-speed visualization experiments at frame rates up to 100 million pictures per second. Second, a quick overview will be given of very recent work on what happens when the air surrounding the drop is replaced by another liquid. (Some of this work is being carried out jointly with Sid Nagel and Itai Cohen.) Next, two examples will be given of how fundamental understanding based on computation and experiment can be used to develop new ways of producing microscopic drops. These science-driven discoveries are expected to impact profoundly the use of ink jet printing in high-technology applications including DNA arraying, printing on diagnostic strips, automatic pipetting of fluids in drug discovery, printing of circuits, and microencapsulation and more traditional ones including printing and coating of various substrates.
Non-equilibrium flow systems often organize themselves into various interesting structures, just like the equilibrium systems do. An example is Turbulent Rayleigh-Bénard convection, which has attracted much attention in recent years. Despite its relatively low Reynolds number (Re), turbulent convection shares many common features that are usually associated with high-Re turbulent flows. These features include coherent structures, intermittent fluctuations, and anomalous scaling. In this talk I will briefly review the recent development in the area and report our recent experimental studies of the large-scale coherent structures in turbulent convection [1-3]. Using the techniques of laser Doppler velocimetry, thermometry, and flow visualization, we measure the large-scale flow structure and the local heat transport in a convection cell filled with water. We also measure the temperature cross-correlation functions at various locations and study the dynamics of thermal plumes near the conducting surface and in the bulk region of the cell. The experiment clearly demonstrates how otherwise random unstable modes (thermal plumes) in a closed cell organize themselves in both space and time to generate a large-scale flow structure, which rotates and oscillates coherently in a turbulent environment.
Many functions crucial to life are carried out by membrane proteins bound to or embedded in lipid bilayers. Conversely, a wide variety of diseases result from deficient or abnormal lipid-protein interactions. Study of these interactions can, therefore, help elucidate the normal functions of these proteins, and the mechanisms by which toxicity is introduced in the case of a disease. Using two-dimensional monolayers as well as supported bilayers as model systems, we have applied isotherm measurements, optical microscopy, scanning probe microscopy, x-ray and neutron scattering techniques to address fundamental questions concerning lipid-protein interactions: What is the effect of the protein on the stability of the phases of the lipid film? How does the protein alter the surface morphology of the system? How does the protein change the ordering of the host lipid layer? To what extent and how does the protein associate with membrane lipids? How are the observed phenomena related to biological functions? To illustrate the capability of these techniques, their applications to the understanding of (1) the aggregation of Alzheimer's beta-amyloid peptides, and (2) the use of triblock copolymers as membrane sealants will be discussed.
Liquid foams are soft matter systems with complex structure whose evolution is governed by two main processes: liquid flow (drainage) and gas exchange (coarsening). Characterizing drainage and coarsening behavior requires knowledge of material properties (such as interfacial rheology) as well as purely geometrical information (such as the shape of the bubbles). Foams of different make-up can therefore show qualitatively different dynamics in experiment. We point out a way to describe these differences within a generalized picture, and try to answer questions such as: Are beer foams and soap froths alike? How do you make the head on a glass of beer last longer? What is the link between bubble geometry and foam aging?
For many years biologists have looked to physics for guidance in the development of theoretical approaches to biological systems. After first contrasting Ptolemaic and Newtonian models of planetary motion, this talk will consider current approaches to uncovering fundamental principles of organization in the mammalian cerebral cortex. Evidence will be presented that appropriately structured models can reveal principles that apply across multiple levels of biological scale, and may have the kind of generality often lauded in physics. A case will also be made, however, that models focused on such generalities at the outset are doomed to fail.
In this talk I present a random process model for the standard trading mechanism used in most financial markets. This is called the limit order book. It can be regarded as a device for storing supply and demand. The theory predicts several of the most basic properties of prices such as volatility, liquidity, and the bid-ask spread, as a function of order flow rates. It predicts the average price shift for an order of given size has a universal concave form that seems to match the observed behavior of NYSE stocks. Enhancements of the basic model may make it possible to understand other properties of prices as well, such as the fat-tailed distribution of price changes. This work demonstrates how techniques such as dimensional analysis and statistical mechanics can be useful for understanding markets. It also illustrates the importance of modeling market institutions, and shows that for some purposes it can be useful to begin by modeling human behavior as random, adding a little rationality as needed.
A modern market-based economy is an example of a complex adaptive system, consisting of a decentralized collection of autonomous adaptive agents interacting over time in various market contexts. These massively parallel local interactions give rise to global regularities such as trade networks, market protocols, and the common adoption of technological innovations. In turn, these global regularities feed back into the determination of local interactions. The recent advent of powerful computational tools, in particular object-oriented programming, permits new approaches to the study of this complex two-way feedback between microstructure and macrostructure. In this talk I will discuss the potential usefulness of one such approach -- agent-based computational economics (ACE) -- the computational study of economies modelled as evolving systems of autonomous interacting agents. For concreteness, I will illustrate how controlled experiments in ACE frameworks have shed light on the following important economic issue: Can strategic learning and network effects prevent the reliable prediction of market outcomes from market structure?
During the last two decades numerical simulations have proved to be an invaluable tool in working out predictions of cosmological models of structure formation. In this talk I will discuss some numerical algorithms most commonly used in cosmological simulations and will review the current status of structure formation models highliting both their biggest successes and problems. Specifically, I will 1) review the predictions of Cold Dark Matter models on subgalactic scales and compare them to observations 2) discuss the progress in N-body+gasdynamics simulations of galaxies and galaxy-clusters and current and future efforts in this area.
Penitentes and suncups are structures formed as snow melts, typically high in the mountains. When the snow is dirty, dirt cones and other structures can form instead. Sunlight, heating from air, and dirt all play a role in the formation of structure on an ablating snow surface. This work presents a minimal model for the formation of ablation morphologies as a function of measurable parameters. I derive a single-parameter expression for the melting rate as a function of dirt thickness, which agrees well with a set of measurements by Driedger. The dependence of ablation morphologies on weather conditions and initial dirt thickness are studied, including the initial growth of perturbations away from a flat surface and the nonlinear development and evolution of spatial structure.
I'll also discuss recent laboratory experiments by Vance Bergeron which reproduce penitente-like structures in a controlled environment, as well as other possible applications of this type of modeling.
This work is a collaboration with Bianxiao Cui and Binhua Lin. We have studied the hydrodynamic coupling between Brownian colloidal particles diffusing along a linear narrow channel --- a phenomenon relevant to transport in various systems, such as porous materials, biological ion channels, and microfluidic devices. The quasi-one-dimensional confinement, unlike other constrained geometries, leads to a sharply screened, short-ranged interaction. Consequently, particles move in concert only when their mutual distance is smaller than the channel width, and two-body interactions remain dominant up to high particle densities. The coupling is shown theoretically to reverse sign at a certain distance, yet this unusual effect is too small to be currently detectable.
The concept of theoretical morphology can, in a philosophical sense, be traced at least as far back to the writings of Plato who regarded the natural world as being composed of a finite number of idealized 'archetypes'. The 'type' system used by systematists world-wide has its origins in this ancient concept. Computationally, theoretical morphology traces its origins to the geometric formalisms of the Victorian natural philosopher D'Arcy Wentworth Thompson. Thompson created a primitive version of a 'morphing' algorithm and argued that physical forces were responsible for creating morphological novelty through the deformation of pre-existing organismal shapes according to a finite number of deformational modes. While computational difficulties prevented Thompson's formalisms from being turned into analytic tools in his own time, with the advent of analog and digital computers in the early 1960s David Raup and colleagues succeeded in realizing the promise of theoretical morphology for particular classes of organic shapes (e.g., mollusk shells, echinoderm plates, brachiopod shells). Unfortunately, the difficulties inherent in representing complex, irregular, organic shapes have prevented this valuable concept from being applied more widely in systematic contexts to date.
Geometric morphometrics is also derived from Thompson's work, at least in part. In its current formulation geometric morphometrics represents a powerful set of analytical tools, created out of a synthesis between Thompson's deformational geometrical approach and the school of linear multivariate analysis whose origins can be traced to Thompson's contemporaries Francis Galton and Karl Pearson. Contemporary morphometricians make a distinction between their methods and those of theoretical morphologists, arguing that, in addition to differences in computational approach, the former is used to study covariances between morphology and sets of external variables whereas the latter is used to study systems of shapes per se. It is the contention of this presentation that these distinctions are illusory. The current formulation, geometric morphometrics operationalizes all of the major tenets of theoretical morphology and does so in a manner that transcends the shape-representational barriers that have limited the application of both theoretical morphology and morphometrics throughout systematics. The stage is now set of a renaissance of morphological systematics. Indeed, such a renaissance is demanded by independent advances in our understanding of phylogeny and be recent advances is molecular systematics. Examples of combined theoretical morphology/geometric morphometric approaches to a variety of systematic studies (e.g., shape characterization, character-state definition, ontogenetic) and using a variety of organic (e.g., vertebrate, invertebrate, microscopic, botanical) and inorganic (e.g., sand grains) shape will be used to illustrate the power and the generality of this approach to the study of form. Images and Ideas: Exhibiting Science in Museums, University of Chicago.
Note: Dr MacLeod will also speak in KPTC 206 at 2:15 Tuesday June 17 in our meeting on Science Museums. His title for that talk is "PaleoBase: Images, Databases, Collection Catalogues, and Commercialism in the Emerging Virtual Museum." Please see the meeting web page http://jfi.uchicago.edu/Science_Museum_Meeting/
Thanks to experimental advances over the past decade, it is now possible directly to study the mechanical properties of individual macromolecules. The new techniques have already begun to make important contributions to several fields, most to notably structural biology, where they can, for example, give information about molecules that are difficult to study by conventional means such as X-ray crystallography. In this talk, I consider one of the conceptually simplest such micromechanical experiments, the mechanical denaturation, or "unzipping," of double-stranded DNA. I show that the fact that DNA is usually a heteropolymer gives rise a jagged energy landscape for unzipping that can dominate both the static and the dynamic properties. In particular, equilibrium force-extension curves, rather than being smooth, will consist of a series of flat plateaus followed by sharp jumps, and the unzipping dynamics will be subdiffusive over a substantial range of forces. Many of these features should appear not only in DNA unzipping, but also in mechanical denaturation experiments on more complicated molecules. I conclude by commenting on current work on two extensions of these results, to the question of whether point mutations can be detected with DNA unzipping and to methods for inferring RNA secondary structure from its response to an applied force.
It has been claimed that the response of quasistatic granular materials to applied forces exhibits departures from elasticity, even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that such departures are expected at small scales [below O(100) particle diameters], at which continuum elasticity is invalid, and vanish at large scales. These models exhibit force chains on small scales, and force and stress distributions which agree with experimental findings. Effects of anisotropy, disorder and boundary conditions are discussed as well. In this context, a general microscopic derivation of elasticity is proposed. This derivation pertains to disordered systems and inhomogeneous strains, unlike the classical derivations which pertain only to (nearly) uniformly strained lattices. As a first step, microscopically exact expressions for the displacement, strain and stress fields are derived. Conditions under which linear elastic constitutive relations hold are studied theoretically and numerically. It turns out that standard continuum elasticity is not self-evident. As perhaps expected, it applies only above certain spatial scales, which depend on details of the considered system and boundary conditions. The results may be relevant to nanoscale systems.
We consider the motion of a filament that forms behind a falling drop of polymer solutions and surfactant solutions, both analytically and experimentally, and observe several interesting new phenomena.
We generalize Segur's theory for the free boundary problem of a cylindrical Newtonian filament to non-Newtonian fluids, and are able to provide a general condition for the existence of solutions. This is a generic approach which allows any constitutive relation to be evaluated. An exact solution for a non-Newtonian flow is unusual, yet for two standard non-Newtonian models we have found an analytic solution that describes the filament motion. Comparisons of this exact solution with experiments using a viscoelastic polymer solution show strong quantitative agreement and provides insight as to how the molecular dynamics couple with the filament's motion.
In experiments with micelle-forming surfactant solutions (so-called "worm-like" micelles), we have found a striking transition from fluid to gel-like behavior in the stretching filament of the drop. Moreover, the drop can slow down and even stop ("stall") for some time as it falls away from the orifice. A detailed study of a simple model for the filament using an appropriate constitutive equation indicates that fluids with low solvent viscosity, high elasticity, and high molecular weight can stall; these results are consistent with the properties of the micellar solutions used in our experiments.
I will talk about the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two-dimensional interacting elements (or "spins"). This family is defined to contain under the same framework, among others, the XY-model and the Self-Driven Fluid model introduced by Vicsek et al. in 1995. Each model is distinguished only by the rules that determine the set of elements with which each element interacts. As a new member of the family, a vectorial network model is proposed, in which a given fraction of the elements interact through direct random linkages. The numerical and analytical study of this model reveals the existence of a phase transition belonging to the same universality class as the Mean Field Theory, even for cases with a small fraction of random linkages. This result leads to the conclusion that the long-range correlations produced by the introduction of randomness in the selection of the linkages are the underlying cause of the phase transition for all models in this family, regardless of other equilibrium or nonequilibrium dynamical properties.
Mars is mostly covered by rocks, sand, and dust, granular material that can, in rare circumstances, reveal the presence of near-surface water. The Mars Orbiter Camera has returned images of numerous dark streaks that are the result of down-slope mass movement occurring under present-day martian climatic conditions. A systematic survey of over 23,000 high-resolution images allows to study their geographic distribution, orientation, and timing. The data suggest that small amounts of water are transiently present in low-latitude near-surface regions of Mars and undergo phase transitions at times of high insolation.
Time permitting, I will also talk about rhythmic landscapes formed by fluvial erosion. A small-scale version of that can be observed on a daily basis on the beach. Periodic channelization is also reproduced in a table-top seepage experiment. As a result of field observation and experiment, the theoretical problem is formulated in terms of flow through a porous medium with an adjustable watertable and a growing outlet channel. According to this theory, small deformations of the underground watertable amplify the flux into the channels. Piracy of groundwater occurs over distances much larger than the channel width.
(Joint work with Oded Aharonson, Bill Jensen, Samar Khatiwala, Arshad Kudrolli, and Daniel Rothman)
In many simple experiments, the behavior of non-Newtonian fluids can be a challenge to common intuition. When a solid sphere settles through the free surface of a viscoelastic fluid, the interface is stretched downwards into a funnel shape which surprinsingly loses its axial symmetry. The interface folds, generating a pattern of creases after pinchoff.
Using fluids that are strongly birefringent under stress, we show experimentally that stress boundary layers form at the interface, a consequence of the strain-hardening behavior of viscoelastic fluids in extensional flows. This allows a simplified treatment of the problem in terms of a stretched elastic membrane. Formally, this model is a generalization of the equations governing soap films and static interfaces with an anisotropic, strain-dependent surface tension.
The folding process can then be identified as a buckling instability which occurs when the elastic effects give rise to a formally negative surface tension.
Similar instabilities are indeed common in stretching flows of viscoelastic fluids, and could be responsible for the bidimensional cusp sometimes observed at the trailing edge of rising bubbles.
The quadratic non-linearity of Navier-Stokes equations allows for two type of coupling in the Fourier representation: one involving triads of wave-numbers with comparable size (local interactions) and one involving elongated triads of wave-numbers, with one short leg and two long legs (non-local interactions). The analysis of high-resolution direct numerical simulations shows that at small scales, the dynamics is dominated by the non-local interactions, through the advection and stretching of the small eddie by the large eddies. I show how the predominance of non-local interactions results in a new model of turbulence in which large and small scales are dynamically coupled through a linear, stochastic, inhomogeneous equations of Langevin type. As an illustration of the model, I compute the heat transport in a turbulent horizontal layer heated from below, as a function of the Rayleigh and the Prandtl number This computation reveals the existence of logarithmic corrections to scaling consistent with available experimental measurements.
It is known that complex wave interference makes the phase coherent transport in a disordered system non-selfaveraging, requiring a full probability distribution for the sample-specific physical quantities. In this talk I will treat such fluctuations for an N-channel disordered conductor in terms of the scattering matrix, randomized maximally,i.e., subject only to the known conditions of symmetry(time reversal invariace), unitarity(flux conservation)and that of the law of composition appropriate to short length scales.Here,.the probability distribution associated with a very small length scale(the building block) is selected on the basis of the maximum Shannon entropy criterion.This leads to a diffusion equation for the full probability distribution of interest evolving in the multi-channel sample length.Implications for mesoscopic fluctuations and random lasing will be discussed. The approach,admittedly macroscopic,is non-perturbative,and agrees with the exact results for the one-channel case, known from the microscopic theory based on invariant imbedding.
Networks with complex topology describe systems as diverse as the cell or the World Wide Web. The emergence of these networks is driven by self-organizing processes that are governed by simple but generic laws. The analysis of the metabolic and protein network of various organisms shows that cells and complex man-made networks, such as the Internet or the world wide web, share the same large-scale topology. I will show that the scale-free topology of these complex webs have important consequences on their robustness against failures and attacks, with implications on drug design, the Internet's ability to survive attacks and failures, and our ability to understand the functional role of genes in model organisms.
For further information and papers, see http://www.nd.edu/~networks
Humans are distinguished by the ability to acquire and use language. This ability allows us to transmit information in a non-genetic manner across generations. As a result it becomes possible for us to have a sense of history, culture, and tradition. Curiously enough, language may be viewed as a formal object with words and grammatical rules. Language learning may then be viewed as an inductive inference procedure that infers these formal objects from data. This allows one to take a computational view of language acquisition and indeed, this view has dominated current thinking in artificial intelligence, cognitive science, and linguistics.
Now language learning is the mechanism by which language is transmitted from one generation to the next --- children acquire the language of the mature speakers in the population. In this talk, we consider the interplay between learning by individuals and language change and evolution by populations. By considering an ensemble of language learners, one can derive various dynamical systems that show how the population might evolve under those assumptions. We will consider several such dynamical systems and see how they might shed light on questions such as dialect formation, language evolution, convergence on shared languages and so on. Along the way, the mathematical framework will be elaborated and connections to other disciplines will be emphasized.
E. coli and Salmonella use rotating helical filaments to swim. These cells swim forward when the filaments turn counter-clockwise and form a bundle. The cells change direction by a process in which one or more of the filaments turns clockwise, disperses from the bundle, and changes helical pitch. Motivated by these phenomena, we use slender-body theory to numerically compute the flow induced by two rotating rigid helices. We show how the flow field depends sensitively on the phase difference between the two helices. We further argue that kinematic reversibility and symmetry rule out a time-averaged attractive or repulsive force between rigid helices, but allows the tipping force responsible for the initial wrapping motion. Finally, we present experimental results from our macroscopic scale model consisting of a tank of high-viscosity silcone oil containing helices driven by stepper motors.
With the advent of scalable computers, atomistic simulations are contributing new insights into the nature of failure dynamics. Exciting findings include a crack instability in rapid brittle fracture, a dynamic brittle-to-ductile transition in ductile materials, supersonic crack motion in layered solids & work hardening in plastic deformation. Most important, these simulations are based on an "abinitio" description of materials failure where atomic systems as large as one billion atoms are employed.
However, a complete treatment of materials failure based solely on atoms is not computationally possible and not necessary. In brittle fracture, we need atoms only near the crack tip and, maybe, quantum electrons for the snapping of chemical bonds. Indeed, a challenging paradigm in the computational sciences is the coupling of the continuum, the atomistic and the quantum descriptions of matter for a unified dynamic treatment of a physical problem. This requires the simultaneous use of the tools of engineering, physics and chemistry in a seamless formalism. We have accomplished this for the study of the brittle fracture of silicon.
I will describe these simulation studies with an emphasis on their computational complexity and with several movies.
Cytokinesis is an elegant cell shape change that leads to the division of the mother cell into two daughter cells. It is essential for cell proliferation, making it of interest medically as a potential source of novel drug targets for the treatment of hyperproliferative diseases. Our research focuses on the biochemical basis for the mechanics of cytokinesis. We are developing a multi-faceted approach where we are combining genetics, mechanistic biochemistry, cellular biophysics and mathematical modeling to study the mechanisms of cytokinesis. Our discoveries also have implications for general cell shape changes that form the basis for diverse cellular functions, including chemotaxis and neuronal extension.
I will present some of our recent laboratory experiments that illustrate how mass-dependent kinetic isotope fractionations arise during mass transfer within (e.g. by diffusion) or between (e.g. by evaporation) phases. Once calibrated, kinetic isotopic fractionations can be used as "fingerprints" for the manner and extent of mass transfer and I will illustrate how we have used them to infer the thermal history of some of the oldest and most primitive materials in our solar system. When considered in detail, the experimental results have various troubling features with regard to generally accepted theoretical expectations. For example, the degree of isotopic fractionation during evaporation from a variety of molten silicate liquids is significantly less than what the commonly accepted theory leads us to expect. Other unanticipated results include that chemical diffusion in molten silicates is often much more effective at fractionating isotopes than is the case for comparable species diffusing in water. On the other hand, dissolved noble gases diffusing in water are fractionated to a greater degree than they would be by diffusing in a gas. Can computations help us develop better expectations and a better understanding of kinetic isotopic fractionation during mass transport?
The study of biological phenomena is best appreciated from the perspective of evolutionary theory. I will describe how this informs the analysis of brain and behavior, to place the neurobiological work in context. I will then describe some recent results in the study of birdsong learning and production, and place these in the context of various models. Understanding these phenomena will require multiple perspectives including the participation of biologists and physicists.
The resonant response of a single nonlinear oscillator to periodic forcing is well understood, yet little is known about frequency locking in spatially-extended oscillatory systems such as arrays of Josephson junctions or the heart. We use an experimental and a numerical reaction-diffusion system driven far from equilibrium to study the effects of frequency locking on pattern formation. I will introduce a quantitative description of resonant patterns which allows us to identify transition between pattern states as the forcing strength is varied. The resonant patterns observed in the experiments show qualitative agreement with our numerical model and with an analysis of an amplitude equation, suggesting that they are general features of frequency locking in oscillatory continua.
A solid bead deposited on a tilted plane immediately starts rolling down with uniform acceleration. We propose two complementary situations. We first describe how this simple experiment can be conducted using a droplet of water in place of the bead. The conditions of surface super-hydrophobicity required will be discussed. In the second part, we study the motion of a solid sphere on a slippery wall (a plane coated with a layer of viscous liquid). The sphere simultaneously slides and rolls down along the plane. Depending on the physical parameters of the experiment, different regimes are observed. In particular, an overhang configuration exhibits a "viscous adhesion" of the sphere to the wall.
Illustrated examples are available on the web page: http://web.mit.edu/nnf/jose/Research.html
The surface of Mars exhibits abundant evidence that the climate of the planet was radically different early in the history of the Solar system. Many features indicate a warm and wet planet with flowing surface waters and an active hydrological cycle. The evidence includes networks of river-like features, an apparent ocean basin, and a variety of glacial deposits. All extant theories of the climate of Early Mars involve the warming effect of a carbon dioxide atmosphere having surface pressure in excess of 1-2 bars.
In this talk I will focus on the dynamical aspects of the Early Mars climate, with particular emphasis on the seasonal cycle of temperature and winds. The hypothetical CO2 atmosphere has more thermal inertia than the present Earth atmosphere, but far less than the Earth's global ocean. Hence (apart from the possible effects of a Martian polar ocean) the seasonal cycle on Mars is expected to be extreme, though not so extreme as in the present thin-atmosphere case. The magnitude of the seasonal cycle is important because it bears on the question of whether the climate could support seasonal meltwater even if the annual mean climate were below freezing. It also affects the glacial dynamics of the polar regions. These questions are addressed within a simplified axisymmetric fluid dynamical model incorporating the essentials of the Hadley cell dynamics.
As a sideshow, I will use this calculation to illustrate the many virtues of using the interpreted high-level language Python as a tool for organizing scientific simulations.
...is a common experience for the uninspired novel writer, for the cook and the driver under a heavy rain. I hope this talk will help making links with these people:
The uninspired novel writer looks through the window and sometime fixes the rain drops attached to the glass. We first show that the shape of these drops is described by the classical pendulum equation.
The cook knows that a water drop on a hot frying pan can stand alive more than a minute, a surprisingly long time. We study calefaction paying a special attention to the vapor layer standing between the drop and the pan.
The driver under a heavy rain observes the centimetric spots that result from the impact of millimetric drops. We study the impact and show that the maximal extension corresponds to the deformation of the drop under an effective acceleration field which depends on its initial velocity and size.
The availability of the complete sequence and large scale gene expression data has made it possible to decipher the regulatory code of a genome. Such code specifies when and where different genes should be turned on or off. I will describe a few approaches that we have developed to tackle this problem. One approach is based on statistical analysis and pattern discovery, i.e., identifying patterns in the genome that are likely to be regulatory elements. Another approach is to use genome-wide gene expression data to extract relevant regulatory elements and determine their logical interrelations. A third approach is to compare the regulatory regions of orthologous genes across species. Results from analyzing model organisms will be presented.
Jamming occurs in a wide variety of situations. Normally one thinks of traffic jams on a highway or the jamming that occurs when solid particles become impacted on leaving an orifice. I will argue that the transition from a flowing to a jammed state may be similar in many respects to other situations as well. The case I have in mind is the glass transition where a liquid becomes progressively sluggish as the temperature is lowered until it eventually becomes a glass where it stops moving entirely. In the present talk, I will emphasize the jamming transition at zero temperature near close packing. Although in many ways it resembles a critical point, this transition also has unique properties that distinguish it from ordinary critical behavior.
Einstein's equations of general relativity are prime candidates for numerical solution on supercomputers. There is some urgency in being able to carry out such simulations: Large-scale gravitational wave detectors are now coming on line, and the most important expected signals cannot be predicted except numerically.
Problems involving black holes are perhaps the most interesting, yet also particularly challenging computationally. One difficulty is that inside a black hole there is a physical singularity that cannot be part of the computational domain. A second difficulty is the disparity in length scales between the size of the black hole and the wavelength of the gravitational radiation emitted. A third difficulty is that all existing methods of evolving black holes in three spatial dimensions are plagued by instabilities that prohibit long-term evolution.
I will describe how two ideas that have been successful in other areas of computational physics are being introduced in numerical relativity to deal with these problems. The first technique, multidomain spectral methods, can deal with the multiple length scales. The second idea is to seek new formulations of Einstein's equations that are manifestly hyperbolic to control the instabilities. And it turns out that these two techniques together can deal with the black hole singularities. Needless to say, no knowledge of general relativity will be assumed for the talk.
The problem of determining the ground state of particles packed on spherical shells was first posed for physicists by J. J. Thomson in 1904 as a model for the periodic table. Icosadeltahedral packings, similar to fullerene molecules or the panels of a soccer ball, describe how proteins are arranged in the shells of spherical viruses. We argue that these regular packings must become unstable to either faceting and a proliferation of grain boundaries for sufficiently large R/a, where R is the sphere radius and a is the particle spacing. The theory is relevant to the shapes of large viruses, crystallization of lipid molecules in spherical vesicles and "colloidosomes", where the particle packings can be imaged directly with confocal microscopy.
According to the conventional model, the geomagnetic field is generated by the hydromagnetic dynamo action in the Earth's outer core, consisting mainly of liquid iron. There are, however, a number of problems with this model. For example, there is no evidence of hydrodynamic motion in the outer core independent of the belief that this motion is the raison d'etre of the geomagnetic field (and therefore must exist). Also, it is not clear what could drive the motion. Natural convection is a viable mechanism, but thermal buoyancy is insufficient, and may even have a wrong sign. Compositional buoyancy is thought to be the answer; it arises because lighter components dissolved in the liquid iron are rejected at the inner-core boundary where the liquid solidifies to form the inner core. This mechanism, however, could not operate before the inner core appeared, ~ 2 billion years ago, and reached some reasonable size, whereas the paleomagnetic evidence indicates that the field existed, at about the same strength as today, since much earlier times. Other serious problems exist as well. In this talk, I will briefly summarize the puzzles and paradoxes of the conventional model, and propose a new hypothesis concerning the origin of the Earth's magnetic field. This will be the first public presentation of the hypothesis; I expect a lively debate.
Nature uses a very small number (~1000) of folds (chain geometries) to make proteins. Is this an arbitrary outcome of evolution or is there a selection principle behind. Has nature exhausted all the possibilities? Can we discover protein folds not found by nature? We address these questions starting from simple models to more complex and realist models that require extensive computation to experimentation. The talk will be at a very pedagogical level and no prior knowledge of protein structures is required.
This paper discusses a type of reasoning that I call "asymptotic reasoning". Such reasoning plays an essential role a wide range of problems and investigations in physics and applied mathematics. Philosophers of science who are interested such methodological issues as the nature of scientific explanation and various reductive relations between theories can learn much from the study of this type of reasoning. I examine various issues about explanation, understanding, and reduction in the context of a particular illustrative example involving the wave and ray theories of light.
The role of mathematics in Developmental Biology has a long and vexed history in the U.S., and it raises critical questions about differences in the meanings of 'theory' and 'explanation' assumed by workers in the Mathematical and Biological Sciences. Indeed, I argue for a difference in "epistemological culture." There is evidence, however, of a convergence now taking place between these two cultures, and I will examine some of the conditions currently forcing the changes (in both cultures) that facilitate convergence.
This talk will describe experiments and simple analytical theory for flow of immiscible fluids in microfluidic channels. We have observed that there is an instability in such flows that leads to formation of droplets on pL scale at low values of the Capillary number and the Reynolds number. I will explain -- from the experimental point of view -- why this system works while many other systems don't. I will show how this instability can be used to make droplets made up of several solutions. This gives us the ability to understand mixing of these solutions. Mixing can be accomplished by recirculating flows inside flowing drops, and I will show examples where this works well and where it does not. I will discuss our simple approach to mixing inside droplets using the principle of chaotic advection, which is significantly more robust than mixing by steady recirculation. I will then present our theoretical thoughts on the scaling of mixing. I will also talk about several other issues, such as merging and splitting of droplets. In conclusion, I will show how this system can be used to measure chemical reaction kinetics better, faster and with lower sample volumes than it is currently done. I will also raise questions that are important for the field and may be addressed computationally/theoretically. Time permitting, I will give an overview of several other projects we are pursuing where interaction between computation and experiment may provide exciting opportunities.
If it is ever completed, the National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory will be the largest and most powerful laser in the world. The facility has been beset by controversy from the beginning. Some physicists have insisted that it will not achieve its advertized goal of "ignition", and there are questions whether the lenses can withstand the power of the beams. NIF was originally slated to open in 2003 at a cost of $1.2 billion. Laboratory managers now say it will open in 2008 and its costs are variously estimated at $3.5 to $5 billion. NIF's cost overruns have already brought down one Director of Lasers at the Livermore Laboratory as well as the Laboratory director himself and have provoked a Congressional investigation. But what is the laser for? To different constituencies it is, variously, our best hope for a clean energy future, a useful tool for applied astrophysics, an essential technology for maintaining the nuclear stockpile, a threat to world peace, or a colossal waste of money. Hugh Gusterson is an anthropologist who has been studying the organizational culture of the Livermore Laboratory since 1987. His talk seeks to make sense of the contending views of NIF and the light it may throw on the enterprise of "Big Science" in the post-cold war era.
The thermodynamic hypothesis, enunciated by C.B. Anfinsen, proposes that the amino acid sequence of a protein contains all the necessary information to determine its three-dimensional structure as the thermodynamically most stable one. We have developed empirical potential functions and global optimization algorithms to compute the native structures of polypeptides and proteins. The evolution of this methodology, leading to our current procedures to compute the three-dimensional structures of globular proteins, will be described.
When a tape plunges into or is pulled from a pool of liquid, the contact line of solid/liquid/gas coexistence is moving relative to the substrate. Huh and Scriven discovered 30 years ago that the fluid motion near the contact line entails a singularity of the energy dissipation. Thus ordinary hydrodynamics needs to be augmented to include some of the micro-scale corrections usually unobservable on large scales. This invasion of chemistry into the seemingly simple problem of predicting the shape of the fluid interface has initiated long-standing and heated debates. In this talk, I will give a brief overview and then focus on two subjects:
(a) What experimental observations exist that allow to distinguish between different microscopic mechanisms near the contact line?
(b) What type of instabilities limit the speed at which the tape can be pulled?
Please note special date (Thursday) and place!
We develop a microscopic statistical model for the continuous double auction under the assumption of random order flow, and test this model on data from the London Stock Exchange. We investigate the model using methods from statistical mechanics. While the predictions of the model are not perfect, they are extremely good in many respects, e.g., they explain about 70% of the variance in the daily bid-ask spread. We show that in non-dimensional coordinates the short term price impact of trading, which is closely related to supply and demand functions, approximates a universal function. New York Stock Exchange data shows similar behavior.
On a broader level, this work demonstrates that stochastic models based on zero-intelligence agents are useful to probe the effect of market institutions. Like perfect rationality, a stochastic zero-intelligence model can be used to make strong predictions based on parsimonious assumptions, even if these assumptions are highly oversimplified. The standard research program in contemporary economics is to perturb equilibria based on perfect rationality, adding imperfections such as asymmetric information or bounded rationality. We propose inverting this approach, perturbing zero-intelligence models by adding a little intelligence.
The study of pattern formation in complex systems has proved extremely useful to deal with the problem of morphogenesis in living organisms. In this talk I shall examine a general model to describe the spatio-temporal dynamics of two morphogens. The diffusive part of the model incorporates the dynamics, growth and curvature of one and two dimensional domains.
Numerical calculations are performed by using a third order activator-inhibitor mechanism for the kinetic part in two dimensional growing domains having different geometries. The simulations show the crucial role of both, growth and curvature, on pattern selection. Centrosymmetric patterns are obtained for small domains. It is shown that both effects might be biologically relevant in explaining the selection of some observed patterns.
I implement the scale-free topology into the Boolean network model proposed by Stuart Kauffman in 1969 to describe generically the dynamics involved in the processes of gene regulation and cell differentiation. In the original Kauffman model, the network topology is homogeneously random and the parameters of the model have to be fine-tuned in order to achieve the dynamical stability required by living organisms to perform with reliability. Such fine-tuning is contrary to experimental observations. However, when the scale-free topology is implemented into the Kauffman model, stable dynamics are obtained without fine-tuning the parameters of the model. Additionally, by analyzing how perturbations propagate through the network, one can conclude that the scale-free topology provides the network with both the dynamical stability and the evolvability essential for living organisms to perform with reliability and at the same time to adapt and evolve. It seems that the scale-free topology favors the evolution and adaptatioin of the network functioning.
We present an experimental study of the buckling cascades that are formed along the edge of a torn plastic sheet. The edge is composed of an organized cascade with up to six generations of waves. The waves are similar in shape but differ greatly in scale, leading to the formation of a fractal edge as an equilibrium configuration. We show that the tearing process prescribes a highly curved hyperbolic metric near the edge of the sheet. This metric should be satisfied in order to reduce the stretching energy. However, we show that isometrics of such surfaces cannot be generated by buckling in a single wave along the edge. More waves are necessary in order to generate the prescribed geodesic curvature, which increases towards the edge. The formation of a cascade of waves is, thus, geometrically inevitable. However, our data show that the precise scaling of the cascades is not given by geometry alone. It depends on the sheet thickness as well, indicating the relevance of bending-stretching competition at all scales. This might be an indication for the absence of a smooth imbedding of the generated metrics in Euclidean space. Similar geometrical features (Similar metrics) could result from very simple growth mechanisms. We, thus, suggest that some of the complex shapes of leaves and flowers might result from this buckling instability. The complexity, in this case, results from elasticity and not from complex growth processes, as commonly accepted. Finally, I will present preliminary results from experiments in plants and environmentally responsive gels.
Complex adaptive systems (CAS) are structures composed of many components that interact and reproduce while adapting to a changing environment. These systems often have numerous nested levels of interaction that span many scales of measurement. A few examples of CAS include bacterial populations with chemical, cellular, microscopic, and macroscopic ranges of interaction; economic markets with individual, local, regional, national, and global scales of transactions; and ecosystems with individual, group, and species scales of dependencies. In many cases, traditional analytical, statistical, optimization, and simulation modeling techniques may no longer be adequate to support further research into these systems. Agent-based modeling and simulation (ABMS) offers a solution. ABMS captures the behavior of CAS using sets of agents and frameworks for simulating the agent's decisions and interactions. ABMS can show how a given CAS evolves through time from a multi-level or multi-scale perspective. The foundations and future of ABMS will be discussed in relation to the question: Can complexity be captured with agent-based modeling and simulation?
Michael J. North is the Deputy Director of the Center for Complex Adaptive Systems Simulation at Argonne National Laboratory. Mr. North has over twelve years of experience developing advanced modeling and simulation applications for various branches of the federal government and several international agencies. Mr. North has authored several referred journal articles and many published conference papers on ABMS. Mr. North is active in teaching ABMS in a variety of contexts including the Santa Fe Institute and the University of Chicago. More information on Mr. North's work can be found at http://www.cas.anl.gov/.
What makes ATT unusual is the challenge of operations at extraordinary scale. This talk will describe how access to operations is creating a new research frontier in speech, networking, information mining and software.
June 25, 2003
Whether or not the Euler equations for incompressible flow admit solutions with finite-time singularities, it is clear that the nonlocal action of pressure (non-isotropic Hessian terms) plays a critical role. To address this question we contrast the boundary-free, linear strain flow u=-(y+z, z+x, x+y) that has nonunique solutions including some which blowup in finite time, and some bounded flows with similar behavior near the origin, eg, u=-(sin{y}+sin{z}, sin{z}+sin{x}, sin{x}+sin{y}). Using both pseudospectral and power series in time, it is found that there is no evidence for blowup of the bounded flows. The nonuniqueness in the boundary-free flow is interpreted as an arbitrariness of the homogeneous solution of the pressure Poisson equation. The (1-t)-1 blowup follows from the inclusion of the particular solution only. In expanding about the origin, it is found that only the first spherical harmonic contributes to the non-isotropic Hessian. Strong growth in this mode, which is required for desingularization, is exhibited in the solution of the bounded flows. [This is a joint work with late Richard B. Pelz (Rutgers).]
July 2, 2003
The second problem concerns the motion of a sphere, under the action of gravity alone, down an inclined plane which is coated with a thin film of viscous liquid. The steady translation speed and rotation rate of the sphere are determined by the force balance tangential to the plane and the torque balance on the sphere. We consider the dominant effects in the fluid flow in the meniscus and in the narrow gap between the sphere and the plane, and characterize the scaling of the forces and torques that the flow exerts on the sphere. This leads to a theoretical result for the scaling of the translational speed of the sphere, which is compared with the experimental measurements of J. Bico (MIT).
July 9, 2003
July 16, 2003
July 23, 2003
August 13, 2003
August 27, 2003
In view of these facts, I decided to introduce a category, the wrapping, which is built upon structure but differs from it. It is also different from packing. The wrapping assesses the extent of intramolecular desolvation of backbone hydrogen bonds in protein structure and, based on statistical regularities, identifies under-wrapped hydrogen bonds, now termed dehydrons. Dehydrons are inherently adhesive, as exogenous water removal from their surroundings is energetically and thermodynamically favored.
When the wrapping of structure is examined along folding pathways and in protein complexation, one realizes that life, examined at the nanoscale, reveals a struggle for the survival of hydrogen bonds. Inherent structural disorder in a monomeric structure indicates an inability to fulfill intramolecularly minimal wrapping constraints that have been well established.
If under-wrapped regions are adhesive, they are necessarily interactive -if they find a geometric match-, and thus relevant to biological function. A preliminary proteomic proof of their functional role is given by the fact that aminoacid variability at a particular position on the sequence decreases as the level of wrapping of hydrogen bonds engaging the residue at that position decreases.
This being said, and to deal with the molecular basis of disease, I propose to investigate the "derivative" of wrapping with respect to mutation. That is, I will try to address the question: Where is the interactivity of protein structure most affected by a point mutation in the sequence? That is, I will introduce a sort of "wrapping susceptibility". An extreme susceptibility of wrapping to genetic accident may be a signature for cancer, as preliminary evidence suggests.
But how could cancer arise evolutionary? We learned that the folds for protein domains are conserved across species, itself a remarkable fact. On the other hand, the number of dehydrons for a conserved fold across progressively diverging species is not conserved: it increases monotonically as new species diverge. That means that proteins become more interactive, benefiting more and more from water removal on their surface as higher organisms keep diverging in phyla. Then, the sensitivity of wrapping to genetic accident must also increase, since there is a higher probability that more dehydrons are actually wrapped by a single conserved residue (simply because there are more dehydrons!). It is possible that susceptibility hot spots are actually sites for oncogenic mutations, as my preliminary work reveals.
The emerging picture is that cancer is possibly a prize higher organisms must pay for their complexity.
September 3, 2003
We analyze the advanced mixing regime of the Rayleigh-Taylor (RT) incompressible turbulence in the small Atwood number Boussinesq approximation. The prime focus of our phenomenological approach is to resolve the temporal behavior and the small scale spatial correlations of velocity and temperature fields inside the mixing zone, which grows as $\propto t^2$. We show that the $``5/3"$-Kolmogorov scenario for velocity and temperature spectra is realized in three spatial dimensions with the viscous and dissipative scales decreasing in time, $\propto t^{-1/4}$. The Bolgiano-Obukhov scenario is shown to be valid in two dimensions with the viscous and dissipative scales growing, $\propto t^{1/8}$.
September 10, 2003
Vortex and current singularities in fluids and plasmas often grow from smooth initial conditions, and play a crucial role in dynamical processes involving vortex and magnetic reconnection. Reconnection of vorticity and magnetic field lines occur when topological invariants are broken due to the presence of small but finite dissipation. Although vorticity lines in fluids and magnetic field lines in plasmas have very different dynamics, vortex and magnetic reconnection phenomena have similar geometrical underpinnings. The geometrical sites where vortex and current singularities tend to appear are often similar. These are the sites where fast reconnection tends to occur. Although classical analytical models have tended to focus on steady reconnection, reconnection in nature is rarely steady. It is often impulsive or bursty, characterized not only by a fast growth rate, but a rapid change in the time-derivative of the growth rate. Recent computational developments (involving adaptive mesh refinement techniques) have enabled us to investigate vortex and current singularities and their effect on reconnection at high levels of resolution. We will report on recent analytical and computational results involving a variety of fluid and plasma configurations, and their implication for laboratory and astrophysical observations.
September 17, 2003
NOTICE: Seminar given in Room RI-480, same time
This talk describes an exciting new method for approaching two-dimensional problems with interesting geometry. The method is based upon old work by C. Loewner in which he describes how an ordinary differential equation can generate a continually lengthening curve in the complex plane. His evolution equation contains a real function of time, the "forcing", which determines the two-dimensional shape. Smooth forcings generate non-self-intersecting curves. Rough forcings generate shapes with singularities. If the forcing is the stochastic process of Brownian motion, with a parameter , κ which defines the strength of the forcing. For different values of , κ the ensemble of generated shapes depend upon κ. For different values of , κ the resulting ensembles are believed to be identical to the ensemble of random walks, self-avoiding walks, percolation, and the various shapes of critical clusters in critical phenomena.
This talk outlines some of our knowledge in this area, and describes a few exact solutions of the Loewner differential equation.
September 24, 2003
A piece of paper or a leaf flutters and tumbles down in a seemingly unpredictable manner. A casual observer might notice that while falling downward on average, A piece of paper or a leaf can rise momentarily as if picked up by a wind. To investigate how it elevates, we quantify the fluid force by solving the Navier-Stokes equations governing the flow around a falling rigid plate. By comparing the computed forces and torque against the predition of classical theory, we identify a lift mechanism for the center of mass elevation. The comparison further suggests an ODE model of a falling plate, which is somewhat different from those used in the literature. To check our numerical results, we compare them with experiments of falling aluminum strips in water with matching parameters. If time permits, I will discuss some of our recent progress in designing a three dimensional flexible wing driven by muscles on computer.
October 1, 2003
Verification and validation (V & V) tests of numerical methods and models are essential ingredients for establishing credibility in any numerical modeling effort. The strong connection between the ASCI/Alliances Flash Center and the DOE Laboratories enables close collaboration between theorists and experimentalists probing the basic physics of astrophysical events, providing a unique opportunity for validation. The Flash Center has established an ongoing, formal V & V effort for FLASH, a parallel, adaptive-mesh simulation code for the compressible, reactive flows found in many astrophysical settings. In this talk, I will present results of V & V tests of FLASH. The verification tests are designed to test and quantify the accuracy of the code. The two validation tests are meant to ensure that the simulations meaningfully describe the real world by carefully comparing the results of simulations and astrophysically-relevant laboratory experiments. The first experiment consists of a laser-driven shock propagating through a multi-layer target, a configuration similar to the shock propagating outward through a massive star in a core collapse supernova. The second experiment is a "classic" Rayleigh-Taylor fluid instability, where a heavy fluid is accelerated by a light fluid. Our simulations of the multi-layer targets showed good agreement with the experimental results, but our simulations of the Rayleigh-Taylor instability did not. I will discuss our findings and possible explanations for the disagreement.
October 8, 2003
The theory of mixing is based on concepts from dynamical systems theory, as established in the 1980's. In this talk I will present an extension of this theory to accomodate applications for control of mixing. First, I will present a prototypical control of mixing scenario where two maps on a torus are applied in periodic protocols. The problem is to determine protocol with maximal Kolmogorov-Sinai entropy. Then I will discuss a micromixing set-up, the Shear Superposition Micromixer, that was designed based on the ideas from the above theory of shear superposition for mixing and present need for additional theory that needs to be developed because of requirements on mixing. One step towards such theory for control of mixing is a "cost function", that allows for comparing different mixed states of concentrations evolving under nonlinear dynamics. We developed such a cost function, called the mix-norm. This norm is based on weak convergence and has nice properties with respect to the classical notion of mixing in ergodic theory. I will conclude with an application of the mix-norm to optimization of mixing in a micromixing device.
October 15, 2003
In this talk I will describe three recent studies of novel Marangoni flows, i.e. flows that are driven by tangential stresses that are produced by temperature, compositional, or electrical fields. The first two of these are flows driven or modified by the non-uniform in-situ production of surfactants by chemical reactions. Such surfactant gradients give rise to surface tension gradients which drive bulk flows. We study experimentally the effect of such reactions on viscous fingering in the tip-splitting regime, finding that Marangoni stresses result in wider fingers and a suppression of the tip-splitting instability. We then describe an amazing phenomena of spontaneous, self-sustained chemically driven oscillations at the tip of a drop suspended from the tip of a needle and connect this phenomena to the well-known tip-streaming in extensional flow near drops. Finally, we describe theory and experiment on the manipulation of tangential electrical stresses to drive chaotic advection in translating drops of dielectric liquids.
October 22, 2003
The fact that almost all neurons adapt implies that adaptation must be useful to the system in some way. Since the first observations of spiking neurons in the 20s, physiologists have speculated about the role of adaptation in neural information processing. Recent experiments formulate the issue more precisely: natural stimuli are drawn from a distribution that defines their context. Can we see evidence of adaptation to the stimulus context? In the fly visual system, we show that the motion sensitive neuron H1 uses an adaptive code that allows it to optimize its responses for maximal information transmission under conditions where the context of the stimulus changes constantly. The downside of such an adaptive code is the problem of ambiguity: in order to interpret the output appropriately, the system must also have information about the context. We show how this problem is resolved for H1 via a novel decoding strategy. Typical natural stimuli are characterized by long- tailed spatial and temporal distributions. We discuss potential mechanisms which may underlie adaptation on many timescales.
October 27-29, 2003
NOTICE: Due to this special series of talks, there will be no seminar in KPTC 213 on October 29.
Agent-based computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents with learning capabilities. This presentation will discuss the complexity of decentralized market economies, and the potential usefulness of ACE for the constructive study of decentralized market processes. As an illustrative application, attention will be focused on labor institutions in relation to market performance: specifically, on unemployment benefit programs. An ACE labor market will be presented, consisting of strategically interacting workers and employers who evolve their work-site behaviors over time. Experimental findings will be given regarding market performance in response to successive increases in the level of unemployment benefits. These findings will be compared with findings from a parallel labor market experiment conducted with human subjects. Extensive ACE research and teaching resources can be accessed on-line at http://www.econ.iastate.edu/tesfatsi/ace.htm
Agent-based computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents with learning capabilities. This presentation will focus on the development and use of computational laboratories for ACE research. The Trade Network Game (TNG) Lab will be used for concrete illustration. The TNG Lab is designed for the study of trade network formation among buyers, sellers, and dealers who repeatedly engage in risky trades and who evolve their trading strategies over time. The TNG Lab provides run-time visualization of network formation as well as run-time displays of profit outcomes for individual traders. Research papers, manuals, C++ source code, and an automatic installation program for the TNG Lab can be accessed on-line at http://www.econ.iastate.edu/tnghome.htm
Agent-based computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents with learning capabilities. This presentation will discuss the potential usefulness of ACE for electricity market design. Two applications will be discussed. The first application focuses on a short-run wholesale electricity market modeled as a double auction. The key issue addressed is the sensitivity of market performance to changes in market structure when wholesale traders evolve their bid/ask pricing strategies over time. The second application (in progress) focuses on the Wholesale Power Market Platform proposed by the Federal Energy Regulatory Commission in April 2003 for common adoption by U.S. wholesale electricity markets. The key issue addressed is the ability of this market design to sustain fair, efficient, and orderly market outcomes when profit-seeking market participants are free to evolve their pricing strategies over time. Resources related to ACE electricity research (readings, software, and pointers to individuals, groups, and websites) can be accessed on-line at http://www.econ.iastate.edu/tesfatsi/aelect.htm
November 5, 2003
Biocomplexity is the term that is becoming used to describe efforts to understand strongly-interacting dynamical systems with a biological, ecological or even social component. I provide a brief overview of why this field is not only interesting for physicists, but can benefit substantially from their participation. As a case study, I present my own work on geobiological pattern formation.There is increasing evidence that geological features can arise as bacteria interact with purely physical and chemical processes. I describe our on-going attempts to determine the origin of apparently scale-invariant terrace patterns that generically accompany travertine formation at carbonate hot springs throughout the world. Do these striking patterns arise because of the activity of the microbe population that is present in the spring water? The ability to distinguish both ancient and modern geological features that are biologically influenced from those that are purely abiotic in origin can potentially advance our understanding of the timing and pattern of evolution, and may even provide a tool with which to identify evidence for life on other planets.
Work performed in collaboration with: G. Bonheyo, J. Frias-Lopez, H. Garcia Martin, J. Veysey, B. Fouke. Work supported by the US National Science Foundation.
November 12, 2003
Various lines of evolutionary genetic theory suggest that the action of genes should evolve to become modular. In classical terms, this would amount to a tendency for gene action to become more additive across genes. The talk will suggest a mathematical framework for posing the question of whether genes evolve to act more independently or whether tighter interactions should form. The analysis will bear similarities to earlier general theorems on evolution of modifiers of gene action.
Tuesday, November 18, 2003, same time, KPTC 206
To finely disperse a liquid into a gas (i.e. atomise) is one of the most ubiquitous needs in human activities involving chemical/biochemical processes and energy conversion: ground transportation alone requires the atomisation of an estimated global flow rate of about 100 to 300 m3/s on earth. In liquid atomisation, a continuous supply of energy is "directed" to disrupt the bulk liquid and create small droplets of controllable size.I will highlight two current techniques for ultra-fine liquid atomisation, electrospraying and flow focusing. I will briefly discuss how close to the physical "limits" of liquid atomisation in the micro- and nano- scale can we get with these methods. More importantly, I show that when properly combined, the two techniques can impart a larger momentum to the liquid, resulting in smaller jet and droplet diameters. In addition, the gas stream of flow focusing would exert an important stabilization effect on the cone-like meniscus of electrospraying, and would "flush" the spray away from the liquid cone. This allows an enormous increase over the maximum liquid flow rate possible for a stable cone-jet with electrospray alone. Finally this combination may be made so simple that it can be scaled-up for real-world applications. Such a combination atomisation device is not only possible but also brings along additional, unexpected, and rather extraordinary gifts. I will present some of which we have discovered so far, but my belief is that there is an open, rich and deep new valley* for exploration.
*for parametrical optimisation.
December 3, 2003
Turbulence is the state of vortex fluid motions where the properties of the flow field (velocity, pressure, etc.) vary in time and space randomly. First recognized and even baptized by Leonardo da Vinci, turbulence has been studied more than a century by scientists and engineers, including the giants, Kolmogorov, Heisenberg, Taylor, Prandtl and von Kármán.Turbulence at very high Reynolds numbers (often called developed turbulence) was widely considered to be a happy province of the turbulence realm, as it was widely thought that two of its basic results are well-established and will enter, basically untouched, into a future pure self-contained theory of turbulence. These results are the von Kármán--Prandtl universal logarithmic law for wall-bounded turbulent shear flows, and Kolmogorov--Obukhov scaling laws for the local structure of developed turbulent flows.
In this lecture I will present and discuss basically the results obtained by A. J. Chorin, V. M. Prostokishin and myself during the decade 1991--2002, concerning steady wall-bounded turbulent shear flows where the average velocity varies only in the direction perpendicular to the wall. These flows are of basic fundamental and practical importance: flow in pipes is a common, familiar and useful example of such flows.
December 10, 2003
We are all aware of the potential for biological complexity implicit in the independent control of individual genes. Independently modulating the cellular concentration of each protein offers a nearly infinite number of steady-states. In turn, a change in the DNA encoding in even a single gene will affect the behavior of a cell over its remaining lifetime and will be transmitted to its progeny. However, much like people, the cells are defined by their environment and history as much as by their chromosomes. Cells are complex, unstable systems that are continuously responding to their surroundings. Importantly, the time scales of many cell responses are far faster (seconds) and/or slower (years) than characteristic times of gene expression changes or mutations (minutes to days). The answer to this paradox is that many transient and persistent cell responses are mediated by covalent chemical modifications of proteins already present in the cell. Most changes in gene expression are simply down-stream effects.Using a few examples under study in the Kron lab, we will examine protein modifications that underlie the "cognitive", "emotional" and "memory" states of individual cells. Even transient deregulation of protein modifications can lead to cell confusion and human disease. Not surprisingly, the mutations that underlie the malignancy of cancer cells often affect the proteins that modify other proteins. We will touch on recent developments in targeting such chemical modifications as treatments for cancer and other diseases.
January 7, 2004
In a turbulent highly conducting fluid, magnetic fields are amplified since the field lines are generally stretched by randomly moving fluid elements in which these lines are frozen. Such a mechanism of turbulent dynamo is expected to work in a variety of astrophysical systems (galaxy clusters, interstellar medium, stars, planets), is confirmed numerically, and is consistent with simple analytical models.Recently, there appeared the number of high-resolution numerical simulations of MHD turbulence with small magnetic Prandtl numbers [Pm=fluid viscosity/fluid resistivity], where magnetic fluctuations were not amplified. This revived old claims that dynamo does not exist in the Kolmogorov turbulence with Pm << 1. However, astrophysical observations show that magnetic fields are generated by turbulent motion rather effectively in planets and stars where magnetic Prandtl numbers are small (e.g., in the geo-dynamo, Pm=10^-5, in stars, Pm= 0.01). The talk will address this apparent contradiction.
MONDAY, January 12, 2004: MRSEC Seminar, KPTC 206, 12:30 p.m. (Partially sponsored by CAMP, MRSEC, and EFI Theory).
Given a large but finite region, filled with a medium which is a composite of conducting and insulating components, can current flow between two contacts attached to separate parts of the boundary? This is a problem in percolation. Above the percolation threshold $p_c$ current always flows, while below $p_c$ it never does so. But at $p_c$ there is a finite probability, between zero and one, of a connection, and this depends on the shape of the region.In quantum Hall systems, the value of the quantised conductance depends not just on whether there is a connection, but on the number of independent such ones.
These problems share the property of conformal invariance. In two dimensions, there are exact results for them. I shall present these, and discuss the variety of methods by which they have been obtained.
TUESDAY, January 13, 2004: KPTC 206, 1:30 p.m. (Partially sponsored by CAMP, MRSEC, and EFI Theory).
Schramm-Loewner evolution (SLE) describes the statistics of single random curves in 2d critical systems. It relates questions about these curves to simple problems in 1d Brownian motion. Many old and new results can be derived using these methods. I present a generalisation to $N$ curves. The corresponding 1d problem is Dyson's Brownian motion, which describes the statistics of the eigenvalues of random matrices. It is also related to the quantum Calogero-Sutherland hamiltonian. I show that this connection arises also in conformal field theory (and could have been discovered 20 years ago.) The values of bulk critical exponents of 2d systems are given by the spectrum of this hamiltonian.
January 21, 2004
We study the impact of a jet of a viscous fluid in a bath of the same liquid. We measure the radius of curvature of the liquid air-interface where the impact occurs. We show that it decreases exponentially with the capillary number. Above a threshold speed, capillary can not overtake this high confinement and a thin sheet of air is dragged into the bath by the jet, in a trumpet-like form. We measure the threshold speed for which a film of air is dragged into the pool and the thickness of the film.
January 28, 2004: LOCATION: RI L-112
Copepods are micro-crustaceans of 1 to 5 mm in length. They create feeding currents to find food, use hydro-dynamical disturbances to distinguish predators from mates, and 1.347x10exp21 of them populate the vast 3D environments of our fresh and marine waters. I will show (in short videos) results of 30 years of detailed observations of the interaction between these animals and their surrounding water.
February 4, 2004
February 18, 2004
The initial phase of sparking is determined by so-called streamers. These are weakly ionized channels during their growth period. The growth is characterized by a self-induced enhancement of the electric field at the tip of the discharge channel. Streamers propagate with velocities of the order of 1000 km/sec; recent ultrafast photography gives a new view on their dynamics. Streamer concepts are also being applied to recently discovered high altitude lightning, so-called red sprites.I will review recent observations and then explain the state of microscopic modelling, computations and theoretical concepts. Basically, already a single discharge channel has a multiscale structure with a thin ionization front surrounding a rather inert body. I will present computational results with adaptive grids, and I will discuss the properties of ionization fronts, moving boundary approximations for these fronts, and solutions of the moving boundary problem with conformal mapping methods. The result is the prediction that streamers in a sufficiently high potential can branch spontaneously due to a Laplacian instability as is also observed in computations. This quantitative prediction has to be confronted with phenomenological models for spark branching of the type of diffusion limited aggregation.
February 11, 2004
We study the placement of charged particles on a two-dimensional conductor. Particularly, we focus on the placement of N equal discrete charges in the asymptotic limit as N goes to infinity, for both the case of a smooth conductor and also the situation in which the conductor contains cusp-like points.This problem is closely related to diffusion limited aggregation (DLA), and to the two-dimensional motion of viscous fluids (Hele-Shaw). A similar problem has been originally introduced under the notion of "Fekete points". However, in that context, results about the asymptotic placement of the charges as well as the (first order) asymptotic energies have been derived only for domains bounded by analytic curves. In contrast, we are trying to study how non-analyticities of the conductor boundaries affect the charge placements and expansions of equilibrium energies in the number of charges.
Furthermore, systems with an intrinsic symmetry of the conductor show a breaking of this symmetry in the placement of the charges, depending on the number of charges and the local curvature of the boundary.
February 25, 2004
A major challenge in structural biology is to derive a quantitative understanding of the relationship between the structure of a protein and its function, and use this to extract general rules on protein structure-function relationships. While thousands of protein crystal structures have been determined, many proteins have been studied using mutagenesis, and computational approaches have been applied to functional aspects of proteins, this remains a central open problem in biochemistry.I will present work on the use of photoactive yellow protein (PYP) as a model system to identify general principles in protein structure-function relationships. PYP is a photoreceptor protein found in photosynthetic bacteria. Activation of PYP by blue light causes this protein to generate a transient signal within the bacterial cell. This is initiated by the photoisomerization of the covalently attached chromophore buried within PYP. The following findings will be discussed. (i) We have found that photoactivation of PYP results in its transient partial unfolding, challenging the notion that signal transduction only occurs between fully folded proteins. (ii) We have developed a model in which this transient unfolding event is caused by light-triggered proton transfer, which generates a buried charge within PYP that functions as an "electrostatic epicenter" for the "protein quake" that activates PYP. (iii) We found that removal of the chromophore from PYP causes its partial unfolding. This partially unfolded state catalyzed the covalent attachment of the chromophore to itself. This presents the second example in the PYP system of a biological function for a partially unfolded state, challenging the influential notion that only fully folded proteins are functionally active. (iv) We recently initiated a high-throughput biophysics approach to systematically probe structure-function relationships in PYP. Computational methods will be essential in analyzing the experimental data obtained in this project.
TUESDAY, March 2, 2004: IBD Seminar, Crerar Conference Room (Lower Level), 12:00 p.m. (Partially sponsored by the Burroughs-Wellcome Fund)
DNA chips are novel experimental tools that have revolutionized research in molecular biology and generated considerable excitement. A single chip allows simultaneous measurement of the level at which thousands of genes are expressed. A typical experiment uses a few tens of such chips, each devoted to one sample - such as material extracted from a tumor. Hence the results of such an experiment consist of a table, of several thousand rows (one for each gene) and 50 - 100 columns (one for each sample). Extracting relevant information from such a large, complex and noisy data set requires development of novel methods of analysis.This talk will provide a very basic introduction, with no prior knowledge of any biology assumed. I will explain what genes are, what is gene expression and how it is measured by DNA chips. I will also explain what is meant by clustering and sorting, and demonstrate how standard statistical methods and novel, unsupervised techniques are used to analyse data on various forms of cancer.
March 3, 2004, KPTC 206, 12:15 p.m. (Partially sponsored by the Burroughs-Wellcome Fund)
DNA chips are novel experimental tools that have revolutionized research in molecular biology and generated considerable excitement. A single chip allows simultaneous measurement of the level at which thousands of genes are expressed. A typical experiment uses a few tens of such chips, each devoted to one sample - such as material extracted from a tumor. Hence the results of such an experiment consist of a table, of several thousand rows (one for each gene) and 50 - 100 columns (one for each sample). Extracting relevant information from such a large, complex and noisy data set requires development of novel methods of analysis.In this talk I will briefly explain how gene expression is measured by DNA chips, and demonstrate how we combine standard statistical analysis with these novel unsupervised methods to mine expression data obtained from leukemia samples. If time permits, I will demonstrate how some intriguing design principles can be obtained from recent experiments on stem cells.
THURSDAY, March 4, 2004: RI 480, 1:30 p.m.
Shannon sampling is a special case of the general problem of reconstruction of a function from its values at a discrete set of points. The talk with deal with age-old algorithms for solving this problem and new estimates for their error and efficiency.
March 10, 2004
Glassy dynamics occur in a large variety of systems, such as supercooled liquids, foams and granular matter. They are characterized by an exponentially rapid increase of relaxation times, as a control parameter such as temperature or density in tuned, and by a non-exponential decay of time-dependent correlation functions indicating a broad distribution of time scales. In this talk, I will present an exact solution of a Landau model of an order-disorder transition with activated critical dynamics. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering trajectories rapidly diminishes as the ordered ground state is approached. This leads to an asymmetry in the effective transition rates, which results in a non-exponential relaxation of the order-parameter fluctuations and a Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass transition. I will discuss a lattice model where this class of critical dynamics is realized and I will argue that the Landau model provides a general framework for studying glassy dynamics in a variety of systems.
March 17, 2004
Liquids do not mix easily in microfluidic systems, which are being developed into "labs-on-a-chip" that promise revolutionary applications in biotechnology, chemistry and medicine. Recent studies have suggested that microfluidic stirring via chaotic advection can achieve the efficient mixing required in typical uses. For devices based on continuous flow through microchannels, strategies for inducing chaotic mixing by altering device geometries have been proposed. I will describe a general methodology for introducing chaotic mixing in discrete volume (microdroplet) systems, which allow miniaturization of many standard laboratory protocols that are difficult to realize with continuous flow. The mixing properties of the flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Complete three- dimensional mixing by chaotic advection requires destruction of all flow invariants. As an illustration of this idea, I will demonstrate that complete mixing can be obtained in a time-dependent flow produced by motion of a microdroplet along a two-dimensional path and describe the experiments that optically manipulate and mix microdroplets.
March 31, 2004
I will discuss theoretical models which are useful for understanding the properties of single polymer molecules under mechanical, hydrodynamical and electrical stress.1) If one pulls on a polymer, for example using an atomic-force-microscope (AFM), one obtains a characteristic force-extension profile. For small forces the fluctuation spectrum of the polymer is modified and the response is mostly entropic. For large forces bond lengths and bond angles change which leads to an enthalpic response. The elastic modulus of a wide class of different synthetic and biopolymers can be predicted from ab-initio quantum-chemical calculations and compares well with experimental data at large forces in the nano-Newton range.
2) Motion of a deformable polymer within a viscous medium gives rise to an intricate coupling of shape deformations and hydrodynamic interactions. As a result, uniformly driven polymers will usually align perpendicularly to the direction of the driving force, in agreement with birefringence measurements.
3) Charged polymers are also deformed by applying an electric field, due to their huge polarizability, which is an important factor in understanding the electrophoretic mobility of charged bio molecules. By performing dynamic simulations, the relation between the electrophoretic mobility and the the non-equilibrium perturbation of the polymer structure can be understood.
MONDAY, April 5, 2004, LASR Conference (eastside), 3:30 p.m.
Every couple of years, a celestial body impacts the earth with energy near that of the Hiroshima bomb. On much longer timescales, impacts will occur with the potential to destroy regions, or whole civilizations. This lecture will present an overview on efforts to define the impact threat, followed by a systematic development of the requirements to divert an object on an earth-impacting course. We then examine today's technologies for achieving perturbation magnitudes necessary to protect the planet.
TUESDAY, April 6, 2004, KPTC 206, 12 p.m.
By 1572 the last legitimate heir to the Inca crown had been executed, and many of the important shrines had been desecrated, or destroyed. A great deal of information on Inca social structure, ceremonial activity, and belief is lost. Still, through ethnohistoric accounts, and archaeological fieldwork, it is possible to piece together the sky watching practices of the Inca, and understand some of its use in organizing their empire. From such work we know that as children of the sun god, Inti, the Inca ruled their empire, Tawintinsuyu. This elite position was reinforced through ceremonies honoring the sun, and involving a system of solar markers around the horizon of Cuzco. The remains of such solar markers have now been found at Titicaca, giving flesh to early Spanish accounts. However, this archaeological find demonstrated that the system required the support of other observations. Important clues defining these supporting observations were then found at Machu Picchu.
April 7, 2004
In 1942, Jacques Monod discovered that E. coli bacteria can discriminate between glucose and lactose and decide to consume the glucose first. The talk will present a standard molecular biology description of how the E. coli cell makes this decision. The computational process involves sequence-specific DNA-binding proteins, protein phosphorylation, action of membrane proteins and soluble cytoplasmic enzymes, protein-protein interactions, small molecule messengers and the construction of highly specific nucleoprotein complexes. Because all compartments of the cell are involved in information processing, there is no Cartesian separation into dedicated "informational" and "operational" molecules. Because the DNA participates as a physical component of the nucleoprotein regulatory and transcriptional complexes, it is not simply a software "tape" in the sense of a Turing machine. Our inability to make basic Cartesian or Turing distinctions indicates that biological (i.e. cellular) computation follows a novel computing paradigm.
April 14, 2004
A brief review is given of how convective and stably stratified turbulence occurs in geophysical flows, especially boundary layers. General aspects of the steady/unsteady (plume/puff) eddy structure, as a function of thermal/momentum surface boundary conditions are described using results from lab and field experiments, theory and numerical simulations. These results are important for determining the levels of temperature and velocity fluctuations at the surfaces bounding the convection. In stably stratified turbulent shear layers, perturbation theory and DNS results show how the fluctuations are strongly distorted by the buoyancy forces in such a way as to reduce the transfer of energy from the shear to the turbulence-a more universal and different mechanism to the GI Taylor instability or LF Richardson energy damping mechanisms. Because of its local structure, stably stratified turbulence, except when it is very inhomogeneous, has certain general characteristics found in a variety of different types of flow, except in highly inhomogeneous layers when the results are rather unpredictable (with consequences for weather forecasts). Forecasts are also difficult when convective turbulence is perturbed by weak shear; so that the mean flow can be amplified. In the resulting mean profile jets tend to appear.
April 21, 2004, NOTE time and place: RI L-112 at 2 p.m.
April 28, 2004, BSLC 205 starting at 12:00 p.m.
The evolution of living organisms required developing special strategies for synthesizing complex molecules and creating order and asymmetrical distributions of molecules within their interior. Many of these operations are performed by nanometer-scale "molecular machines" that use chemical energy to drive unidirectional processes, produce linear motion and/or generate mechanical work. I will discuss the mechanism of kinesins, which are motor proteins that use ATP energy to move along microtubules. In humans, there are 45 different kinesin motor proteins that are involved in a myriad of different biological functions including organelle, protein, mRNA transport, mitosis/meiosis, and control of microtubule dynamics. We have used a combination of single molecule motility assays, cryo-electron microscopy, spectroscopy, x-ray crystallography and mutagenesis to identify a new type of mechanical amplification process for kinesin. Recently, we have tested our model by "watching" changes in the structure of an individual kinesin motor protein as it undergoes motility. This work, which involves a combination of protein engineering and low light level fluorescence microscopy, provides new insight into how chemical energy causes the step-wise motion of kinesin along its track.
A general review on kinesin (as well as another motor- myosin): Vale, R. D. and Milligan, R. A. 2000. The way things move: looking under the hood of molecular motor proteins. Science 288: 88-95.
June 9, 2004
Large ensembles of small particles display fascinating collective behavior when they acquire an electric charge and respond to competing long-range electromagnetic and short-range contact forces. We conduct experimental and theoretical studies of the dynamics of conducting microparticles in strong electric field in the air or in poorly conducting liquids. We show that granular media consisting of metallic microparticles immersed in a poorly conducting liquid in strong DC electric field self-assemble a rich variety of novel phases. These phases include static precipitate: periodic honeycombs and Wigner crystals; and novel dynamic condensate: toroidal vortices and pulsating rings. The observed structures are explained by the interplay between charged granular gas and electrohydrodynamic convective flows in the liquid. We developed continuum theory of self-assembly and pattern formation in this system. The theory is formulated in terms of two conservation laws for the densities of immobile particles (precipitate) and bouncing particles (granular gas) coupled to the Navier-Stokes equation for the liquid. This theory successfully reproduces correct topology of the phase diagram and primary patterns observed in the experiment: static crystals and honeycombs and dynamic pulsating rings and rotating multi-petal vortices.
June 16, 2004
Combinatorial enumeration problems arise naturally in many problems of statistical physics. The number of partitions of an integer is one such enumeration problem with a history dating back to Euler. Partitions of an integer is the number of ways a positive integer can be decomposed into sum of smaller parts. Depending on the dimension of the lattice on which these parts are arranged, the partitions are called linear partitions, plane partitions, solid partitions and so on. Very little is known about solid partitions and higher dimensions. In this talk I will present numerical results for the asymptotic behavior of solid partitions. A simple proof for the MacMahon formula for the plane partitions of an integer will also be discussed.
June 23, 2004
To manipulate suspensions of cells and other micron- sized particles in bioengineering or lab-on-a-chip applications, strong hydrodynamic forces on small scales are necessary. Ideally, these forces should both ensure rapid transport of the particles and be strong enough at well-defined locations to porate or rupture cell membranes in order to achieve transfection of large molecules such as drugs or DNA into the cell. We show that ultrasound is an efficient driving mechanism for such microfluidic flows, if the sound energy is focused onto small scales through oscillating microbubbles. The bubbles excite a streaming flow that can be used to aggregate, deform, and rupture lipid vesicles and cells, making it a promising tool for both membrane studies and drug delivery applications. When combining bubbles with passive flow elements, other modes of streaming are excited, allowing for directional microfluidic transport of cells and particles without microchannels. All observed flows are in quantitative agreement with Stokes flow singularity theory.
THURSDAY, July 1, 2004, KPTC 206 at 2:00 p.m.
The generation of a magnetic field by a flow of liquid sodium has been observed in recent experiments (Karlsruhe, Riga). We emphasize two very interesting features displayed by these experiments.We first understand these two observations and give the expected scaling law for the magnetic energy above dynamo threshold. We then consider magnetic fluctuations above dynamo threshold or in MHD turbulence and report a Kolmogorov type spectrum in the inertial range and 1/f noise at low frequency. Finally, we discuss the effect of turbulence and rotation on dynamo onset and saturation in flows without strong geometrical constraints.
- The observed dynamo threshold is in good agreement with the one computed from the mean flow alone, i. e. neglecting turbulent fluctuations although the kinematic Reynolds number is of order 105 to 106.
- On the contrary, the mean magnetic field measured above dynamo threshold is 1000 times larger than the one predicted from a laminar weakly nonlinear calculation.
June 30, 2004
Fluctuations of macroscopic quantities in systems at thermal equilibrium have well known properties. Much less is known for dissipative systems out of equilibrium. We first present several experimental or numerical results on a few examples: fluctuations of the total heat flux in turbulent convection, or of the power needed to drive a turbulent flow in a statistically stationnary regime, fluctuations of the kinetic energy or of the injected or dissipated power in a granular gas, etc. We then propose different methods to characterize these fluctuations and show that some of their statistical properties do not depend on the particular system under consideration.
July 7, 2004
July 14, 2004
Rather than discuss a particular computation, this talk will look at how the producers and consumers of scientific computation communicate, and how these interactions affect the scientific process, e.g. productivity, the quality of results, etc.We can roughly divide software used in research efforts into three groups. In the first group, researchers purchase or download software created by programmers with whom they will never communicate. This software may be very general productivity software like Microsoft Excel, or it may be intended for a very specific use, such as supporting instrumentation. In the second group, a single researcher (or possibly a very small group) writes his/her own software, seeking to produce a novel, computational result. The software is not written for anyone but that researcher (although it may come to be used by others). In the third group, the scientific program involves a larger group or community of researchers, and part of the research requires completion of a set of data and/or computation intensive tasks. In this case, the users and the programmers are not the same people, and communication becomes a critical factor for the atmosphere and success of the project.
After completing a physics PhD involving a fair amount of programming at the University of Chicago, my professional background has been in both custom business software development and database bioinformatics in an academic setting. Rather than bore you with endless details about my experiences, however, I hope that this talk will be interactive. I will present a set of ideas and topics, and then will solicit experiences from the audience for discussion, examining as a group the way we all work.
People who write research code for themselves, who write code for others or who have code written for them are encouraged to attend.
July 21, 2004
In 1979, Hofstadter introduced and briefly discussed a chaotic, recursively-defined function which he called Q:
Q(n) = Q(n-Q(n-1)) + Q(n-Q(n-2))
Over the past 25 years, a number of mathematicians have studied this function and a handful of variants of it, and though some statistical details about Q's type of chaos have been observed, no one has managed to prove a single fact about Q -- not even that it -is- a function! In my talk, I'll describe a new avenue of (mostly empirical) which looks at a family of variants of Q, and which borrows some ideas from other disciplines. It turns out that this family of functions, on the collective level, exhibits an amazing degree of regularity, and yet within the framework of that family-level regularity, there are very weird irregular patterns unlike any seen before. I'll discuss what is currently known and unknown about this new family of functions, presenting the ideas mainly through a series of computer-generated graphs which display the tantalizing eccentricities that have been recently uncovered.
July 28, 2004
It is often difficult to decide whether we can reliably model the behavior of a physical system with a particular program. I will discuss some of the possible applications of PDE-constrained optimization in such situations. There are interesting numerical analytic questions to be addressed. I will summarize some new, very positive, results in the thesis of Andrei Draganescu about the amount of work involved. However, it is not at all clear how to cast the questions we want to answer so that optimal control gives us valuable insight.
August 4, 2004
I investigate how the topology of a network affects its dynamical properties. To this end, I will study the nature of the phase transition from an ordered to a disordered state that occurs in a family of neural network models with noise. These models are closely related to the Majority Voter Model, where a ferromagnetic-like interaction prevails. Each member of the family is distinguished by the network topology, which is determined by the distribution of the number of incoming links. I will show that for homogeneous random topologies, the phase transition always belongs to the mean-field universality class. However, scale-free networks depart from this universality class in the sense that phase transition exponents ranging from 1/2 to infinity are obtained. Furthermore, the scale-free topology provides the first example of a phase transition at finite temperature in networks with infinite average connectivity.
August 11, 2004
Level set method uses a level set function, usually an approximate signed distance function, Phi, to represent the interface as the zero set of Phi. When Phi is advanced to the next time level by a transportation equation, its new zero level set will represent the new interface position. We update the level set function Phi forward in time and then backward to get another copy of the level set function, say Phi_1. Phi_1 and Phi should have been equal if there were no numerical error. Therefore Phi-Phi_1 provides us the information of error and this information can be used to compensate Phi before updating Phi forward again in time. One nice property is that it has the convenience of possibly improving the temporal and spatial order of an odd order scheme simultaneously. We found that when applying this idea to semi-Lagrangian schemes, e.g., CIR scheme (which has no CFL restriction, a nice feature for local refinement), the property is still valid (while MacCormack scheme having similar property may not be easily applied here). This technique coupled with a simple yet less diffusive redistancing technique produces a very efficient algorithm even for unstructured triangle meshes. Numerical results for interface movements with level set equation computed by the new methods will be presented in the talk. Also we would like show some interesting theoretical results for applying this idea to a general linear scheme.
September 1, 2004
September 8, 2004
September 15, 2004
September 22, 2004
September 29, 2004
October 6, 2004
TUESDAY, October 12, 2004: 12 p.m., Crerar Library, Lower Level Conference Room
October 13, 2004
October 20, 2004
October 27, 2004
November 3, 2004
November 10, 2004
November 17, 2004
December 1, 2004
December 8, 2004
January 12, 2005
January 19, 2005
February 2, 2005
February 9, 2005
TUESDAY, February 15, 2005: 12 p.m., Crerar Library, Lower Level Conference Room
February 16, 2005
February 23, 2005
In this talk, two examples that have been investigated with experiments or that have significant practical importance will be considered: vertically vibrated shallow granular layers and vibrated gas fluidized beds of cohesive fine powders. Oscillating shallow granular layers, where the interparticle interaction can be modeled as an instantaneous binary, frictional dissipative collision, exhibit various phenomena including the spatial pattern formation and the so called "horizontal Brazil-nut effect".
They will be discussed, together with the issues in modeling. The second problem examined is the gas fluidized bed of fine particles, often referred to as the powders, where the interstitial gas effects and interparticle forces such as cohesion play an important role. A particle dynamics-based hybrid model is used to study this system, and a multiscale computational method is used to facilitate the efficient computation. It will be shown how the vibration enables fluidizing highly cohesive powders, which are unable to get fluidized otherwise.
March 2, 2005
,
Faculty contact: Sidney Nagel, 
March 9, 2005
,
Faculty contact: Wendy Zhang,
March 30, 2005
,
Faculty contact: Leo Kadanoff,
April 6, 2005
,
Faculty contact: Wendy Zhang,
Since then, there has been much work searching for higher dimensional extensions of this result, in particular due to possible connections to high- temperature superconductivity. The clearest statement of the basic physical reasons to expect such an extension are due to Misguich et. al, who argued that any such system would either have long- range spin order, and hence have gapless spin wave excitations, or else would have a class of topological excitations with vanishing gap. Thus, showing this result in higher dimensions would connect directly to recent ideas on topological order in quantum systems. I will sketch my recent proof of this result, emphasizing connections to these basic physical ideas. In the process, I will derive various results about locality of correlation functions in these systems.
April 13, 2005
,
Faculty contact: Philippe Cluzel 
April 20, 2005
,
Faculty contact: Paul Wiegmann, 
TUESDAY, April 26, 2005: 12 p.m., Crerar Library, Lower Level Conference Room
,
Faculty contact: Aaron Dinner,
April 27, 2005
,
Faculty contact: Leo Kadanoff,
If there is time, I shall morph to a brief discussion of
"Strange Matter" --- a traveling museum exhibition that
highlights Materials Science. The exhibit was a partnership of
he Materials Research Society and Industry with funding through
NSF and a contracted museum design team.
May 4, 2005
,
Faculty contact: Leo Kadanoff,
May 11, 2005
,
Faculty contact: Wendy Zhang,
June 1, 2005
,
Faculty contact: Wendy Zhang,
June 8, 2005
,
Faculty contact: Leo Kadanoff,
The talk will combine a description of what is known and not know about ion channels, and their evolution; a description and some analysis of models; and some preliminary analysis of using data for the evolution of the sequences of voltage gated sodium and potassium channels in conjunction with the models. The great hope is to be able to draw conclusions that are not 'just so' stories.
June 15, 2005
,
Faculty contact: Leo Kadanoff, .
We know that the Euler and continuity equations can be derived from statistical descriptions of fluids. Correspondingly we might ask: What statistical description, if any, stands behind the Madelung and Bohm-Takabayasi equations?
Here we suggest a possible answer to such question in the form of an irreversible mapping in Fourier space with a single free parameter. We find a particular class of probability functions that give rise to the Schroedinger and Pauli equations for which the averages of physical quantities read like the postulates of quantum mechanics. This procedure seems to provide a statistical representation of quantum mechanics.
June 22, 2005
,
Faculty contact: Leo Kadanoff, .
June 29, 2005
,
Faculty contact: Leo Kadanoff,
July 6, 2005 (&)
We have developed a network view of the amino acid table in which every codon is a node and every edge is a mutation. We have used the measures this view generates to analyze the DNA sequences that start the process of affinity maturation in the immune reaction. The results of our analysis suggest three new ideas about selection: First, the traits of amino acids and the potential to change them are a meaningful signal for selection. Second, we found that while the DNA encoding B cell receptors has evolved to generate variable progeny under high rates of mutation, the different gene families differ in the extent to which they will risk their potential viability. Finally, the existence of a transition bias in mutations means that not all movements on the amino acid network are equal. Codons tend to mutate to codons that are a Transiton mutation away from them, dividing the amino acid network into Transition Neighborhoods.
July 13, 2005
,
Faculty contact:Wendy Zhang,
July 20, 2005
, Faculty contact: Wendy Zhang,
In selective withdrawal experiments, two immiscible fluids form a layered
system with a horizontal interface. Fluid is withdrawn from the top layer
through a straw suspended closely above the interface. Cohen et al. found in
their setup that steady state interfaces with sharp tips could be produced
even when the two fluid viscosities were almost matched. This is
surprising since the stress balancing mechanisms in the breakup and withdrawal
situation are closely related. Furthemore, at a certain flow rate the tips
undergo a topological transition into a steady spout state in which both
liquids are entrained simultaneously. We investigate the mechanisms of this
transition numerically in a simplified boundary integral model. In the tip
state, two lengthscales emerge naturally, the deflection of the interface and
the radius of the tip. We study the dependencies of these two lengthscales on
each other and on external flow parameters and on boundary conditions.
August 10, 2005
September 7, 2005 (&)
,
Faculty contact: Leo Kadanoff, .
As a test-bed for our approach we are using bacterial chemotaxis. /E.
coli /bacteria can sense their environment and use that information to control their flagellar motors and move closer to sources of nutrients.
To understand how a single /E. coli/ processes information we decomposed the chemotaxis pathway into simpler information processing units. We then modeled each unit analytically and/or numerically, and when possible tested model predictions with data obtained from measurements in single cells. Finally, we constructed a digital bacterium equipped with the necessary modules to perform chemotaxis: receptors, adaptation module, intracellular signal carriers (response regulator), motors and flagella. Digital chemotaxis assays consisting of more than 1000 independent digital cells swimming in a 3D environment reproduced experimental data from both single cells and bacterial populations.
September 21, 2005 (^)
,
Faculty contact: Wendy Zhang,
Experimental and computational studies point to the existence and importance of coherent structures. Waleffe's `Self-Sustaining Process' theory together with recent full Navier-Stokes computations of unstable traveling waves in plane Couette, Poiseuille, and pipe flows captures remarkably well qualitatively and quantitatively the turbulent structures recently observed in great detail in several 3-d PVI experiments.
However, turbulence itself does not occur on the steady solutions, but on
nearby ergodic attractors. We test the ``recurrent coherrent states''
description of turbulence on a Kuramoto-Sivashinsky model, deploying a new
variational method that yields a large number of numerical unstable
spatiotemporally periodic solutions. For a small but turbulent system, the
attracting set appears surprisingly thin. Its backbone are several Smale
horseshoe repellers, well approximated by local return maps, each with
good symbolic dynamics.
September 28, 2005
,
Faculty contact: Leo Kadanoff,
October 5 , 2005
,
Faculty contact: Wendy Zhang,
(1) the continusously breaking, rearranging and growing actin scaffolding that gives a cell mechanical strength while it moves. Our work focuses on gradients in actin network properties that play an important role at the leading edge of a moving cell.
(2) the deformations of a model cell membrane to local forcing. Shape instabilities and phase separation characterize the membrane response.
October 12, 2005
,
Faculty contact: Leo Kadanoff,
October 19, 2005(^)
,
Faculty contact: Wendy Zhang,
An important advantage of thermal spray is the flexibility with respect to feed materials (most metals and ceramics), a single step material consolidation, limited substrate heating, and ability to process under ambient conditions. These benefits have resulted in a highly versatile and flexible process which has translated to a rapidly growing industry (estimated $4B worldwide). However, complexities associated with far-from- equilibrium treatment of materials involving two rapid phase change operations (melting and solidification) have challenged the fundamental understanding of the process. In the same vein, the extremes that the materials are subjected also offer exciting opportunities for exploratory materials research.
This presentation will provide a brief overview of the process and experimental measurements for splat formation on cold and "warm"
surfaces, under low pressure conditions, and at various impact velocities.
FIG. CAPTION: Top view micrograph of Zirconia splats formed on cold (A) and warm (B) stainless steel substrates displaying elimination of fragmentation in the latter case. Both were processed under identical process conditions under ambient environments. Similar phenonmena has been observed for wide ranging combinations of droplets and substrates.
October 26, 2005 (^)
,
Faculty contact: Leo Kadanoff,
November 2, 2005
,
Faculty contact: Leo Kadanoff,
November 9, 2005 (^)
,
Faculty contact: Wendy Zhang,
November 16, 2005 (^)
,
Faculty contact: Wendy Zhang,
(i) Ink jet printing
Ink-jet printing is considered as the hitherto most successful application of microfluidics. A notorious problem in piezo-acoustic ink-jet systems is the formation of air bubbles during operation. They seriously disturb the acoustics and can cause the droplet formation to stop. We could show that the air-bubbles are entrained at the nozzle and then grow by rectified diffusion. Both high-speed bubble visualizations and numerical results are presented.
(ii) Bubble nucleation
Bubble nucleation at surfaces is a poorly understood phenomenon. We did visualization experiments at structured hydrophobic surfaces and compared the results with model calculations, in particular focusing on bubble-bubble interactions. It is demonstrated that in the many bubble case the bubble collapse is delayed due to shielding effects.
(iii) Surface nanobubbles
It is a more than 200 year old dogma that fluid flowing along a solid wall does not ``slip'', i.e., it sticks to the boundary. On a macroscale this assumption seems to work extremely well. However, recently, a number of micro- and nano-fluidics experiments and simulations have shed increasing doubts on the dogma, because they show strong indications of partial slip. It has been suggested by de Gennes and others that the observed slip could be explained by the presence of surface nanobubbles. We performed controlled surface force atomic force microscope (AFM) studies for different surface materials and liquid conditions, in order to clarify whether the structures seen in the AFM experiments are indeed consistent with an interpretation as ``nanobubbles''. We have also performed molecular dynamics simulations in order to find out why nanobubbles do not dissolve.
The work is done in collaboration with Jos de Jong, Michel Versluis, Hans Reinten and colleagues from Oce (ink-jet printing), Nicolas Bremond, Manish Arora, and C.D. Ohl (cavitation), Stephan Dammer, S. Yang, and Harald Zandvliet and colleagues (surface nanobubbles).
November 30, 2005 (^)
, Faculty contact: Wendy Zhang,
December 7, 2005
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Faculty contact: Leo Kadanoff,
Brunet E, Derrida B Shift in the velocity of a front due to a cutoff Phys. Rev. E 56, 2597 (1997) Effect of microscopic noise on front propagation J. Stat. Phys. 103, 269 (2001)
Brunet E., Derrida B., A.H. Mueller Munier S. A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts preprint 2005
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Cheng Chin,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Todd Dupont,
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Faculty contact: Paul Wiegmann,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
Wendy Zhang,
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Faculty contact: Leo Kadanoff,
Wendy Zhang,
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Faculty contact: Leo Kadanoff,
Wendy Zhang,
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Faculty contact: Leo Kadanoff,
Wendy Zhang,
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Faculty contact: Leo Kadanoff,
Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Tom Witten,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Rustem Ismagilov,
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Faculty contact: Wendy Zhang,
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Faculty contact: Sidney Nagel,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Ka Yee Lee,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Thomas Rosenbaum,
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Faculty contact: Paul Wiegmann,
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Faculty contact: Sidney Nagel,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Robert Fisher,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Daniel Margoliash,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Ridgway Scott,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Wendy Zhang,
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Faculty contact: Wendy Zhang,
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Faculty contact: Tom Witten,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,
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Faculty contact: Leo Kadanoff,