Previous Talks: 2002
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.
...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 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.
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 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.
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.
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?
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.
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.
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.
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.
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
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.
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.
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.
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)
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.
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.
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.
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.
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/
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.
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.
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.
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?
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.
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.
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?
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.
Non-equilibrium flow systems often organize themselves into various interesting structures, just like the equilibrium systems do. An example is Turbulent Rayleigh-BÈnard 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.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.