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Statistical Mechanics Conference

105th Statistical Mechanics Conference

Sunday, May 08, 2011 at 08:00am -

105th Statistical Mechanics Conference: Presentations  |  Program   |  Short Talks

Invited Talk Titles & Abstracts

 

(Asterik [*] identifies speaker. Affiliation listed applies to speaker)

  • Speaker: Michael Aizenman, Princeton University
    Coauthor(s): S. Warzel
    Title: Extended states in a Lifshitz tail regime for Random Operators on Trees
    Abstract: TBA

  • Speaker: Charles Austen Angell, Arizona State University
    Title: Supercooled Water as the Rosetta stone for the "strong" vs "fragile" glassformer problem
    Abstract: Water is famous for its anomalies, seen most clearly in the supercooled liquid state. We noted1 that the rate at which liquids lost their entropy of fusion, leading to the Kauzmann Paradox in the case of glassforming liquids, is a maximum in the case of water. This and other properties made water the most "fragile" of liquids, by thermodynamic criteria. But a parallel examination of water near its glass transition temperature (Tg) revealed that, in this lower temperature range, water is the "strongest" of liquids - even stronger than silica.. Here we will argue, using experimental data and analogies, that the static correlation length for various fluctuations that play a critical role in water's behavior, reverses direction between these two extremes , and then show how this implies that strong liquids go into the glass transition in the face of a correlation length that decreases as the transition is approached. Only for fragile liquids does an increasing static correlation length drive the glass transition, and this length relates to enthalpy fluctuations, not density fluctuations - which behave oppositely. In this phenomenology, water serves as the Rosetta stone, speaking the language of strong liquids at low temperatures and that of fragile liquids at high temperatures. It leads us to demonstrate directly that a high temperature Widom line crossing that determines the behavior of the archetypal glassformer SiO2, is the consequence of a liquid-liquid critical point existing at high pressures (~5 GPa) and lower temperatures for this substance.

  • Speaker: Mustansir Barma, Tata Institute of Fundamental Research, Mumbai
    Coauthor(s): H. Sachdeva and M. Rao
    Title: Transport in a Multispecies Model with Interconversion
    Abstract: Motivated by studies of molecular transport through the Golgi apparatus in cells, we study a multispecies model with boundary injection of one species. The moves include stochastic interconversion between species, coagulation, and driven, diffusive movement of particles, either one at a time or together as a stack. Based on analysis of equations for the current and numerical simulations it is shown that the system exhibits several interesting phases, including a 'growing' phase in which the mass grows indefinitely in time in one spatial region, coexisting with a region with a steady value of the mean mass.

  • Speaker: Cedric Bernardin, Ecole Normale Superieure
    Title: Dynamical phase transition for a coagulation-fragmentation process
    Abstract: TBA

  • Speaker: David Ceperley, University of Illinois Urbana-Champaign
    Title: Ferromagnetism amongst cold atoms
    Abstract: TBA

  • Speaker: David Chandler, University of California, Berkeley
    Coauthor(s): D.T. Limmer
    Title: The putative supercooled liquid-liquid phase transition is actually the crystal-liquid transition in atomistic models of water
    Abstract: Polyamorphism of liquid matter (i.e., more than one liquid phase) is a theoretical possibility, and in liquid mixtures, for example, it is a well-known reality. But does such behavior exist in pure liquid water and similar materials? Some have said yes, proposing that if nucleation of ice could be avoided, supercooled water would exhibit a phase transition between two distinct liquid phases, one of a higher density than the other. With numerical simulation, this idea can be tested for atomistic models of water. In particular, multiple order parameters can be controlled, where one is density and another distinguishes crystal from liquid. We have carried out such simulations to compute free energy surfaces for two atomistic models of water. For a range of temperatures and pressures, separate free energy basins for liquid and crystal are found, and conditions of phase coexistence between these phases are demonstrated. But at no temperatures and pressures is there more than a single liquid basin, even at conditions where amorphous behavior is unstable with respect to the crystal. This result excludes the possibility of the proposed liquid-liquid phase transition for the models we have studied. Further, behaviors that others have attributed to a liquid-liquid transition in water and related systems with these same models are in fact reflections of transitions between liquid and crystal.

  • Speaker: Simona Cocco, Institute for Advanced Study
    Title: Inference of interactions from correlations with the Ising model
    Abstract: Understanding the correlated activity of a population of variables is important problem in several disciplines, such as physics, biology,sociology, finance ... The Ising model provides a natural framework to extract interactions from correlations. In this talk I will present a procedure to infer interactions, based on a cluster expansion of the Ising model entropy at fixed magnetizations and correlations. I will discuss the performance of the procedure and present applications to neurobiological data (multi-electrode recordings of the retina).

  • Speaker: Piers Coleman, Rutgers University
    Title: Strange metals, quantum criticality and the incredible story of YbAlB_6
    Abstract: TBA

  • Speaker: Rafael de la Llave, University of Texas at Austin
    Title: Quasiperidic solutions in lattice dynamical systems
    Abstract: We present some recent progress in the study of solutions of lattice dynamical systems which are quasi-periodic either in space or in time. We wil pay special attention to the problems of breakdown of smooth families of equilibria (the so-called Aubry transition or analyticity breakdown). In models of deposition, this transition is the transition between the free motion and pinning. We will discuss rigorous methods (Kolmogorov-Arnold-Moser theory, Aubry-Mather theory) as well as numerical explorations.
    Joint work with T.Blass, R. Calleja, E. Fontich, A. Luque, Y. Sire, X. Su, E. Valdinoci. Supported by National Science Foundation andi Texas Coordinating Board.

  • Speaker: Ken Dill, University of California, San Francisco
    Title: Using Maximum Caliber to model single- and few-particle trajectories
    Abstract: We are interested in dynamical trajectories in few-particle systems, including the diffusion of colloidal particles in microfluidics devices, the hopping of single particles between two energy wells, and an engineered genetic toggle switch in biology. We use the Maximum Caliber approach to dynamics, akin to the Maximum Entropy approach to equilibrium. Certain measured first-moments of rate quantities are enforced by Lagrange multipliers in a method that otherwise maximizes a path entropy, to determine rate distributions and higher moments. We compare against experiments.

  • Speaker: Weinan E, Princeton University
    Title: Metastability, rare events and spectral geometry
    Abstract: I will give a brief overview of the current issues in the study of rare transition events between metastable states. I will then discuss recent results on the spectral geometry of supersymmetric Fokker-Planck operators as well as the gentlest ascent dynamics (GAD).

  • Speaker: Paul Falkowski, Rutgers University
    Title: The evolution of chirality in nature
    Abstract: TBA

  • Speaker: Roberto Fernandez, Utrecht University
    Title:Convergence of cluster expansions: recent approaches and applications
    Abstract: The convergence of cluster expansions for hard core systems has been recently the subject of renewed scrutiny. This led both to a new convergence criteria and to the rediscovery or a long forgotten result. The talk will review new summability approaches and their consequences for a number of applications (polymer models, hard sphere gases, zeroes of chromatic polynomials, the Lovasz Lemma, entropy of hidden Markov chains).

  • Speaker: Patrik A. Ferrari, Universität Bonn
    Title: From interacting particle systems to random matrices
    Abstract: In the last decade non-Gaussian distributions discovered in random matrices were proven to describe limit laws of fluctuations in physically unrelated models, like the last passage percolation, the asymmetric exclusion process or stochastic growth models in the KPZ class. Similarly, the extension to joint distribution has lead to the discovery of new universal limit processes. I will present some aspects of these developments by focusing on the asymmetric exclusion process.

  • Speaker: Rupert Frank, Princeton University
    Title: How much energy does it cost to make a hole in the Fermi Sea?
    Abstract: The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they both can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation. Joint work with M. Lewin, E. Lieb and R. Seiringer. Phys. Rev Letters.

  • Speaker: Nigel Goldenfeld, University of Illinois at Urbana-Champaign
    Title: The statistical mechanics of hallucinations and the evolution of the visual cortex
    Abstract: In the normal state of vision, neural excitation patterns are driven by external stimuli. However, accepted models of the visual cortex bear formal similarities to non-Hermitian field theories describing spatially-extended ecosystems with activation and inhibition. As such, they are subject to fluctuations which, we show, generically give rise to spatial patterns of neural excitation that would be perceived as hallucinations, masking the true external stimuli. How is this devastating failure mode finessed by the visual cortex? We analyze the phase diagram of the visual cortex model as a function of its long-range connectivity, and show that the neuronal connections in the visual cortex have evolved precisely the global architecture necessary to mitigate the failure mode: sparse long-range inhibition. Our results imply that sparse long-range inhibition plays a previously unrecognized role in stabilizing the normal vision state, and account for the observed regularity of geometric visual hallucinations.
    Work performed in collaboration with T. Butler, M. Benayoun, E. Wallace, Wim van Drongelen and Jack Cowan

  • Speaker: Tim Halpin-Healy, Barnard College, Columbia University
    Title: 25 Years of KPZ...
    Abstract: Driven lattice gases, kinetic roughening phenomena,& directed polymers in random media constitute the sacred triumvirate of KPZ. We focus on the latter topics, highlighting select historical events, and discussing theoretical and expt'l advances of the recent year.

  • Speaker: John Imbrie, University of Virginia
    Title: A Phase-Space Model for Pleistocene Ice Volume
    Abstract: It has been known for 35 years that the cycles of major glaciations in the last 1-2 million years are linked to variations in the Earth's orbital parameters--axial tilt and precession, and eccentricity. However, the nature of the link is still a puzzle because of the difficulty in understanding the appearance and disappearance of 100,000-year cycles. Statistical analysis of the climate record in phase space leads to a pair of evolution equations whose solutions simulate the major features of the record quite well. This leads to an improved understanding of the nonlinear phenomena responsible for ice-age cycles.

  • Speaker: Chris Jarzynski, University of Maryland, College Park
    Coauthor: Suri Vaikuntanathan
    Title: Modeling Maxwell's demon: work, information, and the second law of thermodynamics
    Abstract: Following recent work by Marathe and Parrondo [Phys Rev Lett 104, 245704 (2010)], we construct a classical Hamiltonian system whose energy is reduced during the adiabatic cycling of external parameters, when initial conditions are sampled microcanonically. Combining our system with a device that measures its energy, we obtain a procedure during which energy is extracted from a heat bath and converted to work, in a cyclic manner, in apparent violation of the second law of thermodynamics. This paradox is resolved by deriving an explicit relationship between the average work delivered during one cycle of operation, and the average information gained when measuring the system's energy.

  • Speaker: K. Koga, Joseph Indekeu* and B. Widom, Universiteit Leuven
    Coauthor(s): Kenichiro Koga and Benjamin Widom
    Title: Wetting transitions of infinite order in a mean-field density-functional theory
    Abstract: We consider a fairly standard mean-field density-functional model for three-phase equilibria and wetting. The model features two densities and two control parameters, one of which is related to order parameter asymmetry or spatial anisotropy. The global wetting phase diagram in the space of these two parameters features first-order, second-order, continuously-varying-order and infinite-order wetting transitions. We speculate that varying the spatial anisotropy of the magnetic interaction in ferromagnets with cubic anisotropy might well lead the way towards an experimental realization of infinite-order wetting.

  • Speaker: Harry Kojima, Rutgers University
    Title: Dynamics and Hysteresis in the Phenomena of Supersolid Helium-4
    Abstract: TBA

  • Speaker: T. Kuna, Reading University
    Coauthors: Yu. Kondratiev and N. Ohlerich
    Title: Absence of phase transition for a special class of potentials
    Abstract: We consider a Glauber type dynamics with Gibbs measures as irreversible distribution and derive a spectral gap and hence exponential ergodicity in the thermodynamic limit. We define a special class of potentials with non-trivial attractive part and show that there exists temperatures for which no phase transition occurs for any value of the chemical potential.

  • Speaker: Joachim Krug, University of Cologne
    Title: Statistical topography of fitness landscapes
    Abstract: Fitness is a measure for the reproductive ability of an organism, which can be viewed (at least indirectly) as a function of its genotype. Representing genotypes by binary sequences of symbols indicating the presence or absence of a given mutation, a fitness landscape is formally equivalent to the energy landscape of a spin model. In a remarkable recent development, experimental fitness data involving multiple interacting mutations are now becoming available, which motivate a fresh look at random, spin-glass-like fitness landscape models. The talk will focus in particular on the statistics of accessible evolutionary pathways, defined here as paths of single mutations connecting two genotypes along which fitness increases in each step. The talk is based on joint work with Jasper Franke and Arjan de Visser.

  • Speaker: Erik Luijten, Northwestern University
    Title: Self-assembly of anisotropic particles
    Abstract: I will describe the aggregation of anisotropic building blocks, with an emphasis on (1) spherical "Janus" colloids and (2) tetrapod-shaped colloids in the presence of charged nanoparticles.In addition, I will introduce a general method that greatly accelerates the simulation of mixtures of anisotropic components.
    1. Q. Chen, J.K. Whitmer, S. Jiang, S.C. Bae, E. Luijten and S. Granick, Science 331, 199-202 (2011).
    2. D. Sinkovits and E. Luijten, "Nanoparticle-Controlled Aggregation of Colloidal Tetrapods," submitted.
  • Speaker: Carlangelo Liverani, Universitá degli Studi di Roma "Tor Vergata"
    Title: Fourier law and the weak coupling limit
    Abstract: I consider lattices of weakly interacting Hamiltonian systems. In the limit of vanishing interactions one can show that the systems are essentially in local equilibrium and hence one can deduce, in the appropriate time scale, an autonomous equation for the evolution of the energies alone. One can then try to study such an equation to deduce the Fourier law or the heat equation (works in collaboration with S.Olla and D. Dolgopyat).

  • Speaker: Christian Maes*, K. Netocny and B.Wynants, Institute for Theoretical Physics-Belgium
    Coauthor(s): K. Netocny and B. Wynants
    Title: Monotone return to steady nonequilibrium
    Abstract: I will discuss a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. It measures an excess in dynamical activity rates. The monotone return for a wide range of steady nonequilibra is in contrast with the behavior of approximate Lyapunov functions based on entropy production that far from equilibrium often exhibit temporal oscillations. The proof of monotone behavior works under two conditions: (1) the initial distribution is close enough to stationarity, or equivalently for our context, we look at large times, and (2) a certain spectral sector-condition equivalent to "normal" linear-response behavior is satisfied. The deeper reason for its monotone behavior is that our Lyapunov function is the dynamical fluctuation functional for the occupation times.

  • Speaker: Peter Ortoleva, Indiana University
    Title: Multiscale Theory of Classical and Quantum Nanosystems
    Abstract: Systems from viruses to graphene nanoribbons evolve via the coupling of processes across scales in space and time. Their multiscale character presents a challenge to traditional computational approaches. We present theoretical and computational methods for understanding and simulating these systems. The theory starts with a basic N-particle formulation (i.e., the Schrödinger or classical Liouville equation) and yields equations for the evolution of order parameters characterizing long-time, nanometer-scale dynamics. In the classical case the result is a Smoluchowski or Fokker-Plank equation and algorithm for computing all factors in them. This framework has been implemented as the SimNanoWorldTM software and demonstrated for viruses and RNA, and in applications in computer-aided vaccine design. In the quantum case, coarse-grained wave equations are obtained. Several universality classes of coarse-grained wave equations are obtained that describe the long space-time dynamics of quasi-particles with modified masses and interactions, or collective modes with bosonic character. A new algorithm for efficient quantum many-particle simulations is discussed.

  • Speaker: Leonid Pastur, B.Verkin Institute for Low Temperature Physics and Engineering
    Title: Non-Gaussian Laws of Fluctuation for Spectral Statistics of Random Matrices
    Abstract: We consider spectral statistics of several most studied ensembles of hermitian random matrices. First we show that despite that the analog of the Law of Large Numbers is practically always valid for them as the size of matrices tends to infinity, the Central Limit Theorem is not always valid the linear eigenvalue statistics of hermitian Matrix Models. This is because of the strong correlations between eigenvalues of random matrices, resulting in the boundedness of the variance of linear eigenvalue statistics. Then we consider another class of statistics, the matrix entries of regular functions of random matrices. In this case the variance is of the order of matrix size, as for the sum of i.i.d. random variables, however the Central Limit Theorem is valid for the classical ensembles (Gaussian, classical groups, etc) and is replaced by another limiting law for the general Wigner Ensembles.

  • Speaker: John D. Reppy, Cornell University
    Title: Is Supersolid Superfluid?
    Abstract: Thirty-five years lapsed between the early predictions of a supersolid state of solid 4He by Chester (1968), Andreev and Lifshitz (1969), and Leggett (1970) and the surprising discovery of experimental evidence for its existence. Eunsoeng Kim and Moses Chan in 2004 conducted a series of torsional oscillator experiments with solid 4He and discovered an anomalous unexpected decrease in the period of the oscillator at temperatures below 250 mK. They interpreted this decrease in oscillator period as a result of a superfluid-like decoupling of a fraction of the solid helium moment of inertia from the motion of the oscillator. This discovery generated a flurry of experimental and theoretical interest that remains unabated to this day. The aim of the work presented here is to examine the basic nature of the supersolid phenomenon. Is it really a manifestation of a Bose-condensed superfluid-like state of solid 4He or not? The most recent experiments1 have produced more surprises that require a rethinking of our concept of the supersolid phenomenon in solid 4He.
    1) Phys. Rev. Lett. 104, 255301 (2010).

  • Speaker: Luc Rey-Bellet, University of Massachusetts
    Title: Game theory and statistical mechanics
    Abstract: We discuss some of the connections between evolutionary games and (nonequilibrium) statistical mechanics.

  • Speaker: Peter Sarnak, Princeton University
    Title: Zeros and nodal lines of modular forms
    Abstract: We present some results concerning the behaviour of these zeros in the large weight or eigenvalue limit (ie semi-classical limit).Apparently these behave like zeros of random real projective curves of large degree, which in turn might be related to certain percolation models (Bogomolny-Schmit).

  • Speaker: Michael Shelley, Courant Institute of Mathematical Sciences
    Title: Cytoplasmic pulling and pronuclear migration
    Abstract: TBA

  • Speaker: Yakov Sinai, Princeton University
    Title: Bifurcations in solutions of the 2-dim Navier-Stokes System
    Abstract: In our joint paper with Dong Li we show several bifurcations in solutions of the NSS which can be interpreted as dynamics of viscous vortices.

  • Speaker: Alexander Soshnikov, University of California, Davis
    Title: Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices
    Abstract: TBA

  • Speaker: Roderich Tumulka, Rutgers University
    Title: The general reason for approach to thermal equilibrium of macroscopic quantum systems
    Abstract: Consider a macroscopic quantum system (say, 1023 particles) in a bounded volume. People disagree on what it means for such a system to be in thermal equilibrium. I will describe two views: According to the "ensemblist" view, the system has to be in the mixed state (1/Z) exp(-beta H) for some beta in order to be in equilibrium. According to the "individualist" view, in contrast, some pure states correspond to equilibrium and others do not. The two views also disagree about what it means to approach equilibrium: According to the ensemblist, the density matrix rho_t has to converge to (1/Z) exp(-beta H) as t tends to infinity. For this to happen, the system must be coupled to an infinitely large heat bath. According to the individualist, the system may well be isolated and will reach equilibrium when its pure state enters the appropriate subset of Hilbert space. I will advocate the individualist view and present results about when approach to equilibrium in the individualist sense occurs. One result provides a condition on the Hamiltonian of an isolated system that is sufficient so that for every initial pure state from the "micro-canonical subspace," the subspace of Hilbert space corresponding to a narrow energy interval, the system will spend most of the time in the long run in equilibrium. Another result says that most Hamiltonians satisfy this sufficient condition. I suggest that this is the general reason for approach to equilibrium. Joint work with S. Goldstein, J. L. Lebowitz, C. Mastrodonato, and N. Zanghi.

  • Speaker: Jin Wang, University of New York at Stony Brook
    Title: Landscape and Flux Framework for Non-Equilibrium Dynamical Systems and Networks
    Abstract: Biological rhythms widely exist in living organisms, such as membrane potential oscillations, cardiac rhythms, calcium oscillations, glycolytic oscillations, cell cycles and circadian clocks [1]. In the cells, there are finite numbers of molecules (typical on the order of several hundreds). So the intrinsic statistical fluctuations from finite number of molecules, usually not encountered in the bulk due to the large number averaging, can be significant. On the other hand, the fluctuations from highly dynamical and inhomogeneous environments of cell interior provide the source of the external noise. Yet, the biological oscillations can sustain for long time. Therefore it is important to investigate how the rhythms robustly function against the stochastic fluctuations. Click here to see full abstract.

  • Speaker: Wei-min Wang, Universite Paris-Sud 11
    Title: Supercritical NLS and spectral gap
    Abstract: TBA

  • Speaker: John Weeks* and M. Ranganathan, University of Maryland
    Coauthor(s): M. Ranganathan, Indian Institute of Technology
    Title: Impurity-induced step dynamics in vapor and solution growth
    Abstract: Impurities that impede the motion of surface steps typically produce step-bunching instabilities during vapor growth, and the slower-moving step bunches reduce the crystal growth rate. However DeYoreo, et. al [1] showed that during solution growth of KDP crystals impurities can induce dramatically different behavior. In particular under appropriate conditions as the driving force is increased, large coherent bunches of steps called "supersteps" emerge and begin to move and dominate the subsequent crystal growth.
    We describe a new and general model of impurity effects during crystal growth that can explain these and other regimes. Impurities at step edges reduce the local driving force and can induce step bunching, initially slowing down growth in all regimes. However, the subsequent behavior can be very different in vapor and solution growth because of the different mechanisms of mass transport. Unlike vapor growth, in solution growth the attachment rate at a step is essentially independent of the terrace width in front. This allows a coherent bunch to stay together and move at large driving forces and we argue this is the key feature needed to understand the experiments of DeYoreo et. al.
    This work was supported by the NSF-MRSEC at the University of Maryland, DMR 0520471.
    References: [1] T. N. Thomas,T. A. Land, W. H. Casey, and J. J. DeYoreo, "Emergence of supersteps on KH2PO4 crystal surfaces", Phys. Rev. Lett.92, 216103/1-4 (2004).

  • Speaker: Michael Weinstein, Columbia University
    Title: Engineering Long Lived States and the Emergence of Periodic Structure
    Abstract: TBA

PRESENTATIONS OF TALKS GIVEN AT THE 105th STATISTICAL MECHANICS CONFERENCE

 

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