Statistical Mechanics Conference
Welcome Letter
The 131st Statistical Mechanics Conference
Guests of Honor: Eric Carlen, Eduardo Fradkin, Sid Redner
Dear Colleague:
Welcome!
I hope that you will find the meeting pleasant and stimulating and that you will forgive the unavoidable (and avoidable) inconveniences.
- SHORT TALK SPEAKERS IN SESSION A AND B: THESE ARE 5 MINUTE BLACKBOARD TALKS INCLULDING QUESTIONS. THE BEST THING YOU CAN DO IN THAT TIME IS GIVE AN ABSTRACT OF YOUR TALK WITHOUT EQUATIONS. Please erase the blackboard when you are done with your talk.
- Please put on a name tag so others may know who you are.
- The Journal of Statistical Physics is looking for good papers in all areas of statistical mechanics. The website for the journal is http://springerlink.com/ Springer is generously sponsoring the cocktail hour and concert on Sunday.
- You are invited to participate in the session on human rights and social responsibilities of scientists, on Monday. If you wish to contribute to the Committee of Concerned Scientists, we shall be happy to assist. SEE HUMAN RIGHTS MATERIAL ON OUR TABLES. The website is: http://concernedscientists.org
- PARKING: please visit the conference website for maps of where to park for the conference.
- For the parking lot, the GPS location is 94 Brett Road, Piscataway, 08854
- Do not forget to register for a digital parking permit on the conference website
- Once you register your vehicle, you are permitted to park in Lots 53A, 59, 60A, 60B, and 64. For a map of the parking lots, please visit our conference website. If you have any issues registering your car, please email
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- To connect to your home account, you can use the wireless connection. To connect to the WIFI, use your eduroam account or select the RUWireless WIFI option. Open your web browser and go to a non https website, the click the “Guest Access” button.
- For other relevant events and job opportunities please click on the links at the bottom of page of the conference website.
With all best wishes,
Joel L. Lebowitz
116th SMC Speaker's talks
The documents listed below have all been archived. They are no longer maintained and may not meet accessibility standards. To request content in an accessible format, contact us.
115 SMC Speakers Talk
The documents listed below have all been archived. They are no longer maintained and may not meet accessibility standards. To request content in an accessible format, contact us.
113 SMC Speaker's Talk
The documents listed below have all been archived. They are no longer maintained and may not meet accessibility standards. To request content in an accessible format, contact us.
Directions to Hill Center on Busch Campus
Directions to Hill Center on Busch Campus
Travel Advisory: The NJ Department of Transportation's (NJDOT) construction activities associated with the Route 18 Reconstruction project have begun in the New Brunswick area. As a result, drivers are likely to experience delays, traffic pattern changes and possible lane and road closures when traveling through the area. For more information related to the Route 18 Construction project, visit the Route 18 Update websiteThe scientific lectures scheduled for May 9-11, 2010 will take place at Rutgers University, at the Hill Center building, room 114 which is located on Busch Campus in Piscataway, NJ. Please see below for maps and driving directions.
Location of events on Sunday, May 9, 2010: The location of the Sunday evening cocktails & concert will be the Fiber Optics Auditorium located on Busch Campus next to the Fiber Optic Materials Research building. Dinner will be at the Busch Campus Faculty Dining Room instead of the usual Busch Campus Center. The Busch Faculy Dining Room is located just past the Busch Campus Center.
Maps
Please see links for maps of the immediate area of Busch Campus:
Map 1 of Busch Campus
Driving Directions to Hill Center
From New Jersey Turnpike (North or South)
Turn off at Exit 9, bear right after the tollbooths and follow signs for "Route 18 North - New Brunswick." Stay to the left to continue on Route 18 North. Proceed along Route 18 North, crossing the Raritan River (approximately 3.7 miles). Continue on Route 18 North. For the Busch campus - take the first exit for Campus Road.
From Garden State Parkway (North or South)Southbound (from northern points)
- Turn off at Exit 129 for the New Jersey Turnpike and head south.
- Turn off the Turnpike at Exit 9, bear right after the tollbooths and follow signs for "Route 18 North - New Brunswick."
- Stay to the left to continue on Route 18 North.
- Proceed along Route 18 North, crossing the Raritan River (approximately 3.7 miles).
- For the Busch campus - take the first exit for Campus Road. (The sign also says Rutgers Stadium and Busch Campus
- At the traffic circle, turn right onto Bartholmew Road.
- At the stop sign, turn left onto Brett Road.
- Follow Brett road until it vanishes in a maze of parking lots.
- Park in lot 64 or 60B
Northbound (from southern points)
- Turn off at Exit 105 and follow signs for Route 18 North.
- After approximately 24 miles, you will pass the entrance for the New Jersey Turnpike.
- Proceed along Route 18 North, crossing the Raritan River (approximately 3.7 miles).
- Continue on Route 18 North.
- For the Busch campus - take the first exit for Campus Road. (The sign also says Rutgers Stadium and Busch Campus
- At the traffic circle, turn right onto Bartholmew Road.
- At the stop sign, turn left onto Brett Road.
- Follow Brett road until it vanishes in a maze of parking lots.
- Park in lot 64, 60A, 60B (or at lot 67 near Brett and Bartholomew Roads)
From Route 1 (North and South)
- Turn off Route 1 at exit marked "Route 18 North-New Brunswick."
- Proceed along Route 18 North, crossing the Raritan River (approximately 3.7 miles).
- Continue on Route 18 North.
- For the Busch campus - take the first exit for Campus Road. (The sign also says Rutgers Stadium and Busch Campus
- At the traffic circle, turn right onto Bartholmew Road.
- At the stop sign, turn left onto Brett Road.
- Follow Brett road until it vanishes in a maze of parking lots.
- Park in lot 64, 60A, 60B (or at lot 67 near Brett and Bartholomew Roads)
From Route 287 (North or South)
- Turn off at Exit 9 "River Road, Bound Brook, Highland Park. "
- Proceed East on River Road toward Highland Park. For specific campuses follow the directions below.
- Continue on River Road and you will pass under the overpass for Route 18.
- Make the next left onto Route 18 North.
- For the Busch campus - take the first exit for Campus Road. (The sign also says Rutgers Stadium and Busch Campus
- At the traffic circle, turn right onto Bartholmew Road.
- At the stop sign, turn left onto Brett Road.
- Follow Brett road until it vanishes in a maze of parking lots.
- Park in lot 64, 60A, 60B (or at lot 67 near Brett and Bartholomew Roads)
Via Public Transit
Trains- New Jersey Transit's Northeast Corridor Line provides New Brunswick with both local and express service between Penn Station in New York and Newark and Trenton, New Jersey. (For Information 1-800-772-2222).
- SEPTA (Southeastern Pennsylvania Transportation Authority) provides service at Trenton to and from Philadelphia. (For Information 215/580-7800).
- Amtrak provides limited direct service to New Brunswick, however connections can easily be made via New Jersey Transit trains to principal Amtrak stations at MetroPark, New York and Trenton. (For Information 1-800/USA-RAIL).
Buses
- New Jersey Transit Bus Routes (For Information 973/762-5100):
- M11 - Service between New Brunswick (St. Peter's Hospital) and South River (Main Street and Obert Street). This route also has a stop at the New Brunswick Train Station.
- M14 - Service between North Brunswick (Fashion Plaza Mall) and Edison (Middlesex County College) with a stop at the Rutgers Student Center on the College Avenue Campus.
- M15/M18 - Service between Woodbridge Center and Rutgers Student Center with stops at the Rutgers Student Center on the College Avenue Campus, downtown New Brunswick on George Street near the Civic Square Building, and on the Douglass Campus on George Street near Cooper Dining Hall.
Directions From New Brunswick Train Station to Busch Campus - The New Brunswick Train Station is located at the corner of Albany Street and Easton Avenue across from the Rutgers Bookstore.
- Cab service is available from the train station.
- Campus Bus routes "A" and "H" will provide direct service from the Train Station/ Rutgers Bookstore to Busch Campus.
- Information and directions for reaching other campuses can be found online at the Tranposrtation website: http://parktran.rutgers.edu/campusbuses.shtml
113th - Abstracts of Invited Talks (May 2015)
Natan Andrei Rutgers University
Quench dynamics of quantum integrable models in 1-d
Curt Callan Princeton University
The statistics and dynamics of diversity in the adaptive immune system: of mice and men, T-cells and B-cells
The DNA of the cells of the adaptive immune system have undergone stochastic gene editing to provide the diversity needed to deal with pathogens. High-throughput sequencing is now providing copious data on this diversity. The sequence data by itself does not tell us much: the real subjects of interest are statistical distributions from which such data is drawn, and the way those distributions change with time and with response to infection, aging and so on. This is a problem in statistical inference and we have made some progress in solving it. In this talk I will tell you what we have learned, mathematically and biologically, by working with T cell and B cell data taken from both human beings and mice. There are many similarities between mice and men, but interesting differences as well.
Arup Chakraborty Massachusetts Institute of Technology
How to hit HIV where it hurts: a convergence of physics, biology, & medicine
HIV is a highly mutable virus, which evades natural and vaccine-induced immune responses and is the causative agent for the AIDS epidemic. I will describe methods, rooted in statistical physics, which aim to determine the fitness landscape of HIV – i.e., a definition of the collective sets of mutations that allow the virus to maintain fitness and evade immunity, and those combinations of mutations that cripple it. The Hamiltonian that describes this fitness landscape of HIV is analogous to the Hopfield Hamiltonian for associative memory in neural networks.
I will show how this Hamiltonian reveals encoded ―memories‖ in the HIV population of host-pathogen riposte won by the virus, and scaling laws that describe this phenomenon. I will also present how evolutionary dynamics with our inferred fitness landscape can predict HIV evolution in individual patients, and how this knowledge, combined with other experimental tests, is being harnessed to design and test therapeutic vaccines against HIV.
Pierluigi Contucci Università di Bologna
Mean-field Monomer-Dimer models: toward the understanding
of their quenched measure
The seminar will introduce the mean-field monomer-dimer models starting from a review of the deterministic case in the complete graph solved by Heilmann and Lieb. Two exact solutions will be discussed and their rigorous derivation shown: the quenched diluted model on locally tree-like graphs and the quenched random monomer activities model. Finally the deterministic case with an attractive interaction will be solved and some outlooks presented on their diluted and glassy extensions.
Joint works with Diego Alberici and Emanuele Mingione.
Ivan Corwin Columbia University
Stochastic quantum integrable systems
We describe recent work involving interacting particle systems related to quantum integrable systems. This theory unites all known exactly solvable models in the Kardar-Parisi-Zhang universality class, as well as provides new examples of such systems, and new tools in their analysis.
Alberto Desole University of Rome La Sapienza
W-algebras and integrable systems.
Abhishek Dhar International centre for theoretical sciences
Understanding anomalous transport in one-dimensional systems through fluctuating hydrodynamics
A recent theory of fluctuating hydrodynamics makes detailed predictions on the form of equilibrium correlations of conserved quantities in one-dimensional anharmonic chains. Using the connection between transport coefficients and equilibrium correlations via Green-Kubo, one is then able to make predictions on transport properties. In particular the theory predicts a thermal conductivity diverging with system size as a power law and gives us a value for the associated exponent. In this talk, the theoretical predictions are compared with direct simulation results for the Fermi-Pasta-Ulam chain. It is also explained why the
Rotor model shows normal transport.
Hugo Duminil-Copin University of Geneva
The self-avoiding walk on the hexagonal lattice: from combinatorics to Conformal Field Theory
We will discuss the self-avoiding walk model on the hexagonal lattice. Starting with the combinatorial aspects of the model, and in particular the discussion of a conjecture made by B. Nienhuis regarding the so-called connective constant of the hexagonal lattice, we will then explain how the scaling limit of the model is (conjecturally) described by conformally invariant objets.
This is a joint work with S. Smirnov.
Irene Giardina Istituto Nazionale di Fisica Nucleare
Collective change of state and transport of information in biological groups
Collective changes in biological groups requires all individuals in the group to go through a behavioral change of state. Sometimes these changes are triggered by external perturbations, as in evasive maneuvers of animal groups under predatory attacks. Often, however, they occur spontaneously and are only due to internal behavioral fluctuations. In all cases, the efficiency of information transport is a key factor to prevent cohesion loss and preserve collective robustness. In this talk, I will present an experimental and theoretical study of collective movements in
animal groups. Starting from experimental data on collective turns in starling flocks, I will discuss what is the mechanism that triggers a collective change (a turn) and grants efficient and fast information propagation through the system. I will show how the presence of a behavioral inertia and the related conservation law are responsible for the fast, linear dispersion relation observed in the transport of directional changes in natural flocks. Finally, I will discuss the role of heterogeneities, network unbalance, and boundary effects in initiating a collective change of state.
Ken Golden University of Utah
Statistical physics of sea ice and climate
The precipitous loss of Arctic sea ice has far outpaced expert predictions. We will discuss how mathematical models of composite materials and statistical physics are being used to study key sea ice processes and advance how sea ice is represented in climate models. This work is helping to improve projections of the fate of Earth's ice packs, and the response of polar ecosystems.
Shinobu Hikami Okinawa Institute of Science and Technology
Gaussian random matrix theory with an external source
The s-point correlation function of Gaussian random matrix theory with an external source is solvable and it provides interesting topological invariants by the tuning of the external source. We apply it to the problem of open/closed intersection numbers.
Pablo Hurtado Universidad de Granada
Breakdown of universality in anomalous Fourier's law
Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, though the nature of the anomaly remains
mysterious. Recent results based on nonlinear fluctuating hydrodynamics suggest that the anomaly is universal in $1d$ momentum-conserving systems and belongs in the Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic $1d$ diatomic hard-point fluid. Hydrodynamic profiles for a broad set of parameters all collapse onto an universal master curve, showing that (anomalous) Fourier's law holds even deep into the nonlinear regime. A solution of the macroscopic transport problem for this model is obtained (including the universal master curve) which compares flawlessly with data and, interestingly, implies the existence of a maximal current which sets a fundamental limit for transport in this model. These results question the validity of nonlinear hydrodynamic theories to understand collective behavior in $1d$, offering a new perspective on transport and its anomalies in low dimensions.
Jesper Jacobsen École normale supérieure
Logarithmic correlations in percolation and other geometrical critical phenomena
The purpose of renormalization group and quantum field theory approaches to critical phenomena is to diagonalize the dilatation operator. Its eigenvalues are the critical exponents that determine the power law decay of correlation functions. However, in many realistic situations the dilatation operator is, in fact, not diagonalizable. Examples include disordered systems and geometrical critical phenomena, such as percolation. These situations are described instead by logarithmic (conformal) field theories, in which the power-law behavior of correlation functions is modified by logarithms. Such theories can be obtained as limits of ordinary quantum field theories, and the logarithms originate from a resonance phenomenon between two or more operators whose critical exponents collide in the limit. We illustrate this phenomenon on the geometrical Q-state Potts model (Fortuin-Kasteleyn random cluster model), where logarithmic correlation functions arise in any dimension. The amplitudes of the logarithmic terms are universal and can be computed exactly in two dimensions, in fine agreement with numerical checks.
Mehran Kardar Massachusetts Institute of Technology
Pressure from non-equilibrium fluctuations
Thermal fluctuations in non-equilibrium steady states can lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. The force falls off with slab separation d as kBT/d (at temperature T, and in all spatial dimensions), but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is non-universal and explicitly depends on dynamics.
We also show that in active systems containing self-propelled particles, the pressure can depend on the precise interactions between the system's contents and its confining walls. Generic active fluids therefore have no equation of state. We show how one is recovered in certain limiting cases, which include "active Brownian spheres", a much-studied simplified model of self-propelled particles. Even in these cases, the mechanical pressure can exhibit anomalous properties that defy the familiar thermodynamic description of passive fluid materials.
Werner Krauth École normale supérieure
Two-dimensional melting transitions: New algorithms, new insights
The hard-disk model has exerted outstanding influence on computational physics and statistical mechanics. Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods and by molecular dynamics. It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur even though such systems cannot develop long-range crystalline order. Analysis of the system was made difficult by the absence of powerful simulation methods.
In recent years, we have developed a number of powerful Monte Carlo algorithms for hard disks and related systems. I will in particular show how the powerful event-chain Monte Carlo algorithm which has allowed us to prove that hard disks melt with a first-order transition from the liquid to the hexatic and a continuous transition from the hexatic to the solid. An extension of the event-chain algorithm to general potentials has allowed us to understand the generality of the liquid-
hexatic coexistence scenario that crosses over to KTHNY melting only for sufficiently soft potentials.
S. C. Kapfer, W. Krauth, Soft-disk melting: From liquid-hexatic coexistence to continuous transitions, Physical Review Letters 114, 035702 (2015)
M. Michel, S. C. Kapfer, W. Krauth, Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps, Journal of Chemical Physics 140 54116 (2014)
E. P. Bernard, W. Krauth, First-order liquid-hexatic transition in hard disks, Physical Review Letters 107, 155704 (2011)
E. P. Bernard, W. Krauth, D. B. Wilson, Event-chain algorithms for hard-sphere systems, Physical Review E 80 056704 (2009)
Claudio Landim Instituto Nacional de Matemática Pura e Aplicada
Zero-temperature limit of the Kawasaki dynamics for the Ising lattice gas in a large two-dimensional torus
We consider the Kawasaki dynamics at inverse temperature $\beta$ for the Ising lattice gas on a two-dimensional square of length $2L+1$ with periodic boundary conditions. We assume that initially the particles form a square of length $n$, which may increase, as well as $L$, with $\beta$. We show that in a proper time scale the particles form almost always a square and that the center of mass of the square evolves as a Brownian motion when the temperature vanishes.
Stan Leibler Rockefeller University
TBA
Enzo Marinari Sapienza Universita' di Roma
Spontaneous energy-barrier formation in an entropy-driven glassy dynamics
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough potential energy landscape and we analyse it both numerically and analytically. The model provides an example of dynamics where typical relaxation channels go over finite potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space; we expect this phenomenon to be also relevant in the thermally activated regime of realistic models of glass-formers. In this case, we found that typical dynamical paths episodically reach an high fixed threshold energy unexpectedly giving rise to a simple thermally activated aging phenomenology. In order to unveil this peculiar aging behavior we introduce %here, and contextually use, .l,., a novel description of the dynamics in terms of spontaneously emerging dynamical basins.
Fabio Martinelli Universita degli Studi Roma Tre
The influence of dimension on the relaxation process of East-like models: rigorous results
We consider the relaxation process and the out-of-equilibrium dynamics of natural generalizations to arbitrary dimensions of the well known one dimensional East process. These facilitated models are supposed to catch some of the main features of the complex dynamics of fragile glasses. The main focus of the talk will be on the low temperature regime i.e. small density of the facilitating sites. Joint work with P. Chleboun and A. Faggionato
Clement Mouhot University of Cambridge
Commuting the mean-field and classical limits in quantum mechanics
We report on a joint work with F. Golse and T. Paul, where we establish quantitative mean-field limit estimates for the many-body Schrödinger equation for bosons with binary interaction potential, that are uniform along the classical limit.
This relies on revisiting an argument of Dobrushin for deriving the Vlasov in the classical mean-field limit and introducing a quantum analogous of the Monge-Kantorovich distance.
David Nelson Harvard University
Theory of free-standing graphene ribbons
Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904. These highly nonlinear equations are characterized by a dimensionless coupling constant (the "Foeppl-von Karman number") that can easily reach vK = 10^7 in an ordinary sheet of writing paper. Since the late 1980's, it has been clear that thermal fluctuations in microscopically thin elastic membranes fundamentally alter the long wavelength physics, leading to a negative thermal expansion coefficient, and a strongly scale-dependent bending energy and Young's modulus. Recent experiments from the McEuen group at Cornell that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!) call for a theory of the mechanical deformation of thermally excited membranes with large Foeppl-von Karman number. We present here results for the bending and pulling of thermalized graphene ribbons and tabs in the cantilever mode.
Work done in collaboration with Andrej Kosmrlj.
Dmitry Panchenko University of Toronto
Chaos in temperature in generic 2p-spin models
I will discuss a proof of chaos in temperature for even p-spin models which include sufficiently many p-spin interaction terms. The approach is based on a new invariance property for coupled asymptotic Gibbs measures, similar in spirit to the invariance property that appeared in the proof of ultrametricity, used in combination with Talagrand's analogue of Guerra's replica symmetry breaking bound for coupled systems.
Luca Peliti Istituto Nazionale di Fisica Nucleare
Thermodynamics of accuracy
The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e., by a mechanism which reduces the error rate of the information-handling process by driving it out of equilibrium. We provide a consistent thermodynamic description of enzyme-assisted assembly processes involving competing substrates, in a Master Equation framework. We introduce and evaluate a measure of the efficiency of the proofreading process. We set the work in the perspective of the recent developments in the thermodynamics of information flow, which has several applications in sensing, control, and other cellular processes.
Riccardo Rao (Naples) and Luca Peliti (IAS Princeton)
Charles Radin University of Texas
Phase transitions in large networks
Sidney Redner Santa Fe Institute
Statistics of Basketball Scoring and Lead Changes
Exploiting recent availability of comprehensive data on all scoring events in recent NBA basketball games, the statistics of scoring and lead changes are investigated. Except for anomalies at the start and the end of the game, basketball scoring is well described by a continuous-time anti-persistent random walk, with essentially no temporal correlations between successive scoring events. We also determine the criterion for when a lead of a specified size is "safe" as a function of the time remaining in the game. Finally, we show that the distribution of times when the last lead change occurs and the distribution of times when the score difference is maximal are both given by the celebrated arcsine law, a prediction that is in excellent agreement with basketball game data.
Federico Ricci-Tersenghi University of Rome La Sapienza
Diluted one-dimensional spin glasses with long-range interactions undergo a phase transition in presence of an external magnetic field
The study of the low temperature phase of spin glass models is a notoriously very hard problem. The complexity of that phase has been nicely described at the mean field level by the Parisi hierarchical solution. However below the upper critical dimension all analytical approaches have proved inconclusive and, at present, the most reliable evidences come from Monte Carlo simulations.
Nonetheless even numerical simulations of spin glass models suffer of huge autocorrelation times and strong finite size corrections, making the extrapolation to the thermodynamical limit delicate.
In the last years (with Leuzzi, Parisi and Ruiz-Lorenzo) we have introduced and studied a one-dimensional spin glass model with diluted long-range interactions.
This models has several advantages:
1) allows us to thermalize very large system sizes (L=2^14), thus reducing finite size corrections;
2) running times are linear in the system size, thank to the link dilution, at variance to fully-connected models;
3) varying a single parameter (the interaction decay rate) the critical behavior is controlled either by the mean-field fixed point, either by a non-mean-field one.
I will present some of the numerical results we have obtained on this class of models, with a particular emphasis on the phase transition in presence of an external magnetic field.
Stefano Ruffo Università di Firenze
Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this talk, I will describe the model from a different point of view, emphasizing the equilibrium and nonequilibrium aspects of its dynamics from a statistical
physics perspective. I will discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise.
Shin-ichi Sasa Kyoto University
A fresh look at hydrodynamics
Hydrodynamic equations that describe macroscopic dynamical behavior of simple fluids were established in the nineteenth century, and microscopic understanding of such non-equilibrium dynamics has been developed over the twentieth century. Here, based on the twenty-first century wisdom, I introduce two fresh topics on hydrodynamics: (1) derivation of Stokes' law without hydrodynamic equations and (2) discussion of turbulent behavior from Hamiltonian particle systems.
Tomohiro Sasamoto Tokyo Institute of Technology
A determinantal structure for finite temperature directed polymer
Michael Schick University of Washington
Aligning self-assembled, block copolymer patterns with electric fields and mobile ions
Eduardo Sontag Rutgers University
Scale-invariance (fold-change detection) as a transient dynamical phenotype in cell signaling
Dynamical models of biological mechanisms are meaningful if they can explain experimental data and make a priori predictions of biological behavior, and they should be liable to be invalidated through testing. Although several competing models of a given mechanism can often be made to reproduce experimental data
through parameter tuning, it is sometimes possible to discriminate between models by testing an experimentally observed time-dependent output response for certain qualitative features. We focus here on one such "transient dynamical phenotype", scale invariance, which is a far stronger property than perfect adaptation. Scale invariance (or "fold change detection") behavior has been shown to be relevant to cell signaling, from bacteria (e.coli chemotaxis and B, subtilis aerotaxis) to eukaryotes (NFkappaB and Wnt pathways). We will discuss basic mathematical theory, biological context, and examples of experimental confirmations as well as model invalidation.
Hal Tasaki Gakushuin University
Typicality and thermalization in isolated macroscopic quantum systems
We shall formulate the notion that a pure state in an isolated quantum system represents thermal equilibrium. Then by proving large-deviation type bound (which we call thermodynamic bounds) for the microcanonical ensemble, we show in some systems that to represent thermal equilibrium is a typical property for pure states in the microcanonical energy shell. Under suitable assumptions, we also establish the approach to thermal equilibrium.
Edriss Titi University of California, Irvine
An Algorithm for Advancing Slow Features in Fast-Slow Systems without Scale Separation - A Young Measure Approach
In the first part of the talk, and in order to set the stage, we will offer a multi-scale and averaging strategy to compute the solution of a singularly perturbed system when the fast dynamics oscillates rapidly; namely, the fast dynamics forms cycle-like limits which advance along with the slow dynamics. We describe the limit as a Young measure with values being supported on the limit cycles, averaging with respect to which induces the equation for the slow dynamics. In particular, computing the tube of the limit cycles establishes a good approximation for arbitrarily small singular parameters. We will demonstrate this by exhibiting
concrete numerical examples. In the second part of the talk we will examine singularly perturbed systems which may not possess a natural split into fast and slow state variables. Once again, our approach depicts the limit behavior as a Young measure with values being invariant measure of the fast contribution to the flow. These invariant measures are drifted by the slow contribution to the value. We keep track of this drift via slowly evolving observables. Averaging equations for the latter lead to computation of characteristic features of the motion and the location the invariant measures. To demonstrate our ideas computationally, we will present some numerical experiments involving a system derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow diffusion.
This is a joint work with Z. Artstein, W. Gear, I. Kevrekidis, J. Linshiz and M. Slemrod.
Cristina Toninelli University Pierre and Marie CURIE
Dynamical phase transitions for kinetically constrained particle systems
We consider two cases of kinetically constrained models which have been introduced in physics literature to model liquid-glass transition: East and FA-1f models. We will recall that the dynamics of both models is characterized by the occurrence of dynamical heterogeneities, namely the coexistence of mobile and frozen regions. This is known to correspond to an underlying non-equilibrium phase transition in the large deviation function of the total number of configuration changes. We study the finite size effects around this first order phase transition and analyze the phase coexistence between the mobile and frozen dynamical phases in dimension one. We will discuss generalizations to higher dimensions and open problems.
Salvatore Torquato Princeton University
Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
It has been shown numerically that systems of particles interacting with ``stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform and highly degenerate. Disordered hyperuniform systems have been receiving recent attention because they are distinguishable exotic states of matter poised between a crystal and liquid that are endowed with novel thermodynamic and physical properties. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degenerate ground states in d-dimensional Euclidean space is highly nontrivial because the dimensionality of the configuration space depends on the number density and there is a multitude of ways of sampling the ground-state manifold, each with its own probability measure for finding a particular ground-state configuration. For these reasons, it is theoretically very challenging to devise ensemble theories that are capable of predicting structural attributes and other properties of the ground-state configurations. A new type of statistical-mechanical theory must be invented to characterize these exotic states of matter. I will report on some initial progress that we have made in this direction. Our theoretical predictions for the structure and thermodynamic properties of the stealthy disordered ground states and associated excited states are in excellent agreement with computer simulations across the first three space dimensions. This is joint work with Frank Stillinger and Ge Zhang.
Aernout van Enter University of Groningen
Sharper thresholds for two-dimensional anisotropic bootstrap percolation
The threshold for two-dimensional bootstrap percolation with the anisotropic (1,2)- neighborhood, that is distance 1 in one direction and distance 2 in the other direction, and threshold 3 --which makes this a "critical" model--, equals zero for the infinite square lattice. We will present finite-size corrections up to third order, and mention some results on related models.
Joint work with Hugo Duminil-Copin, Tim Hulshof and Rob Morris.
Eric Vanden-Eijinden New York University
Large Deviations for Fast-Slow Systems
I will discuss how to derive a large deviation rate function for the slow degree of freedoms in systems that also include fast modes — this rate function permits to analyze deviation from the mean limiting behavior of the dynamics that go beyond those described by the central limit theorem. As an illustration, I will present a case study inspired by a fluid mechanics problem in which the fast variables are a linear process that depends parametrically on the slow variables and acts as a quadratic form on these slow variables. This system display metastability between long lived states with a different number of jet-like structures — the relative stability and the most likely path of transition between these jets will be analyzed.
Srinivasa Varadhan New York University
Brownian Motion, translation invariance and Large Deviations
In studying the large deviation behavior of Brownian occupation times translation invariance creates a lack of compactness. For suitable functionals it can be handled by a compactification that respects the invariance. We will look at an example.
Francesco Zamponi École normale supérieure
Progresses on the mean field theory of glasses
In the last three years we obtained an exact solution of infinite-dimensional hard spheres in the glassy regime. Based on this solution, the construction of a quantitative mean field theory of simple glasses, similar in spirit to the HNC treatment of simple liquids, is in progress. I will discuss the current status of the theory and future perspectives.
Jean Zinn-Justin Saclay Nuclear Research Centre
Renormalization Group Approach to Matrix Models
In the late eighties, it was realized that some ensembles of random matrices in the large size and the so-called double scaling limit could be used as toy models for 2D quantum gravity coupled to conformal matter or as examples of statistical models on some kind of random surfaces. This has resulted in a tremendous development of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said. Since the solved models exhibit critical points and universal properties, it was tempting to use renormalization group (RG) ideas to determine universal properties, without solving models explicitly. This can be done in various approximation schemes that I shall describe.
113th - Short Talk Schedule (May 2015)
TBA