Abstracts of Short Talks |
| T. Antal, Boston University Coauthor:I. Scheuring Title:"Survival of Strategies for an Evolutionary Game in Finite Populations" Abstract:A stochastic evolutionary dynamics of two strategies given by $2\times 2$ matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game and for any system size. The games can be classified according to whether the fixation probability or the fixation time exceeds the corresponding value for neutral games. Several statements and conjectures can be made. The asymptotic behavior of the fixation time and the fixation probabilities in the large population size limit can also be obtained directly from the discrete solution, without the use of a diffusion approximation. |
| M. Ciucu, Georgia Institute of Technology Title:"Electrostatics Emerging from Random Tilings with Holes" Abstract: The study of the correlation of holes in dimer coverings (or equivalently tilings) was initiated by Fisher and Stephenson in the early 1960's, who analyzed the correlation of two unit holes (monomers). Motivated by this, in earlier work we studied the asymptotics of the joint correlation of an arbitrary finite collection of even size triangular holes on the hexagonal lattice, and found that it is given precisely by the electrostatic energy of the physical system obtained by regarding the holes as electrical charges. In this talk we present a natural way to define a discrete vector field in our model, and show that its scaling limit is precisely the electric field. Our result can be speculatively interpreted as indicating that the electric field emerges from the quantum fluctuations of the vacuum. |
| F. Colomo, INFN, Firenze Coauthor: A. Pronko Title:"Square Ice, Alternating Sign Matrices and Orthogonal Polynomials" Abstract:The six-vertex model, or square ice, with Domain Wall Boundary Condition, is considered in connection with the combinatorial problem of Alternating Sign Matrices (ASM) enumerations. Using standard techniques from the theory of classical orthogonal polynomials, we provide a unified and simplified treatment of all ASM enumerations. In particular, previously known results can be recovered in a very simple and straightforward way, while the long standing problems of refined 3-enumeration, and of all doubly refined enumerations are completely solved. |
| G.F. Dell'Antonio,University of Roma, La Sapienza Title:"Dynamics on Metric Graphs as Limit of Constrained Systems" Abstract: Please click here for abstract. |
| Y. Deng, New York University Coauthors:W.A. Guo and H.W.J. Bloete Title:"Cluster Simulation on the O (N) Loope Model Abstract: Critical slowing down is one of the prominent problems in Monte Carlo studies of statistical systems undergoing phase transition. For the Potts model, a significant breakthrough was made by Swendsen and Wang in 1987. The Swendsen-Wang (SW) cluster algorithm has then been generalized and applied to many other statistical systems. An example is the Chayes-Machta method that enables cluster simulations of the q-state Potts model with nointeger q. However, for the O(N) loop model, another important class of statistical models, the cluster simulation remains as a long-standing problem. Recently, by making use of the equivalence between loop configurations and low-temperature graphs of a $N$-color Ashkin-Teller model, we formulated an embedding Swendsen-Wang-type algorithm for the O(N) loop model. This cluster algorithm was then applied to the honeycomb O(N) loop model. The numerical data strongly imply that, for $N >1$, the critical slowing down hardly exists. |
| P. Dubovski, Stevens Institute of Technology Title:"New Model of the Coagulation Kinetics" Abstract:The celebrated Smoluchowski coagulation equation assumes that two colliding particles just merge together with some probability. However, the experiments demonstrate that the increase in the particle size is overlapped by splitting the particles during a shorter time interval. We simulate such collisions and derive a new balance kinetic model. We compare analytically and numerically the results for both coagulation models (Smoluchowski and new one) and show a surprising coincidence in the results: both models have same or almost same time-dependent solutions, equilibria, critical phase transition times, etc. |
| R. Fisch, n/a Title:"Finite-Size Scaling of the Domain Wall Entropy for the 2D + -J Ising Spin Glass" Abstract:The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for L x L square lattices with L <= 20, and x = 0.25 and 0.5, where x is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. Under these conditions, almost all domain walls have an energy E_{dw} equal to 0 or 4. The probability distribution of the entropy, S_{dw}, is found to depend strongly on E_{dw}. The results for S_{dw} when E_{dw} = 4 agree with the prediction of the droplet model, that S_{dw} scales with L like L^{d_S / 2}. Our results for S_{dw} when E_{dw} = 0 agree with those of Saul and Kardar. In addition, we find that the distributions do not appear to be Gaussian in that case. The special role of E_{dw} = 0 domain walls is discussed, and the discrepancy between the prediction of Fisher and Huse and the result of Saul and Kardar is explained. |
| J. Frank, MIT Coauthor: Mehran Kardar Title:"Defects in Flexible Nematic Sheets" Abstract:The morphology of living organisms often results from the interplay of rod-like molecules and flexible membranes. A continuum model of nematic order coupled to surface curvature reveals equilibrium shapes for topological defects that resemble tip growth in systems as diverse as pollen and neurons. |
| A. Giuliani, Princeton University Coauthors:J.L. Lebowitz and E.H. Lieb Title:"Ising Models with Long-Range Dipolar and Short Range Ferromagnetic Interactions" Abstract:We study the ground state of a d-dimensional Ising model with long range antiferromagnetic interaction equal to 1/r^p, p>d, and nearest neighbor ferromagnetic interaction of strength J>=0. If d=1 we give a complete characterization of the ground state for any J>=0 and p>d. If d>=2 we obtain upper and lower bounds on the ground state energy, with the same dominant asymptotic behavior for J large. |
| S. Henkes, Brandeis University Coauthor:B. Chakraborty Title:"A Field Theory of Jamming" Abstract:In the paradigm of the jamming phase diagram, we're investigating the nature of point J by studying a 2d system of soft, frictionless grains along the packing fraction axis. >From the conditions of force and torque balance, we are able to map the system to a scalar field defined on the granular network. We construct a field theory using this field and compare the predicted transition to simulation results. |
| C-K. Hu, Academia Sinica (Taipei) Coauthor:D. Saakian Title:"Some Analystic Results of Biological Evolution Models" Abstract:In this talk, I will present some analytic results of biological evolution models, including (1) Exact solution of the Eigen model with general fitness functions and degradation rates, [Proc. Natl. Acad. Sci. USA 103, 4935 (2006)]; (2) Phase diagram of diploid biological evolution models. |
| S. Huntsman, Naval Postgraduate School Title:"Gauge Theory and Descriptive Thermodynamics" Abstract:A universal metaformat for data produced by generic complex interacting systems that draws on the Ehrenfest model allows many systems such as computer networks to be treated completely thermodynamically. (D. Ford and SH, cond-mat/0510030; to be published in Physica A.) The methods of this "descriptive thermodynamics" can be used to gain understanding about these systems in real time. We will review the metaformat before outlining how to construct a nonabelian gauge theory based on it. |
| N. Izamailian, Academia Sinica, Taipei, Taiwan Coauthors: V.B. Priezzhev, P. Ruelle and C-K. Hu Title:"Boundary Effects in the Dimer Model" Abstract:We study the finite-size corrections of the dimer model on planar $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of $N$, and we show that such unusual finite-size behavior can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory. |
| S. Ji, Rutgers, The State Univerity Of New Jersey Title:"The Bohr-Elsasser Incompleteness Theroem: The Inability of Physicochemical Theories to Explain Life" Abstract: In 1933, Niels Bohr (1885-1962) suggested that the laws of physics and chemistry may be insufficient to completely account for the phenomenon of life just as the laws of Newtonian mechanics are insufficient to explain the structure of the hydrogen atom [1]. Based on his research in the s through the s, the physicists-turned theoretical biologist Walter Elsasser (1904-1991) came to the same conclusion, but the rationale for his conclusion was different. According to Elsasser, the laws of physics and chemistry depend, for their mathematical derivations, on the assumption that the size of the classes (also called sets or ensembles) of objects under consideration is infinite. In comparison, the size of the classes of living organisms is invariably finite (and heterogeneous) and hence the usual mathematical equations that converge at infinities break down when applied to finite classes [2]. If this conjecture turns out to be true upon further analysis, it may be said that s finite (and heterogeneous) class argument provides a logical foundation for the validity of s intuitive notion that physics and chemistry are insufficient to explain life. The combination of the ideas expressed by Bohr and Elsasser was named the Bohr-Elsasser Incompleteness Theorem in 1991 [3]. Bohr and other physicists successfully modeled the atom in the early decades of the 20th century. I predict that biologists will succeed in constructing computational models of the cell in the early decades of the 21st century. The method employed by physicists in modeling the atom was essentially based on mathematics without relying on the computer, but the method that biologists will need to model the cell may turn out to be, not mathematics, but mainly logic- and computer-based. This conclusion was strongly influenced by the ideas and concepts advocated by three main scientists, W. Elsasser, G. Simpson (1902-1984), and S. Wolfram (1959- ) whose ideas may be briefly summarized as follows:
2)W. Elsasser -- Physicists study objects that belong to pure classes to which mathematical methods can be applied; biologists study objects that belong to heterogeneous classes to which logic, but not mathematics, can be applied. 3)S. Wolfram -- All structures and phenomena, whether internal or external, can be modeled on the computer as fractals, namely, the structures and patterns that emerge as the consequences of iterating the application of sets of simple rules n times, where n can be a large number (10-1000?). The complex of these broad ideas may be referred to as Simpson-Elsasser-Wolfram framework for modeling living , including the cell, the atom of life. [2] Elsasser, W. (1987). Reflections on a Theory of Organisms: Holism in Biology. The Johns Hopkins University Press, Baltimore. [3] Ji, S. (1991). Biocybernetics: A Machine Theory of Biology. In: Molecular Theories of Cell Life and Death (Ji, S., ed.), Rutgers University Press, New Brunswick. 1-237. |
| J. Joo, Penn State University Coauthors: Eric Harvill and Reka Albert Title:"Effects of Noise on Ecological Invasion Processes: Phage-mediated Competition in Bacteria" Abstract:Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in nature. Using an experimental system of bacteriophage-mediated competition in bacterial population and a deterministic model, we showed that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of other phage and host parameters. We also showed that the above conclusion is robust against internal stochastic fluctuations. |
| J. Kalb, Brandeis University Coauthor:Bulbul Chakraborty Title:"Polymer Dynamics and Statics in Confined Geometries" Abstract:Current work on biological systems and glass forming polymers has led to an interest in the study of single polymer systems. The main questions concern relaxation phenomena and the shape adopted by single polymers under hard and soft boundaries. We study what role self-avoidance effects and confinement length scales play. |
| E. Kamber, Brandeis University Coauthor: Jane Kondev Title:"Lattice Dimers and the Tilting Transition" Abstract:We study the statistics of dimer coverings of the honeycomb lattice by Monte Carlo simulations. Dimer configurations are given by placing dimers on adjacent sites with the constraint that every site is covered by one and only one dimer. We implement the pocket algorithm [1], which is believed to be ergodic on the space of dimer coverings. The pocket algorithm enables global updates of dimer configurations without violating the packing constraint. Dimer configurations can be mapped to a height model [2], which associates a discrete interface with every dimer covering. If the dimers are aligned along one direction of the honeycomb lattice, the height interface will be tilted. We investigate the fluctuations of the associated height model, when the system undergoes a transition from an untilted rough interface to a tilted smooth interface. We impose a fixed tilt of the interface and measure fluctuations of the height. For a tilted surface the height fluctuations are anisotropic with a variance that increases logarithmically with system size. We compute the effective stiffness of the interface and find that it increases with increasing tilt. This work is supported by NSF DMR-0403997. JK is a Cotrell Scholar of Research Corporation. [1] W. Krauth , R. Moessner, Phys. Rev. B 67, 2003. [2] H.W.J. Blote , H.J. Hilhorst , J. Phys. A 15, 1982. |
| N. Khatiashvili, Tbilisi State University Title:"On Two-Dimensional Fluid Flow Problem With a Free Boundary" Abstract:The two-dimensional problem for steady waves in incompressible heavy fluid is studied.The model of Lavrenti'ev and Shabat is discussed. In the early works of the author this model is transformed to the non-linear one dimensional integral equation for a free boundary (ON THE NON LINEAR PLANE BOUNDARY PROBLEM.Reports of VIAM.,Vol.10,N 1,1995,46-48,)(ON STOKES WAVE NONLINEAR INTAGRAL EQUATION,Integral Methods in Science and Engineering,Res. Notes in Math.Series 418,CHAPMAN&HALL/CRC,2000,200-204). In this talk the method of approximation of this integral equation is suggested. The asymptotics of the waves at the pikes is given. |
| P. Kleban, University of Maine Coauthors: J. Simmons and R.M. Ziff Title:"Crossing and Connection Probabilities in Critical 2-D Percolation Abstract: We calculate the probability that a cluster crossing a long trapezoid connects with another. In the limit of a small angle, this itself may be interpreted as a crossing. Some related quantities may also be presented. |
| M.S.. Li, Inst. of Physics, Polish Academy of
Sciences Coauthors:D.K. Klimov and D. Thirumalai Title:"Scaling of Cooperativity of Folding-Unfolding Transition in Globular Proteins" Abstract:We have predicted that the cooperativity of the folding-unfolding transition in single domain globular proteins grows with the number of amino acids by a power law. The corresponding exponent is universal and equal to 2.2. Our theoretical prediction, based on the second order phase transition, is confirmed by simulation and experimental results. |
| Y. Liu, Brandeis University Coauthor: B. Chakraborty Title:"Statistical and Mechanical Properties of Semiflexible Polymers in an External Field" Abstract:We make use of Bond Fluctuation Algorithm to study the behavior of semiflexible polymers for all persistence lengths and investigate the relationship of their shape to the persistence length, the chain length and the external field. |
| W. McHarris, Michigan State University Title:"Bell's Theorem Meets Nonextensive Thermodynamics" Abstract:A number of the so-called paradoxes generated within the Copenhagen interpretation of quantum mechanics can be resolved through parallels in nonlinear dynamics and chaos theory [i.a., WCM, in "Quantum Theory: Reconsideration of Foundations-3," ed. by G. Adenier, A. Yu. Khrennikov, and Th. M. Neuwenhuizen, AIP Conference Proceedings, Vol. 810, p. 367 (2006)]. Among these is the inferred nonexistence of "local reality" from experiments thwarting Bell-type inequalities (experiments that rule in favor of quantum over classical mechanics and imply Einstein's "spooky action at a distance"). However, most "classical" derivations of Bell-type inequalities implicitly rely on noncorrelated statistics, but nonextensive thermodynamics (e.g., Tsallis nonextensive entropy) demonstrates that such does not necessarily apply classical systems oftentimes exhibit correlated statistics. The resulting implication is that the classical content of most such inequalities is faulty, rendering them moot in ruling out classical (nonlinear) dynamics. |
| A. Middleton, Syracuse University Coauthors:P. Le Doussal and K. Wiese Title:"Computing the Functional Renormalization Group Fixed Point for Interfaces" Abstract:We compute the fixed point function that is the central feature of the FRG for interfaces in disordered media by finding exact ground states for elastic interfaces in a disordered background. We confirm the shape of this function and especially the linear cusp at small argument, validating the FRG approach. |
| K. Oliveira, Federal University of Alagos Coauthor: M. Viana, IMPA Title:"Equilibrium States and Thermodynamical Formalism Beyond Hyperbolic Systems" Abstract:In this talk we discuss extensions of the Thermodynamical Formalism developed for the expanding/hyperbolic maps by Sinai, Ruelle and Bowen. We consider Local Diffeomorphisms on arbitrary dimensional manifolds and construct a "weak" Gibbs measure with positive Lyapounov exponents, proving that it is the unique equilibrium measure for a open class of potentials close to zero. For this aim, we prove that there exists a eigenfunction for the transfer operator. |
| O. Peters, UCLA and Santa Fe Institute Coauthors: D. Nelson, M. Girvan. G. Pruessner Title:"Universality in Self-Organized Critical Systems" Abstract:Universal behavior near continuous phase transition is intellectually appealing and the main justification for studying simple models of critical phenomena. Despite the great importance of universality, it has not received the recognition it deserves in studies of self-organized critical (SOC) systems. I will present the problem of obtaining universal behavior in SOC models and potential solutions. An experimental study of atmospheric precipitation will serve to illustrate how these considerations might translate into the real world. |
| A. Schenkel, University of Helsinki Coauthor:Raphael Lefevere Title:"Normal Heat Conductivity in Strongly Pinned Chains of Anharminic Oscillators" Abstract:We consider a chain of coupled and strongly pinned anharmonic oscillators subject to a non-equilibrium random forcing. Assuming that the stationary state is approximately Gaussian, we first derive a stationary Boltzmann equation. By identifying the nontrivial collisions, we next invert the linearized collision operator and establish the behaviour of the heat conductivity in the limit of strong pinning. In particular, we show that these are the four-body umklapp collisions between phonons which are responsible for a normal heat conductivity in pinned anharmonic chains. |
| V. Shneidman, NJIT Coauthor:G. Nita, NJIT Title:"Transient Nucleation in a Supercooled Lattice Gas" Abstract:TBA |
| J. Soriano-Pradera, Weizmann Institute of Science, Israel Coauthors: I. Breskin, E. Moses and T. Tlusty Title:"Percolation in Living Neural Cultures" Abstract:We study living neural networks by measuring the neurons' response to a global electrical stimulation and for gradually weaker neural connectivity. We use a graph-theoretic approach to quantify the size distribution of connected components. The connectivity undergoes a percolation transition as a giant component disintegrates, with a critical exponent beta = 0.66 ± 0.15. This exponent is independent of the culture details, indicating that it is an intrinsic property of the network. Numerical simulations show that beta corresponds to a neural connectivity characterized by a Gaussian rather than a power law distribution. |
| A. Toom,UFPE, Brazil Title:"Every Continuous Operator has an Invariant Measure" Abstract:We prove existence of invariant measure for a large class of processes with random interaction with a special attention to some processes with variable length, which are nonlinear. |
| P. Virnau, MIT Coauthors:Leonid Mirny and Mehran Kardar Title:"Searching for Knots in Proteins" Abstract:Although knots are abundant and complex in globular homopolymers, they are rare and simple in proteins. Our analysis of the Protein Data Bank reveals 36 knots, including the most complicated knot discovered to date. We suggest that the topology of this particular protein protects it against degradation. |
| Y. Yang, Brandeis University Coauthors: Bulbul Chakraborty and Jane Kondev Title:"Transition Rates in a Lennard-Jones Binary Mixture" Abstract:In the simulation of a Lennard-Jones Binary Mixture, we used the strongest branch method to construct metabasins from inherent structures. The transition rates between metabasins and the implication will be discussed. |
| J. Wehr, University of Arizona Coauthors: M. Lewenstein, A. Niederberger and L. Sanchez-Palencia Title:"Continuous Spin Systems in a Symmetry Breaking Random Field Abstract:We discuss a possibility that a random field directed along the Y axis causes the two-dimensional XY model to magnetize in the X direction, with generalizations to Heisenberg models and quantum analogs which may be realized in a laboratory using ultracold atomic gases. |
| V. Zagrebnov, University Aix-Marseille II and
CPT-Luminy Coauthors: J. Pulé and A. Verbeure Title:"Non-homogeneous Bose-Einstein Condensation" Abstract:We prove that for boson systems with superstable interacction a non-zero mode condensation imply also a spontaneous breaking of translation invariance. |
| F. Zamponi, LPT, Ecole Normale Superieure Coauthor: G. Parisi Title: "Amorphous Packings of Hard Sphere" Abstract:I will present a replica method that allows to compute properties of amorphous packings of hard spheres from first principles. The method is based on mean-field ideas, so it is approximated in finite dimension; nevertheless, the results we obtain compare well with numerical simulations. Finally I will discuss the limit of infinite dimension in which the method might lead to exact results. |
| W. Zhou, NYU Coauthor: J. Percus Title:"Description of Ion Clusterization in Electrolyte Models" Abstract: I will present two new ideas concerning the theorectical description of ion clusterization, which is highly nonlinear and a dominant factor in the low temperature thermodynamics of electrolytes. The first idea is to recursively rescale the ion size until linear methods is applicable. The second is to define neutral clusters through electric energy instead of the more conventional distance between ions. For more details, please check our recent publication: Physical Review Letters, 95, 235701(2005). |
| N. Zimbovskaya, University of Puerto Rico at
Humacao Title:"On the Mechanism of Electron Transport in Conducting Polymer Nanofibers" Abstract:Here, we present theoretical analysis of electron transport in polyaniline based (PANi) nanofibers assuming the metalic state of the material. To build up this theory we treat conducting polymers as a special kind of granular metals, and we apply the quantum theory of conduction in mesoscopic systems to describe the transport between metallic-like granules. Our results show that the concept of resonance electron tunneling as the predominating mechanism providing charge transport between the grains is supported with recent experiments on the electrical characterization of single PANi nanofibers. By contacting the proposed theory with the experimental data we estimate some important parameters characterizing the electron transport in these materials. Using the Buttiker dephasing model within the scattering matrix formalism we analyze dephasing effects, and we show that these effects could be reduced enough to allow the structure of the electron transmission function to be exposed in the experiments on the electronic transport through fibers. Also, we discuss the origin of rectifying features observed in current-voltage characteristics of fibers with varying cross-sectional areas. 1. N. A. Zimbovskaya, A. T. Johnson, Jr., and N. J. Pinto, Phys. Rev. B 72, 024213 (2005). 2. N. A. Zimbovskaya, J. Chem. Phys. 123, 114708 (2005). |