Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session X39: Miscellaneous Topics in Statistical Physics |
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Sponsoring Units: GSNP Chair: Bill Klein, Boston University Room: Morial Convention Center 231 |
Friday, March 14, 2008 8:00AM - 8:12AM |
X39.00001: Enhancement of epidemic extinction by random vaccination Ira Schwartz, Mark Dykman We study the probability of epidemic extinction in large populations. We use the susceptible-infected-susceptible (SIS) model since it forms the foundation of many epidemic processes. Fluctuations in the SIS system have two sources. The major source is the randomness of the ``reactions'' in which the number of susceptibles and/or infected changes. In addition, we assume that vaccination is done at random, leading to the decrease of the number of susceptibles. The vaccination is modeled by a Poisson process. The probability distribution is found from the master equation, which is solved in the eikonal approximation. It is shown that, even in the absence of vaccination, the logarithm of the extinction rate displays scaling dependence on the parameters. It scales as the square of the distance to the parameter value where the average number of infected vanishes. This is very different from the familiar 3/2 scaling law for saddle-node bifurcations. Finally, we show that even weak vaccination can dramatically increase the extinction probability. The correction to the logarithm of the probability becomes exponential in the vaccination rate when this rate is not too small. [Preview Abstract] |
Friday, March 14, 2008 8:12AM - 8:24AM |
X39.00002: Inhomogeneous Coupling in 2-Channel Asymmetric Simple Exclusion Processes Konstantinos Tsekouras, Anatoly Kolomeisky Asymmetric exclusion processes for particles moving on parallel channels with inhomogeneous coupling are investigated theoretically. Particles interact with hard-core exclusion and move in the same direction on both lattices, while transitions between the channels is allowed at one specific location in the bulk of the system. An approximate theoretical approach describing the dynamics in the vertical link and horizontal lattice segments exactly but neglecting the correlation between horizontal and vertical transport is developed. It allows us to calculate stationary phase diagrams, particle currents and densities for symmetric and asymmetric transitions between the channels. It is shown that in the case of the symmetric coupling there are three stationary phases, similarly to the case of single-channel totally asymmetric exclusion processes with local inhomogeneity. However, the asymmetric coupling between the lattices lead to a very complex phase diagram with ten stationary-state regimes. Extensive Monte Carlo computer simulations generally support theoretical predictions, although simulated stationary-state properties slightly deviate from calculated in the mean-field approximation, suggesting the importance of correlations in the system. Dynamic properties and phase diagrams are discussed by analyzing constraints on the particle currents across the channels. [Preview Abstract] |
Friday, March 14, 2008 8:24AM - 8:36AM |
X39.00003: Brownian Gas: a field theory with a Poissonian ground state Andrea Velenich, Claudio Chamon, Dirk Kreimer As a first step towards a satisfying field theory of Brownian particles in interaction, we study exactly the non-interacting case, its combinatorics and its non-linear time-reversal symmetry. The field theory is nevertheless interacting: the vertex is the hallmark of the original particle nature of the gas and enforces the constraint of a strictly positive density field as opposed to a Gaussian free field. We compute exactly all the n-point density correlation functions, determine non-perturbatively the Poissonian nature of the ground state and emphasize the futility of any coarse-graining assumption for the derivation of the field theory. [Preview Abstract] |
Friday, March 14, 2008 8:36AM - 8:48AM |
X39.00004: Wave electrophoretic trapping and chaos Boyd Edwards, Lloyd Carroll, Aaron Timperman, Jarrod Schiffbauer, Jon Mease Synchronized oscillating electric potentials are applied to a periodic array of stationary cylindrical electrodes in a stationary conducting viscous fluid. These potentials produce a longitudinal traveling wave that traps high-mobility ions and partially traps intermediate-mobility ions in periodic and narrowband chaotic attractors with average velocities that are commensurate with the wave speed. Incommensurate broadband chaotic attractors feature ascending and descending geometric series of orbit transitions that converge at the same unstable trapped orbit. [Preview Abstract] |
Friday, March 14, 2008 8:48AM - 9:00AM |
X39.00005: Experimental Study of Energy Localization in a Nonlinear Electrical Lattice Lars English, Ritoban Basu Thakur, Ryan Stearrett Experimental results are presented that reveal the formation of intrinsic localized modes (ILMs) in a nonlinear electrical lattice. The lattice studied is a discrete transmission line consisting of two inductors and a diode (with voltage-dependent capacitance) per unit cell, and it forms a ring. We show that when this ring circuit is driven uniformly at large amplitudes, an instability of the uniform mode leads to the appearance of sharply localized features. Under certain driving conditions, these ILMs can become locked to the driver. [Preview Abstract] |
Friday, March 14, 2008 9:00AM - 9:12AM |
X39.00006: Multiple traveling solitons in one-dimensional monatomic quartic lattices Sanghamitra Neogi, Gerald Mahan We discuss the generation of traveling soliton waves in a one- dimensional monatomic quartic lattice using numerical techniques. We apply an external forcing function or a pulse to the end atom of a free chain of monatomic atoms to generate traveling solitons. When the strength of the forcing function is above a threshold value, multiple traveling solitons are observed to flow down the chain. The number of traveling solitons in the chain increases rapidly with the increase in pulse strength beyond this critical value. The amplitudes and velocities of these multiple solitons increase with the increase in pulse strength for small pulse strengths. For larger values of pulse strengths, the amplitudes and velocities of all the multiple solitons saturate. The frequencies and wave vectors of all the traveling solitons on the quartic lattice are within a very narrow range of values. These values are independent of the pulse strength. [Preview Abstract] |
Friday, March 14, 2008 9:12AM - 9:24AM |
X39.00007: Statistical mechanics rooted in maximum entropy method shows absence of the Gibbs paradox Chih-Yuan Tseng Studying the Gibbs paradox problem indicates Gibbs's statistical mechanics may not be a general theory for thermodynamics. We found that most of conventional resolutions only provide explanations for ``supplementary'' introduction of the Gibbs correction rather than re-develop statistical theory to comprehend corresponding aspects. In this talk, we will show a general theory of statistical mechanics based on generalized maximum entropy method, which is designed for inductive inference. The general theory integrates prior knowledge of the system and measurements of macroscopic properties into a general ensemble. Based on the general theory, the 1/N! is simply a prior distribution that denotes our prior knowledge for indistinguishability of N microstates instead of the correction for the canonical ensemble. There is no Gibbs paradox. It is simply a consequence of incomplete statistical description for classical thermodynamic systems. [Preview Abstract] |
Friday, March 14, 2008 9:24AM - 9:36AM |
X39.00008: High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows Michael Hinczewski, A. Nihat Berker The recently developed tensor renormalization-group (TRG) method [1] provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related [2] to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than $10^{-5}$ along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range $D$) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with $D=24$, corresponding to 4624-dimensional renormalization-group flows. [1] M. Levin and C.P. Nave, Phys. Rev. Lett. 99, 120601 (2007). [2] M. Hinczewski and A.N. Berker, arXiv:0709.2803v1 [cond-mat.stat-mech], Phys. Rev. E, in press. [Preview Abstract] |
Friday, March 14, 2008 9:36AM - 9:48AM |
X39.00009: Nucleation in a long-range repulsive model. Kipton Barros, William Klein We employ a model with long-range repulsive interactions to study nucleation from a fluid to a crystalline phase. The long-range interactions make the metastable fluid phase long lived. From our simulations we find a divergence of the susceptibility at the spinodal, as predicted by mean-field theory. We also observe nucleation events and verify that the nucleating droplets, when they occur, match the numerical saddle point solutions of the free energy functional. In one dimension, where Alexander-McTague type symmetry arguments cannot be satisfied, we find that nucleation does not occur and that the fluid-solid transition is continuous. In two and three dimensions the transition is first order, with nucleating droplets of hexagonal and bcc symmetries. [Preview Abstract] |
Friday, March 14, 2008 9:48AM - 10:00AM |
X39.00010: Phase transitions in the long-range antiferromagnetic Ising model. Rachele Dominguez, Kipton Barros, William Klein We study the long-range antiferromagnetic Ising model to understand microphase separation in block-copolymer systems and dipolar Ising models. When quenched to low temperatures, the system initially obeys a Cahn-Hilliard-Cook-like linear theory and then orders into a ``stripe" or ``clump" phase. The system also exhibits order-to-order transitions between the stable stripe and clump phases. From the free energy density obtained from coarse graining the Ising model, we use Langevin dynamics to investigate these transitions. I will discuss the nature of the transitions into the ordered phases as well as computational and theoretical methods for obtaining the phase diagram of the system. [Preview Abstract] |
Friday, March 14, 2008 10:00AM - 10:12AM |
X39.00011: Emergent Structures in Dissipative Wave-Particle Systems Davit Sivil, Alfred Hubler We study the motion of a particle with mass m on a vibrated string of length L. We assume that there is a friction force between the particle and the string. The string is sinusoidally forced at both ends. We find that the particle has attractors located at x=L/2 - $n\pi c/2 \omega$, where $\omega$ is the frequency of the waves on the string, and $n \in {\boldmath Z}$. We also study the attractors of the same system with multiple driving frequencies. We also compared our results with numerical simulations. [Preview Abstract] |
Friday, March 14, 2008 10:12AM - 10:24AM |
X39.00012: Absence of structural glass transition in a monoatomic model liquid predicted to undergo an ideal glass transition Matthias Troyer, Charlotte Gils, Helmut Katzgraber We study numerically a monodisperse model of interacting classical particles predicted to exhibit a static liquid-glass transition. Using a dynamical Monte Carlo method we show that the model does not freeze into a glassy phase at low temperatures. Instead, depending on the choice of the hard-core radius for the particles, the system either collapses trivially or a polycrystalline hexagonal structure emerges. [Preview Abstract] |
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