Bulletin of the American Physical Society
80th Annual Meeting of the APS Southeastern Section
Volume 58, Number 17
Wednesday–Saturday, November 20–23, 2013; Bowling Green, Kentucky
Session DC: Statistical and NonLinear Physics 
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Chair: Sanju Gupta, Western Kentucky University Room: 2 
Thursday, November 21, 2013 1:30PM  1:42PM 
DC.00001: Extinction in four species cyclic competition Ben Intoy, Michel Pleimling When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. We study through numerical simulations the extinction processes that can take place in this system both in the well mixed case as well as on different types of lattices. The different routes to extinction are revealed by the probability distribution of the domination time, i.e. the time needed for one team to fully occupy the system. If swapping is allowed between neutral partners, then the probability distribution is dominated by very longlived states where a few very large domains persist, each domain being occupied by a mix of individuals from species that form one of the teams. Many aspects of the possible extinction scenarios are lost when only considering averaged quantities as for example the mean domination time.\\[4pt] [1] B. Intoy and M. Pleimling, J. Stat. Mech (2013) P08011. [Preview Abstract] 
Thursday, November 21, 2013 1:42PM  1:54PM 
DC.00002: Network Reliability: A novel betweenness measure using structural motifs Yasamin Khorramzadeh, Stephen Eubank, Mina Youssef This paper applies the concept of network reliability, introduced by Moore and Shannon in 1956, for studying the effect of network structure on the spread of diseases. We exhibit a representation for the reliability polynomial in terms of what we call structural motifs that is well suited for reasoning about the effect of a network's structural properties on diffusion across the network. We illustrate by deriving several general results relating graph structure to dynamical consequences. We conclude by exploring a novel centrality measure based on structural motifs. [Preview Abstract] 
Thursday, November 21, 2013 1:54PM  2:06PM 
DC.00003: Dynamics of the Ising model on lattices in the hyperbolic plane Howard L. Richards Over the past few years, students at the REU in computational physics at Marshall University have studied the dynamics of the Ising model on lattices in the hyperbolic plane, in particular metastable decay and domain coarsening. In both cases the dynamics are slower than on the corresponding Euclidean lattices. The Ising model with shortranged interactions on a regular lattice has a spinodal in the hyperbolic plane  meaning that below a nonvanishing magnetic field, the time required for an infinite system to experience metastable decay diverges; in the Euclidean plane this divergence only happens at zero magnetic field. In domain coarsening, feature size grows as $t^{0.13}$ in the hyperbolic plane, but as $t^{1/3}$ in the Euclidean plane. The former result can be explained quantitatively and the latter qualitatively in terms of the differences between hyperbolic and Euclidean circles. [Preview Abstract] 
Thursday, November 21, 2013 2:06PM  2:18PM 
DC.00004: Nonequilibrium relaxation properties of vortex lines in disordered typeII superconductors Hiba Assi, Ulrich Dobramysl, Michel Pleimling, Uwe C. T\"{a}uber Technological applications of typeII superconductors require a deep understanding of the properties of vortex matter in these disordered systems. This involves a careful investigation of the relaxation properties of interacting vortex systems, subject to randomly placed point or correlated columnar pinning sites, from an initial outofequilibrium state. We model the vortices in the London limit as interacting elastic lines, and employ a Langevin molecular dynamics algorithm to simulate their dynamics. We aim to disentangle the effects of flux line interactions and pinning centers, and to compare the system's relaxation features in the presence of point or columnar disorder. Furthermore, we consider experimentally more realistic initial conditions by applying magnetic field quenches, i.e., suddenly adding or removing vortex lines. We study various twotime correlation functions to study magnetic field quenches, and carefully analyze finitesize effects on the system relaxation. [Preview Abstract] 

DC.00005: ABSTRACT WITHDRAWN 
Thursday, November 21, 2013 2:30PM  2:42PM 
DC.00006: Break

Thursday, November 21, 2013 2:42PM  2:54PM 
DC.00007: A mean field approach to $Z_N$enhanced generalized MayLeonard models Shahir Mowlaei, Ahmed Roman, Michel Pleimling MayLeonard (ML) models have been used to describe the rich dynamics of a range of systems in biology and ecology. In this report we study a class of extended cyclic ML models of N species in the mean field limit, enhanced with $Z_N$ symmetry, and investigate the space of their (unstable) coexistence fixed points. We start with a brief review of the well studied ML model of three species, expand on the generalized class and provide expressions for the unstable invariant manifold near single fixed points of a subclass of the mentioned extensions. For the purely cyclic ML model with an odd number of species we derive the complex GinzburgLandau normal form. [Preview Abstract] 
Thursday, November 21, 2013 2:54PM  3:06PM 
DC.00008: Magnetic friction between two threedimensional Potts systems Linjun Li, Michel Pleimling Magnetic systems, whose surfaces are coupled by boundary spins, experience magnetic friction if one system is moving with a relative velocity along the coupled surface. In our research, we focus on systems consisting of two threedimensional (3D) magnetic Potts blocks as well as on the systems consisting of one 3D magnetic Potts wedge and one 3D magnetic Potts block. We study cases where the total number of Potts states rang from two (Ising case) to nine. By varying the strength of the coupling between the two contacting layers and/or the value of the relative velocity, we find interesting nonequilibrium behavior emerging at the contacting surfaces and tips. [Preview Abstract] 
Thursday, November 21, 2013 3:06PM  3:18PM 
DC.00009: FiniteTime Dynamic Systems 'Kale Oyedeji, Ronald E. Mickens While the mathematical models of many important physical systems have dynamics taking place over an infinite time interval, in practice these systems cease their ``actions'' in finite times. Particular examples of such systems include a liquid flowing out of a hole in the side of a cylinder, the oscillations of a nonlinear vibrator, the cooling and/or heating of an object in a constant temperature environment, and a particle acted upon only by a purely resistive force. We show that all these cases can be unified within the framework of a single mathematical structure. We also discuss and examine closely the role played by the existence and uniqueness theorems of differential equations, and why, in spite of the fact that the usual conditions do not hold, unique solutions do exist, and this is fully in agreement with the physics controlling the dynamics of these systems. [Preview Abstract] 
Thursday, November 21, 2013 3:18PM  3:30PM 
DC.00010: Analytical Integral Solution of Inverse Lagrangian Problems via Heaviside Operational Schemes Valentino A. Simpao In this brief note, a relatively straightforward method for exact integral solution of ILP [Inverse Lagrangian Problems] is presented. An exact quadrature solution (i.e., Lagrangian) of the Inhomogeneous Lagrange Equation [ILE] is constructed for given inhomogeneous term of arbitrary dependence upon its arguments, via Heaviside operational schemes. Thus an inverse ILE problem is solved: a Lagrangian obtains in the form of an integral of the arbitrarily prescribed inhomogeneous term. [Preview Abstract] 
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