Bulletin of the American Physical Society
78th Annual Meeting of the Southeastern Section of the APS
Volume 56, Number 9
Wednesday–Saturday, October 19–22, 2011; Roanoke, Virginia
Session HB: Statistical and Nonlinear Physics I |
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Chair: Michel Pleimling, Virginia Polytechnic Institute and State University Room: Crystal Ballroom B |
Friday, October 21, 2011 10:45AM - 10:57AM |
HB.00001: Boundary conflicts and cluster coarsening: Waves of life and death in the cyclic competition of four species Ahmed Roman, Michel Pleimling In the cyclic competition among four species on a two-dimensional lattice, the partner particles, which swap positions on the lattice with some probability, produce clusters with a length that grows algebraically as $t^1/z$ where $z$ is the dynamical exponent. Further investigation of the dynamics at the boundary of the clusters is realized by placing one partner particle pair in the upper half of the system and the other pair in the lower half. Using this technique, results about the fluctuations of the interface are obtained. We also observe wave fronts in the case of non-symmetric reaction rates where extinction of a partner particle pair takes place. [Preview Abstract] |
Friday, October 21, 2011 10:57AM - 11:09AM |
HB.00002: Stochastic evolution of four species in cyclic competition: exact and simulation results Sara Case, Clinton Durney, Michel Pleimling, R.K.P. Zia We study a stochastic system with $N$ individuals, consisting of four species competing cyclically: $A+B \longrightarrow A+A$, $\cdots$, $D+A \longrightarrow D+D$. Randomly choosing a pair and letting them react, $N$ is conserved but the fractions of each species evolve non-trivially. At late times, the system ends in a static, absorbing state $-$ typically, coexisting species $AC$ or $BD$. The master equation is shown and solved exactly for $N=4$, providing a little insight into the problem. For large $N$, we rely on simulations by Monte Carlo techniques (with a faster dynamics where a reaction occurs at every step). Generally, the results are in good agreement with predictions from mean field theory, after appropriate rescaling of Monte Carlo time. The theory fails, however, to describe extinction or predict their probabilities. Nevertheless, it can hint at many remarkable behavior associated with extinction, which we discover when studying systems with extremely disparate rates. [Preview Abstract] |
Friday, October 21, 2011 11:09AM - 11:21AM |
HB.00003: The effects of mobility on the one-dimensional four-species cyclic predator-prey model David Konrad, Michel Pleimling The dynamics of a one-dimensional lattice composed of four species cyclically dominating each other is very much dependent on the rates of mobility in the system. We realize mobility as the exchange of two particles located at two nearest neighbor sites with some species dependent rate $s$. Allowing for only one particle per site, the different species interact cyclically, with species dependent consumption rate $k$, such that $k + s \leq 1$. When varying the exchange rates, we see vastly different behavior when compared to the three-species model. The patterns of domain growth and decay still show an overall power law behavior, however the fundamental trend of domain growth does not follow the three-species case. We also look at the space-time diagrams to see precisely how the domains form, grow, and decay. [Preview Abstract] |
Friday, October 21, 2011 11:21AM - 11:33AM |
HB.00004: Quenched Spatial Disorder in Cyclic Three-Species Predator-Prey Models Qian He, Uwe C. Tauber We employ individual-based Monte Carlo simulations to study the effects of quenched spatial disorder in the reaction rates on the co-evolutionary dynamics of cyclic three- species predator-prey models with conserved total particle density. To this end, we numerically explore the oscillatory dynamics of two different variants: (1) the model with symmetric interaction rates near the center of the configuration space, and (2) a strongly asymmetric model version located in one of the three ``corners'' of configuration space. We find that spatial rate variability has only minor effect on the dynamics of generic, not strongly asymmetric systems (variant 1). In stark contrast, spatial disorder can greatly enhance the fitness of both minor species in ``corner'' systems (2). Furthermore, through both mean-field analysis and numerical simulation, we conclude that the evolutionary dynamics of two-species Lotka-Volterra predator- prey models is well approximated by such strongly asymmetric cyclic three-species predator-prey systems. Refs.: Qian He, Mauro Mobilia, and Uwe C. Tauber, Phys. Rev. E 82, 051909 (2010); Qian He and Uwe C.Tauber, in preparation (2011). [Preview Abstract] |
Friday, October 21, 2011 11:33AM - 11:45AM |
HB.00005: Epidemic spreading on preferred degree adaptive networks Shivakumar Jolad, Wenjia Liu, R.K.P. Zia, Beate Schmittmann We report our study of SIS epidemic spreading model on networks where individuals have a fluctuating number of connections around some preferred degree. By making our preferred degree depend on the level of infection, we model the response of individuals to the prevailing epidemic. This helps us to explore the feedback mechanisms between the dynamics on the network and dynamic of the network. We will discuss the effect of such feedback mechanisms on the SIS phase diagram. We have also explored the SIS model on two communities with a coupling between them. [Preview Abstract] |
Friday, October 21, 2011 11:45AM - 11:57AM |
HB.00006: Aging behavior in disordered systems Hyunhang Park, Michel Pleimling Using Monte Carlo simulations we investigate aging behavior during phase ordering in two-dimensional Ising models with disorder and in three-dimensional Ising spin glasses. The time-dependent dynamical correlation length $L(t)$ is determined numerically and the scaling behavior of various two-time quantities as a function of $L(t)/L(s)$ is discussed. For disordered Ising models deviations of $L(t)$ from the algebraic growth law show up. The generalized scaling forms as a function of $L(t)/L(s)$ reveal a simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. [Preview Abstract] |
Friday, October 21, 2011 11:57AM - 12:09PM |
HB.00007: Time-dependent mechanical response of the cytoskeleton Nasrin Afzal, Michel Pleimling Motivated by a series of experiments that study the response of the cytoskeleton in living cells to time-dependent mechanical forces, we investigate, through Monte Carlo simulations, a three-dimensional network subjected to perturbations. After having prepared the system in a relaxed state, shear is applied and the relaxation processes are monitored. We measure two time quantities and discuss the possible implications of our results for relaxation processes taking place in the cytoskeleton. [Preview Abstract] |
Friday, October 21, 2011 12:09PM - 12:21PM |
HB.00008: Drop Formation from a Wettable Nozzle Brian Chang, Gary Nave, Sunghwan Jung Drop formation from a nozzle is a common occurrence in our daily lives. It is essential in ink-jet printers and spray cooling technology. However, most research has already been done on the pinch-off mechanism from a non-wettable nozzle. In this study, we focus on the formation of a drop from a wettable nozzle. Initially, a drop will climb the outer walls of the wettable nozzle because of surface tension. This initial upward motion is closely related to the capillary rise phenomenon. Then, when the weight of the drop becomes large enough, the force of gravity would overcome surface tension causing the drop to fall. By changing the nozzle size and fluid flow rate, we have observed different behaviors of the droplets and developed a mathematical model that predicts the motion of the drop. Two asymptotic solutions in the initial and later stages of drop formation are then obtained and show good agreement with the experimental observations [Preview Abstract] |
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