Session M2: Statistical and Nonlinear Systems

Flux line dynamics following current quenches in disordered type-II superconductors1

We describe the disordered vortex system in type-II superconductors with an elastic line model, whose dynamics we investigate numerically by means of Langevin Molecular Dynamics. We study the effects of sudden changes of the driving current on the time evolution of the mean flux line gyration radius and the associated transverse displacement correlation functions. Within the moving regime, we obtain fast exponential relaxation to a new non-equilibrium stationary state. Upon quenching from the moving into the pinned glassy regime, we observe algebraically slow relaxation, with breaking of time translation invariance and indications of aging scaling behavior. Furthermore, we are studying the relaxation of flux lines after quenching the driving current from the moving into the critical depinning regime besides looking at flux-line dynamics in the presence of planar disorder or twin boundaries in the superconducting sample.   

The effect of particle shape on granular flow

It has long been observed that the pressure at the bottom of a granular container, for instance a grain silo, saturates as the height of the container increases relative to its width. However, the precise effect grain shape has on the buildup of sidewall pressure is not well understood. Using a model silo, we investigated the influence of grain shape on sidewall pressure during the filling process. Our silo is 125 cm tall and 16 cm in diameter and is filled with either corn, peas, or rice via a cone shaped hopper. As the silo fills, we monitor the pressure the grains exert on four sections of the wall. We see that the corn and peas behave very differently from the rice. When using the rice, the pressure frequently reaches a peak value and then decays with time. We attribute this decay to rice's large aspect ratio which causes grains higher in the silo to jam and shield the lower grains from the weight above. However, this decay is not as pronounced when using the peas or corn. Since the peas and corn are more round, they can more easily rearrange than the irregular rice particles and are not as effective at screening the pressure.   

Aging properties of Voter models

The time dependent dynamical scaling of the autocorrelation and autoresponse functions is investigated for two different Voter models. Using Monte Carlo simulations, we investigate the scaling regime and discuss the aging properties of these models. Different non-equilibrium exponents are determined and the universality class of the models is discussed.   

Evaporation of Water in Hydrophobic Confinement

Evaporation of water from hydrophobic pockets has been thought to play an important role in many biomolecular assembly processes such as folding of globular proteins, formation of cell membranes, aggregation of fibrils etc. Hence, understanding the thermodynamics and kinetics of this phenomenon is important for delineating the underlying mechanisms of these processes. Since liquid to vapor transition of water under hydrophobic confinement is an activated event, Indirect Umbrella Sampling (INDUS) method has been applied in molecular dynamics simulation to determine the magnitude of the free energy barrier associated with the transition under varying conditions.   

Aging in a system composed of Kuramoto oscillators

The Kuramoto model has been successfully used in different contexts to describe a wide variety of synchronization patterns. In this contribution we discuss aging in a system of Kuramoto oscillators that are coupled through frustrated bonds. The system evolves in the presence of a constant or an oscillatory external field which is turned off after some waiting time. The emerging aging processes are studied through autocorrelation functions.   

Ligand-receptor binding kinetics in surface plasmon resonance cells: A Monte Carlo analysis

Surface plasmon resonance (SPR) chips are widely used to measure association and dissociation rates for the binding kinetics between two species of chemicals, e.g., cell receptors and ligands. It is commonly assumed that ligands are spatially well mixed in the SPR region, and thus a mean-field rate equation description is appropriate. This approximation ignores the spatial fluctuations and temporal correlations induced by local rebinding events, which become prominent for slow diffusion rates and high binding rates. We report detailed Monte Carlo simulations of ligand binding kinetics in an SPR cell subject to laminar flow. We extract the binding dynamics by means of the techniques employed in experimental analysis that are motivated by the mean-field approximation. We find major discrepancies in a wide parameter ramge between the thus extracted rates and the known input simulation values. These results underscore the crucial quantitative importance of spatio-temporal correlations in binary reaction kinetics in SPR cell geometries, and demonstrate the failure of a mean-field analysis of SPR cells in the regime of high association rates, where the spatio-temporal correlations due to diffusive transport and ligand-receptor rebinding events dominate the dynamics of SPR systems.   

A numerical study of coarsening in the two-dimensional complex Ginzburg-Landau equation

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose-Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate the coarsening dynamics following a quench from a strongly fluctuating defect turbulence phase to a long-range ordered phase. We start from a simplified amplitude equation, solve it numerically, and then study the spatio-temporal behavior characterized by the spontaneous creation and~ annihilation of topological defects (spiral waves). We check our simulation results against the known dynamical phase diagram in this non-equilibrium system, tentatively analyze the coarsening kinetics following sudden quenches between different phases, and have begun to characterize the ensuing aging scaling behavior. ~   

Computational study of a multi-species predator-prey system in the presence of mutation and natural selection

With the purpose of studying mechanistic origins of biodiversity, computational experiments are performed on a predator-prey community of two predator species competing for prey. Predator individuals are assigned predation efficiency, for which Darwinian evolutionary adaptation is introduced. Competing for their limited prey drives predators' predation efficiency to optimized high values. This natural selection strongly impacts the population dynamics and evolutionary dynamics so that one predator species will go extinct asymptotically. We emphasize the importance of direct competition between the two predator species to establish stable coexistence for all three species in the system.   

A Field-Theoretic Analysis Of A Cyclic Predator-Prey System (May-Leonard Model)

Spatially extended stochastic population dynamics models with cyclic predation interactions display intriguing time evolution and spontaneous structure formation. We study a general May-Leonard cyclic competition model in d dimensions with diffusive particle propagation. We use the second-quantized Doi-Peliti formalism and ensuing coherent-state path integral representation to construct its continuum representation and explore its collective dynamics. Expanding the resulting action about the mean-field species concentrations enables us to compute the diagonalized harmonic propagators and hence 'masses', i.e., relaxation rates and eigenfrequencies of the fundamental modes. Furthermore, operating near the Hopf bifurcation point, we identify the validity range for the necessary time scale separation that allows us to project out the purely relaxing eigenmode. The remaining oscillating fields obey the complex Ginzburg-Landau equation, which is consistent with spiral pattern formation.