Session P2: Invited Session: Large Fluctuations Far From Equilibrium

Characterizing Order in Glassy Systems

Crystals and quasicrystals can be characterized by an order that is a purely geometric property of an instantaneous configuration, independent of particle dynamics or interactions. Glasses, on the other hand, are ostensibly amorphous arrangements of particles. A natural and long-standing question has been whether they too have, albeit in a hidden way, some form of geometric order. I will examine a recent proposal for a coherence length that applies to systems which are typically characterized as amorphous, as well as to those that are conventionally ordered. The question of whether exotic order can arise in physical systems will be addressed.   

Drift, diffusion and barrier crossing of small objects on a surface assisted by an external noise: roles of non-linear friction

We study experimentally the behaviors of several driven diffusive systems that involve the sliding and rolling of small solid objects or liquid drops on a surface with an external noise and an external field. The displacement statistics here are non-Gaussian at short observation time, but they tend towards a Gaussian behavior at long time scale. Furthermore, in each of these cases, the drift velocity increases sub-linearly, but the diffusivity increases super-linearly with the strength of the noise. These observations reflect the underlying non-linear friction control of their stochastic dynamics. Specific experiments have also been designed to study the hopping of a small object over a physical barrier assisted by an external noise. These results mimic the classical Arrhenius behavior from which an effective temperature may be deduced. However, the regimes controlled by a Coulombic like friction and a linear kinematic friction need to be treated somewhat differently. All the drifted diffusive systems studied here exhibit substantial negative fluctuations of displacement at a short observation time that diminishes at longer time scale. Using the integrated fluctuation theorem, we characterize the persistence time of negative fluctuations in terms of the diffusivity and the drift velocity that can be measured experimentally.   

Noise induced stabilization in population dynamics

We investigate a model where strong noise in a sub-population creates a metastable state in an otherwise unstable two-population system. The induced metastable state is vortex-like, and its persistence time grows exponentially with the noise strength. A variety of distinct scaling relations are observed depending on the relative strength of the sub-population noises.   

Speeding up spontaneous disease extinction

The dynamics of epidemic in a susceptible population is affected both by the random character of interactions between the individuals and by environmental variations. As a consequence, the sizes of the population groups (infected, susceptible, etc.) fluctuate in the course of evolution of the epidemic. In a small community a rare large fluctuation in the number of infected can result in extinction of the disease. We suggest a novel paradigm of controlling the epidemic, where the control field, such as vaccination, is designed to maximize the rate of spontaneous disease extinction. We show that, for a limited-scope vaccination, the optimal vaccination protocol and its impact on the epidemics have universal features: (i) the vaccine must be applied in pulses, (ii) the spontaneous disease extinction is synchronized with the vaccination. We trace this universality to general properties of the response of large fluctuations to external perturbations.   

Cooperativity-Driven Singularities in Cooperative Asymmetric Exclusion

We investigate the effect of cooperative interactions on the asymmetric exclusion process. In the simplest case a particle can hop to its vacant right neighbor only if its left neighbor is occupied. We show that an initial density downstep develops into a rarefaction wave that can have a jump discontinuity at the leading edge, while an upstep results in a shock wave. We also investigate a more general model in which the particle velocity can be an increasing function of the density. Within a hydrodynamic theory, initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves. These unusual phenomena arise because the current versus density relation has an inflection point, so that the group velocity can either be an increasing or a decreasing function of the density on either side of the inflection point.