Related papers: Non-equilibrium steady states with a spatial Marko…
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
This paper investigates a distributed robust Nash Equilibrium (NE) seeking problem for second-order players subject to external disturbances and uncertain dynamics while communicating via semi-Markov switching topologies. To accommodate the…
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…
A statistical model of self-organization in a generic class of one-dimensional nonlinear Schrodinger (NLS) equations on a bounded interval is developed. The main prediction of this model is that the statistically preferred state for such…
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…
We consider the extension of a tractable NEG model with a quasi-linear log utility to continuous space, and investigate the behavior of its solution mathematically. The model is a system of nonlinear integral and differential equations…
We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to…
We address the question of how a non-equilibrium steady state (NESS) is reached in the Linbdladian dynamics of an open quantum system. We develop an expansion of the density matrix in terms of the NESS-excitations, each of which has its own…
The one dimensional symmetric simple exclusion process (SSEP) is one of the very few exactly soluble models of non-equilibrium statistical physics. It describes a system of particles which diffuse with hard core repulsion on a one…
We demonstrate that the nonequilibrium steady state (NESS) of an open-system Holstein model with linear bias displays extreme sensitivity to the closed system parameters. This sensitivity is shown to correspond to avoided crossings in the…
Disordered hyperuniform structures are an exotic state of matter having suppressed density fluctuations at large length-scale similar to perfect crystals and quasicrystals but without any long range orientational order. In the past decade,…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
We present a variety of results analyzing the behavior of a class of stochastic processes --- referred to as Stochastic Hybrid Systems (SHSs) --- in or near equilibrium, and determine general conditions on when the moments of the process…
Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional…
In the 1980s it was theoretically predicted that correlations of various observables in a fluid in a non-equilibrium steady state (NESS) are extraordinarily long-ranged, extending, in a well-defined sense, over the size of the system. This…
Recent results have shown how to partition the space of Markov systems into dynamical equivalence classes. These equivalence classes structure transport properties in such a way that makes, among other features, their responses fully…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
The idea is advanced that strong perturbations of an initially equilibrium Bose-condensed gas lead to the sequence of nonequilibrium states whose order is inverse to the sequence of states arising in the process of the Bose-gas relaxation…