Related papers: Pattern stability in reaction-diffusion systems de…
Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…
We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…
This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically,…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the…
This paper considers the problem of stabilizing a discrete-time non-linear stochastic system over a finite capacity noiseless channel. Our focus is on systems which decompose into a stable and unstable component, and the stability notion…
Equilibrium statistical mechanics provides a robust framework for characterizing phase transitions in systems whose microsopic dynamics are time-reversible. Efforts to develop and validate theoretical frameworks for time-irreversible,…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…
Nonequilibrium conditions fundamentally change how systems undergo phase separation. In systems with temperature gradients, attractive particles have been shown to form periodic patterns and steady convective currents, but a clear…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…
Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities such as matter, energy and charge flow from outer reservoirs across a system, and how they irreversibly degrade from one form to another. Stochastic…