Related papers: Interrelations between Stochastic Equations for Sy…
This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
The aim of this paper is to prove results about the existence and stability of multiple steady states in a system of ordinary differential equations introduced by R. Lev Bar-Or to model the interactions between T cells and macrophages.…
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably…
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…
We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast $J$ = 0, 2, 4, 6, 8 states. Previous studies, limited only to $J$ =…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
Extending the stochastic mean-field model by including pairing, an approach is proposed for describing evolutions of complex many-body systems in terms of an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is…
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary…
We consider a stochastic, continuous state and time opinion model where each agent's opinion locally interacts with other agents' opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of…
The past two decades have seen a revolution in statistical physics, generalizing it to apply to systems of arbitrary size, evolving while arbitrarily far from equilibrium. Many of these new results are based on analyzing the dynamics of the…
A thermodynamics for systems at a stationary states is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density ans its conjugated nonequilibrium…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We…