Related papers: A stochastic min-driven coalescence process and it…
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…
We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not…
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule…
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…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
Small systems in a thermodynamic medium --- like colloids in a suspension or the molecular machinery in living cells --- are strongly affected by the thermal fluctuations of their environment. Physicists model such systems by means of…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
The dynamics of an infinite system of point particles in $\mathbb{R}^d$, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of…
We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…
The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase field crystal free…
The coagulation of cosmic dust grains is a fundamental process which takes place in astrophysical environments, such as presolar nebulae and circumstellar and protoplanetary disks. Cosmic dust grains can become charged through interaction…