7 Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. 9 To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system ẋ(t)=f(x(t)) into the Itô form dx(t)=f(x(t)) dt + g(x(t)) dw(t), and show that 11 although the ...

Aerosol filtration in fibrous filters is one of the principal methods of removal of solid particles from the gas stream. The classical theory of depth filtration is based on the assumption of existing single fiber efficiency, which may be used to the recalculation of the overall efficiency of the entire filter. There are several reasons for inappropriate estimation of the single fi...

Abstract. The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk increments, leads to some natural dynamics. In this paper we consider the corresponding dynamics for the Brownian web. In particular, pairs of coupled Brow...

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, s...

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are...