Two multiscale (hybrid) stochastic reaction-diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction-diffusion models. The first hybrid model is based on the models previously developed in the literature. The second hybrid model is based on the application of a recently developed two-regime meth...

Following classical work by Freidlin [Trans. Amer. Math. Soc. (1988) 305 665–657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504–537] and Peszat [Probab. Theory Related Fields (1994) 98 113–136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction–diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, ass...

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further th...

The spatiotemporal oscillations of the Escherichia coli proteins MinD and MinE direct cell division to the region between the chromosomes. Several quantitative models of the Min system have been suggested before, but no one of them accounts for the behavior of all documented mutant phenotypes. We analyzed the stochastic reaction-diffusion kinetics of the Min proteins for several E. coli mutants...

By discretising space into compartments and letting system dynamics be governed by the reaction–diffusion master equation, it is possible to derive simulate a stochastic model of reaction diffusion on an arbitrary domain. However, there are many implementation choices involved in this process, such as choice discretisation method derivation diffusive jump rates, not clear priori how these affec...

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, some models such as reaction–diffusion equations, p-Laplace equation porous media are established.

Oxidation reaction of CO on a single platinum crystal is a reaction-diffusion system that may exhibit bistable, excitable, and oscillatory behavior. We studied the effect of a stochastic signal artificially introduced into the system through the partial pressure of CO. First, the external signal is employed as a turbulence suppression tool, and second, it modifies the boundaries in the bistable...

We consider the control of programmable selfassembling systems whose dynamics are governed by stochastic reaction-diffusion dynamics. In our system, particles may decide the outcomes of reactions initiated by the environment, thereby steering the global system to produce a desired assembly type. We describe a method that automatically generates a program maximizing yield based on tuning the rat...

A hybrid multiscale kinetic Monte Carlo (HMKMC) method for speeding up the simulation of copper electrodeposition is presented. The fast diffusion events are simulated deterministically with a heterogeneous diffusion model which considers site-blocking effects of additives. Chemical reactions are simulated by an accelerated (tau-leaping) method for discrete stochastic simulation which adaptivel...