Related papers: An Allen-Cahn equation with jump-diffusion noise f…
We investigate a stochastic version of the Allen-Cahn-Navier-Stokes system in a smooth two- or three-dimensional domain with random initial data. The system consists of a Navier-Stokes equation coupled with a convective Allen-Cahn equation,…
The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we…
We consider the stochastic Allen--Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$, and study the semidiscretisation in time of the equation by an Euler type split-step…
We study the long-time behaviour of a stochastic Allen-Cahn-Navier-Stokes system modelling the dynamics of binary mixtures of immiscible fluids. The model features two stochastic forcings, one on the velocity in the Navier-Stokes equation…
Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…
We consider a system of stochastic Allen-Cahn equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative Gaussian noise driven stochastic Allen-Cahn equation is given with possibly different…
Descriptions of complex physical or biological systems often include stochastic contributions, and these are commonly simulated using Wiener processes. In many cases however, non-Gaussian fluctuations may originate from non-Wiener processes…
We prove existence and uniqueness of a solution for the stochastic Allen-Cahn equation with logarithmic potential and multiplicative Wiener noise, under homogeneous Neumann boundary condition. The existence of a solution is obtained in the…
A typical phase field approach for describing phase separation and coarsening phenomena in alloys is the Cahn-Hilliard model. This model has been generalized to the so-called Cahn-Larch\'e system by combining it with elasticity to capture…
This paper is devoted to the global well-posedness of two Diffuse Interface systems modeling the motion of an incompressible two-phase fluid mixture in presence of capillarity effects in a bounded smooth domain $\Omega\subset \mathbb{R}^d$,…
This paper studies the sharp interface limit for a mass conserving Allen-Cahn equation added an external noise and derives a stochastically perturbed mass conserving mean curvature flow in the limit. The stochastic term destroys the precise…
We study the steady states and the coarsening dynamics in a one dimensional driven non-conserved system modelled by the so called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In…
In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the…
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to…
We study the asymptotics of Allen-Cahn-type bistable reaction-diffusion equations which are additively perturbed by a stochastic forcing (time white noise). The conclusion is that the long time, large space behavior of the solutions is…
We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds…
We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one…
This study presents a novel coupled mechano-electro-chemical formulation for predicting stress corrosion cracking (SCC) phenomena in steel structures using the phase field method. SCC is a complex damage process that arises from the…
This article analyzes an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise, in a bounded spatial domain with smooth boundary in dimension $d\le 3$. The splitting strategy is…