Related papers: Stochastically forced cardiac bidomain model
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…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
In this note, we study an infinite reaction network called the stochastic Becker-D\"oring process, a sub-class of the general coagulation-fragmentation models. We prove pathwise convergence of the process towards the deterministic…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity, such as wave re-entry caused by ischaemia. In terms of mathematical modelling, the…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac Bidomain model, describing the propagation of the electric impulse in the cardiac tissue.…
We analyze energy spreading for a system that features mixed chaotic phase-space, whose control parameters (or slow degrees of freedom) vary quasi-statically. For demonstration purpose we consider the restricted 3~body problem, where the…
We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. We establish existence of martingale solutions which are strong in the PDE sense and study their large-time behavior. Our…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
This paper concerns with existence, uniqueness and asymptotic behavior of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…