相关论文: Stochastically forced cardiac bidomain model

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…

This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between…

A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential…

Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational…

Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. These types of systems are often modelled by a system of…

The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in $\mathbb{R}^{3}$ with large initial…

Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…

We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…

This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions,…

We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii)…

The existence of global nonnegative martingale solutions to a stochastic cross-diffusion system for an arbitrary but finite number of interacting population species is shown. The random influence of the environment is modeled by a…

This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's…

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…

When modelling tissue-level cardiac electrophysiology, continuum approximations to the discrete cell-level equations are used to maintain computational tractability. One of the most commonly used models is represented by the bidomain…

We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…

In this paper we study the class of backward doubly stochastic differential equations (BDSDEs, for short) whose terminal value depends on the history of forward diffusion. We first establish a probabilistic representation for the spatial…

In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based…