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The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…
We present a fully adaptive multiresolution scheme for spatially two-dimensional, possibly degenerate reaction-diffusion systems, focusing on combustion models and models of pattern formation and chemotaxis in mathematical biology.…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
We extend the application of the adaptive resolution technique (AdResS) to liquid systems composed of alkane chains of different lengths. The aim of the study is to develop and test the modifications of AdResS required in order to handle…
A graph reaction--diffusion (RD) equation is a system of differential equations that is defined on the nodes of a graph. Consider a sequence of growing graphs that converges in cut norm to a limiting graphon. We show that the solutions of…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…
We describe a method to obtain the reduced density matrix (RDM) correct up to second order in system-bath coupling in \emph{nonequilibrium} steady state situations. The RDM is obtained via a scheme based on analytic continuation, using the…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
The Drift-Diffusion Model (DDM) is widely used in neuropsychological studies to understand the decision process by incorporating both reaction times and subjects' responses. Various models have been developed to estimate DDM parameters,…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
We show that discrete distributions on the $d$-dimensional non-negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks. We…
Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle…
Wetting and dewetting dynamics of simple and complex liquids is described by kinetic equations in gradient dynamics form that incorporates the various coupled dissipative processes in a fully thermodynamically consistent manner. After…
In this paper, a boundary scheme is proposed for the two-dimensional five-velocity (D2Q5) lattice Boltzmann method with heterogeneous surface reaction, in which the unknown distribution function is determined locally based on the kinetic…
Computational systems biology has provided plenty of insights into cell biology. Early on, the focus was on reaction networks between molecular species. Spatial distribution only began to be considered mostly within the last decade.…