Related papers: Adaptive two-regime method: application to front p…
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal…
The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provided that the reaction rate is large enough. The wavefront…
Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…
In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution). aims: This paper provides theoretical…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
We introduce a distribution-free lattice Boltzmann formulation for general compartmental reaction--diffusion systems arising in mathematical epidemiology. The proposed scheme, termed a single-step simplified lattice Boltzmann method…
In this paper, we address the modeling issues of cell movement and division with a special focus on the phenomenon of volume exclusion in a lattice-based, exact stochastic simulation framework. We propose a new exact method, called Reduced…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…
We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…
Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…
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…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
Suspension flows are ubiquitous in nature (hemodynamics, subsurface fluid mechanics, etc.) and industrial applications (hydraulic fracturing, CO$_2$ storage, etc.). However, such flows are notoriously difficult to model due to the variety…
Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…
Wildland fires are complex multi-physics problems that span wide spatial scale ranges. Capturing this complexity in computationally affordable numerical simulations for process studies and "outer-loop" techniques (e.g., optimization and…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
With a purpose of constructing a robust evolution system against numerical instability for integrating the Einstein equations, we propose a new formulation by adjusting the ADM evolution equations with constraints. We apply an adjusting…