Related papers: Algorithm for Mesoscopic Advection-Diffusion
The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded)…
In molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this work, we show a novel approach where the latest version of the…
Typical multispecies compressible Navier-Stokes computations employ conservative equations for mass fraction transport. Upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces…
There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…
We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…
When comparing measurements to numerical simulations of moisture transfer through porous materials a rush of the experimental moisture front is commonly observed in several works shown in the literature, with transient models that consider…
Reaction-diffusion equations are often used in epidemiological models. In this paper we generalize the algorithm of Meerschaert and Tadjeran for fractional advection-dispersion flow equations to a coupled system of fractional…
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.…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
Various biological processes such as transport of oxygen and nutrients, thrombus formation, vascular angiogenesis and remodeling are related to cellular/subcellular level biological processes, where mesoscopic simulations resolving detailed…
In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore…
Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
The interaction potential between two colloidal particles typically spans a few nanometers. Hence the correct appraisal of the potential in simulations requires very short time steps. However, it is often possible to combine one…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of…
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on a two-range pseudo-potential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short range repulsive…