Related papers: An integration scheme for reaction-diffusion model…
A kinetic description of lattice-gas automaton models for reaction-diffusion systems is presented. It provides corrections to the mean-field rate equations in the diffusion-limited regime. When applied to the two-species Maginu model, the…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed…
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
The accurate and robust simulation of transcritical real-fluid flows is crucial for many engineering applications. Diffused interface methods are frequently employed and several numerical schemes have been developed for simulating…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
Based on the superconvergent approximation at some point (depending on the fractional order $\alpha$, but not belonging to the mesh points) for Gr\"{u}nwald discretization to fractional derivative, we develop a series of high order…
A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
A novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations is introduced. The new methods outperform existing schemes for relatively high Peclet number due to their favorable…
A system of a parabolic partial differential equation coupled with ordinary differential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn diffusion reaction model is studied. A…