相关论文: Particle-based simulations of reaction-diffusion p…
We introduce and analyse a mathematical model describing the dynamics of particles generated by charge-exchange interactions. The model extends the well-established exchange-driven growth model, previously studied in several works, by…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…
This paper gives an overview of the particle transport theory essentials, the basics of particle-material interaction simulation, physical quantities needed to simulate particle transport and interactions in materials, Monte Carlo…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
A new approach to simulating warm and hot dense matter that combines density functional theory based calculations of the electronic structure to classical molecular dynamics simulations with pair interaction potentials is presented. The new…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…
In this paper, we present a novel numerical framework for solving a specific biological reaction-diffusion-advection system of cancer growth in three dimensions (3D) using particles of variable mass. We adopt empirical particle measures to…
-Molecular simulations allow the study of properties and interactions of molecular systems. This article presents an improved version of the Adaptive Resolution Scheme that links two systems having atomistic (also called fine-grained) and…
"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address…
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…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…
In this paper, we survey five different computational modeling methods. For comparison, we use the activation cycle of G-proteins that regulate cellular signaling events downstream of G-protein-coupled receptors (GPCRs) as a driving…
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…