相关论文: Particle-based simulations of reaction-diffusion p…

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarse-grained deterministic…

Computational modelling is helpful for elucidating the cellular mechanisms driving biological morphogenesis. Previous simulation studies of blood vessel growth based on the Cellular Potts model (CPM) proposed that elongated, adhesive or…

We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…

Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply…

Among the multiple causes of high error rates in spreadsheets, lack of proper training and of deep understanding of the computational model upon which spreadsheet computations rest might not be the least issue. The paper addresses this…

In assumed probability density function (pdf) methods of turbulent combustion, the shape of the scalar pdf is assumed a priori and the pdf is parametrized by its moments for which model equations are solved. In non-premixed flows the beta…

Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed,…

Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from…

The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the…

This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…

This perspective paper deals with an overview of particle-in-cell / Monte Carlo collision models applied to different plasma-propulsion configurations and scenarios, from electrostatic (E x B and pulsed arc) devices to electromagnetic (RF…

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such…

The calcium transport in biological systems is modelled as a reaction-diffusion process. Nonlinear calcium waves are then simulated using a stochastic cellular automaton whose rules are derived from the corresponding coupled partial…

This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…

In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…

We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…

In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…

For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…

In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in human organism with a deficient immune system, during…