相关论文: A $p$-adic Reaction--Diffusion Model of Branching …

We study a reaction-diffusion model posed on two distinct spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles within a porous material. In this model, the macroscopic…

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…

The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…

We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the…

We propose a stochastic branching particle-based method for solving nonlinear non-conservative advection-diffusion-reaction equations. The method splits the evolution into an advection-diffusion step, based on a linearized Kolmogorov…

A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of…

Oscillatory Zoning (OZ) is a phenomenon exhibited by many geologically formed crystals. It is characterized by quasi periodic oscillations in the composition of a solid solution, caused by self-organization. We present a new model for OZ.…

We describe our optical and electron-microscopy observations of pearlite structures in eutectoid steels which seem to imply that the mechanisms of formation of pearlite colonies in these steels differ from those observed earlier for…

Atolls are traditionally explained as the result of coral reefs accreting around volcanic islands followed by gradual subsidence, yielding a hollow, ring-shaped rim that can extend for kilometres. However, satellite imagery shows that…

Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…

We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…

While biological crystallization processes have been studied on the microscale extensively, models addressing the mesoscale aspects of such phenomena are rare. In this work, we investigate whether the phase-field theory developed in…

We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…

In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the…

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…

Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…

Calcium and reactive oxygen species (ROS) interact with each other and play an important role in cell signaling networks. Based on the existing mathematical models, we develop an age-dependent feedback control model to simulate the…

Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during…

We investigate the qualitative behaviour of the solutions of a stochastic boundary value problem on the half-line for a nonlinear system of parabolic reaction-diffusion equations, from a numerical point of view. The model describes the…