Related papers: Reaction-diffusion systems derived from kinetic th…
Multi-agent systems can be successfully described by kinetic models, which allow one to explore the large scale aggregate trends resulting from elementary microscopic interactions. The latter may be formalised as collision-like rules, in…
Multiple Sclerosis is a degenerative condition of the central nervous system that affects nearly 2.5 million of individuals in terms of their physical, cognitive, psychological and social capabilities. Researchers are currently…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…
We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the…
We develop an general formalism of single enzyme kinetics in two dimension where substrates diffuse stochastically on a square lattice in presence of disorder. The dynamics of the model could be decoupled effectively to two stochastic…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
We provide a short historic of the early development of kinetic theory in plasma physics and synthesize the basic kinetic equations describing the evolution of systems with long-range interactions derived in Paper I. We describe the…
We discuss many-body fermionic and bosonic systems subject to dissipative particle losses in arbitrary spatial dimensions $d$, within the Keldysh path-integral formulation of the quantum master equation. This open quantum dynamics…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as…
A model multilevel molecule described by two sets of rotational internal energy levels of different parity and degenerate ground states, coupled by a constant interaction, is considered, by assuming that the random collisions in a gas of…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…