Related papers: Homogenization results for a coupled system of rea…
Fluid flow through bimodal porous media, characterized by a distinct separation in pore size distribution, is critical in various scientific and engineering applications, including groundwater management, oil and gas production, and carbon…
Exchange of biochemical substances is essential way in establishing communication between bacterial cells. It is noticeable that all phases of the process are heavily influenced by perturbations of either internal or external parameters.…
We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal…
Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
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…
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
The cytoplasm of a living cell is crowded with several macromolecules of different shapes and sizes. Molecular diffusion in such a medium becomes anomalous due to the presence of macromolecules and diffusivity is expected to decrease with…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…