Related papers: Homogenization Theory of Ion Transportation in Mul…
Metabolic substrates, such as oxygen and glucose, are rapidly delivered to the cell through filtration across microvessels walls. Modelling this important process is complicated by the coupling between flow and transport equations, which…
We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-mechanical setting, by promoting the design of unit cells characterized both by an…
Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly-interacting environment, leading to the formation of discrete layers of charges at interfaces. Here, we propose a continuum theory that captures the…
The study explores perpendicular transport through macroscopically inhomogeneous three-dimensional disordered conductors using mesoscopic methods (real-space Green function technique in a two-probe measuring geometry). The nanoscale samples…
In this paper we establish a homogenization result for a doubly nonlinear parabolic system arising from the hygro-thermo-chemical processes in porous media taking into account memory phenomena. We present a meso-scale model of the composite…
This paper presents a new homogenized model of two-component electrolyte transport through a weakly piezoelectric porous medium. The model relevant to the microscopic scale describes quasi-stationary states of the medium while reflecting…
Mathematical modeling is an important theoretical tool which provides researchers with quantification of the permeability of dialyzing systems in renal replacement therapy. In the paper we provide a short review of the most successful…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing…
Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different…
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…
Biological functionality of cellular aggregates is largely influenced by the activity and displacements of individual constituent cells. From a theoretical perspective this activity can be characterized by hydrodynamic transport…
The paper addresses the homogenization of a family of micro-models for the flow of a slightly compressible fluid in a poroelastic matrix containing periodically distibuted poroelastic inclusions, with low permeabilities and with imperfect…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
Multicellular organisms comprise a diverse collection of stable tissues built from different cell types. It remains unclear how large numbers of interacting cells can precisely coordinate their gene expression during tissue…
A gap in understanding the link between continuum theories of ion transport in ionic liquids and the underlying microscopic dynamics has hindered the development of frameworks for transport phenomena in these concentrated electrolytes.…
We explore an idealized theoretical model for the transport of ions within highly asymmetric ionic liquid mixtures. A primitive model (PM)-inspired system serves as a representative for asymmetric ionic materials (such as liquid crystalline…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion, which controls cellular functionality. Here, we investigated two…
Electrical neural signalling typically takes place at the time-scale of milliseconds, and is typically modeled using the cable equation. This is a good approximation for processes when ionic concentrations vary little during the time course…