Related papers: Generation and motion of interfaces in a mass-cons…
Inspired by recent experimental observation of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particle-like inclusions which stimulate its growth. We find that…
Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…
We investigate a reaction-diffusion problem in a two-component porous medium with a nonlinear interface condition between the different components. One component is connected and the other one is disconnected. The ratio between the…
The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different dynamics…
Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory,…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases,…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by 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…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained…