Related papers: Non-Local Cell Adhesion Models: Steady States and …
We study the existence, bifurcations, and stability of stationary solutions for the doubly-nonlocal Fisher-KPP equation. We prove using Lyapunov-Schmidt reduction that under suitable conditions on the parameters, a bifurcation from the…
The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning…
In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence of two competing species. We provide a deeper…
A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…
Cell cell and cell matrix adhesions are fundamental in all multicellular organisms. They play a key role in cellular growth, differentiation, pattern formation and migration. Cell-cell adhesion is substantial in the immune response,…
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
We investigate the dynamics of stage II retinal waves via a dynamical system, grounded on biophysics, and analysed with bifurcation theory. We show how the nonlinear cells coupling and bifurcation structure explain how waves start,…
Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation…
The differential Adhesion Hypothesis (DAH) is a theory of the organization of cells within a tissue. In this study we introduce a stochastic model supporting the DAH, that can be seen as a continuous version of a discrete model of Graner…
In this paper we investigate pattern formation in Keller--Segel chemotaxis models over a multi--dimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its…
In this paper, we study two PDEs that generalize the urban crime model proposed by Short \emph{et al}. [Math. Models Methods Appl. Sci., 18 (2008), pp. 1249-1267]. Our modifications are made under assumption of the spatial heterogeneity of…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
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…
We study the steady states of a system of cross-diffusion equations arising from the modeling of chemotaxis with local sensing, where the motility is a decreasing function of the concentration of the chemical. In order to capture the many…