Related papers: Nonlocal Adhesion Models for Microorganisms on Bou…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type have long been used in tissue modelling. In 2006, Armstrong,…
Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue…
Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
Local well-posedness is established for a highly nonlocal nonlinear diffusion-adhesion system for bounded initial values with small support. Macroscopic systems of this kind were previously obtained by the authors through upscaling in [32]…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
In this paper we address the analytical investigation of a model for adhesive contact, which includes nonlocal sources of damage on the contact surface, such as the elongation. The resulting PDE system features various nonlinearities…
We investigate a continuum mechanical model for an adherent cell on two dimensional adhesive micropatterned substrates. The cell is modeled as an isotropic and homogeneous elastic material subject to uniform internal contractile stresses.…
We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The…
We study the (generalized) one-dimensional population model developed by Anguige \& Schmeiser [1], which reflects cell-cell adhesion and volume filling under no-flux boundary condition. In this generalized model, depending on the adhesion…
We review theoretical results for the adhesion-induced phase behavior of biomembranes. The focus is on models in which the membranes are represented as discretized elastic sheets with embedded adhesion molecules. We present several…
Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…
In this paper we analyze a new temperature-dependent model for adhesive contact that encompasses nonlocal adhesive forces and damage effects, as well as nonlocal heat flux contributions on the contact surface. The related PDE system…
We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial nonlocality…
A thermodynamically consistent phase-field model is introduced for simulating multicellular deformation, and aggregation under flow conditions. In particular, a Lennard-Jones type potential is proposed under the phase-field framework for…
In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…
In this paper we examine boundary effects in a fractional chemotactic equation derived from a kinetic transport model describing cell movement in response to chemical gradients (chemotaxis). Specifically, we analyze reflecting boundary…
The purpose of this work is to propose a non-Markovian and nonlinear model of subdiffusive transport that involves adhesion affects the cells escape rates form position x, with chemotaxis. This leads the escape rates to be dependent on the…