Mathematical and computational models can assist in gaining an understanding of cell
behavior at many levels of organization. Here, we review models in the literature that focus …

The employment of nonlocal PDE models to describe biological aggregation and other
phenomena has gained considerable traction in recent years. For cell populations, these …

We discuss several continuum cell-cell adhesion models based on the underlying
microscopic assumptions. We propose an improvement on these models leading to sharp …

Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell
migration during tissue development, homeostasis, and repair, allowing cell populations to …

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …

Mathematical models of motility are often based on random-walk descriptions of discrete
individuals that can move according to certain rules. It is usually the case that large masses …

The ability to locally degrade the extracellular matrix (ECM) and interact with the tumor
microenvironment is a key process distinguishing cancer cells from normal cells, and is a …

In recent years, there has been a spike in interest in multiphase tissue growth models.
Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law …

We present a numerical approach for computing attractive-repulsive power law equilibrium
measures in arbitrary dimension. We prove new recurrence relationships for radial Jacobi …

We introduce a method to numerically compute equilibrium measures for problems with
attractive-repulsive power law kernels of the form $ K (xy)=\frac {| xy|^\alpha}{\alpha}-\frac …