Related papers: The numerical solution of the free-boundary cell m…

Biological organisms swimming at low Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper we present an analysis of locomotion near a free surface with surface tension. Using a…

At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…

We study a linear problem that arises in the study of dynamic boundaries, in particular in free boundary problems in connection with fluid dynamics. The equations are also very natural and of interest on their own.

An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with…

Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…

This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…

A model of unsteady filtration (seepage) in a porous medium with capillary retention is considered. It leads to a free boundary problem for a generalized porous medium equation where the location of the boundary of the water mound is…

We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary…

Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia represents a serious complicating factor in wound healing. In this paper we analyze a recently developed mathematical model…

We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.

We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…

Spatially localised defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar 'actin' filaments and 'myosin' motor proteins that (un)bind to filaments and exert active contractile…

A very simple model for cell swelling by osmosis is introduced, resulting in a parabolic free boundary problem. In case of radially symmetric initial conditions, it is shown that the model can be viewed as a gradient flow involving entropy,…

The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non-migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in…

We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for explaining observed collective behaviors such as those in…

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…

A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…

Cell motility in higher organisms (eukaryotes) is crucial to biological functions ranging from wound healing to immune response, and also implicated in diseases such as cancer. For cells crawling on hard surfaces, significant insights into…

We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…

Living systems are capable of locomotion, reconfiguration, and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, "active" molecules that create and manipulate non-equilibrium…