Related papers: A diffuse interface framework for modelling the ev…
We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biological phenomenon that increasingly attracts attention by both…
Diffuse interface models are widely used to describe evolution of multi-phase systems of different nature. Dispersed "inclusions", described by the phase field distribution, are usually three dimensional objects. When describing elastic…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic…
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…
Cell spreading is investigated at various scales in order to understand motility of living cells which is essential for a range of physiological activities in higher organisms as well as in microbes. At a microscopic scale, it has been seen…
We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
Soft particles such as microgels and core-shell particles can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. Here we develop a…
In order to study the effect of cell elastic properties on the behavior of assemblies of motile cells, this paper describes an alternative to the cell phase field (CPF) \cite{Palmieri2015} we have previously proposed. The CPF is a…
The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…
We give a description of cell diffusion in a soft tissue, paying special attention to the coupling of force, matter, and microforce balance laws through a suitable dissipation principle. To this end, we cast our framework into a multi-level…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
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 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…