Related papers: Sharp interface analysis of a diffuse interface mo…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
A solid-liquid-gas moving contact line is considered through a diffuse-interface model with the classical boundary condition of no-slip at the solid surface. Examination of the asymptotic behaviour as the contact line is approached shows…
Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are…
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…
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a…
According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and an order parameter coupled to a non-diffusive conserved field coincide with those of the linear interface depinning…
The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We suggest a 3D phase field model to describe 3D cell spreading on a flat substrate. The model is a simplified version of a minimal model that was developed in [1]. Our model couples the order parameter $u$ with 3D polarization…
The simulation of morphogenetic problems requires the simultaneous and coupled simulation of signalling and tissue dynamics. A cellular resolution of the tissue domain is important to adequately describe the impact of cell-based events,…
We use a sharp interface model for active cells to study the jamming transition point and behavior near it by varying cell concentration, active velocity and elasticity, including a binary mixture of soft and stiff cells. We determine the…
Interactions mediated by the cell membrane between inclusions, such as membrane proteins or antimicrobial peptides, play important roles in their biological activity. They also constitute a fascinating challenge for physicists, since they…
We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems with interfacial mass. Since the published work is not fully consistent, we provide a rigorous derivation of the local balance equations and…
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 characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
We report on a non trivial dynamics of the interface between shear bands following a start-up of flow in a semi-dilute wormlike micellar system investigated using a combination of mechanical and optical measurements. During the building of…
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…