Related papers: Generation and motion of interfaces in a mass-cons…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
We have studied by Molecular Dynamics computer simulations the dynamics of water confined in ionic surfactants phases, ranging from well ordered lamellar structures to micelles at low and high water loading, respectively. We have analysed…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes require changes in external conditions, or whether the…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
Experimental studies of cell motility in culture have shown that under adequate conditions these living organisms possess the ability to organize themselves into complex structures. Such structures may exhibit a synergy that greatly…
This study builds upon a model proposed by Joanny and collaborators that examines the dynamics of interfaces between two distinct cell populations, particularly during tumor growth in healthy tissues. This framework leads to the…
We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which…
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on…
Abstract. The present work considers a change in the momentum under the transfer of a solution through the interface. It is shown that pressure related to the partial volumes of components arises in a solution under diffusion. As a result,…
Many natural and industrial systems involve particle-laden interfaces. Because interfacial particles prevent the coalescence and coarsening of drops, they hold promise for various applications requiring stable emulsions. Despite their…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved…