Related papers: On a stochastic phase-field model of cell motility…
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…
We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective…
We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
In ABP systems, phase separation is accompanied by the emergence of vapor bubbles within liquid domains. Using large-scale particle-based simulations, we study the stochastic dynamics of these bubbles and find that most nucleate, grow, and…
We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
We consider a model of congestion dynamics with chemotaxis: The density of cells follows a chemical signal it generates, while subject to an incompressibility constraint. The incompressibility constraint results in the formation of patches,…
The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn-type equation, which distinguishes the body from the…
Solid fuel ignition models, for which the dynamics of the temperature is independent of the single-species mass fraction, attempt to follow the dynamics of an explosive event. Such models may take the form of singular, degenerate,…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
Chemical signaling is one of the ubiquitous mechanisms by which inter-cellular communication takes place at the microscopic level, particularly via chemotaxis. Such multi-cellular systems are popularly studied using continuum, mean-field…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
We study a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effects. This model also takes into account some significant mechanisms such as active transport and nonlocal interactions of…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and…
In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover it is regarded as a…
We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a "thin-front limit," we are able to deduce a Hamilton-Jacobi equation with a suitable effective Hamiltonian on the road…