Related papers: Control of reaction-diffusion equations on time-ev…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
Emulsions often act as carriers for water-insoluble solutes that are delivered to a specific target. The molecular transport of solutes in emulsions can be facilitated by surfactants and is often limited by diffusion through the continuous…
Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific…
We study the effect of transport processes (diffusion and free--streaming) on a collapsing spherically symmetric distribution of matter in a self--similar space--time. A very simple solution shows interesting features when it is matched…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
Molecular transport maintains cellular structures and functions. For example, lipid and protein diffusion sculpts the dynamic shapes and structures on the cell membrane that perform essential cellular functions, such as cell signaling.…
We present a general, physically motivated non-linear and non-local advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
We investigate a model, inspired by (Johnston et al., Sci. Rep., 7:42134, 2017), to describe the movement of a biological population which consists of isolated and grouped organisms. We introduce biases in the movements and then obtain a…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…