Related papers: Coarsening dynamics of chemotactic aggregates
We consider the two dimensional parabolic-elliptic Patlak-Keller-Segel model of chemotactic aggregation for radially symmetric initial data. We show the existence of a stable mechanism of singularity formation and obtain a complete…
We poorly understand the macroscopic properties of complex fluids and of amorphous bodies in general. This is mainly due to the interplay between phenomena at different levels and length-scales. In particular, it is not necessarily true…
Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through…
This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their…
Many types of motile cells perform durotaxis, namely, directed migration following gradients of substrate stiffness. Recent experiments have revealed that cell monolayers can migrate toward stiffer regions even when individual cells do not…
For a Keller-Segel model for chemotaxis in two spatial dimensions we consider a modification of a positivity preserving fully discrete scheme using a local extremum diminishing flux limiter. We discretize space using piecewise linear finite…
We prove uniqueness in the class of integrable and bounded nonnegative solutions in the energy sense to the Keller-Segel (KS) chemotaxis system. Our proof works for the fully parabolic KS model, it includes the classical parabolic-elliptic…
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: a) the mobility $\mu$ of particles depends on the locally-averaged particle…
Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…
We formulate the Smoluchowski equation for a run-and-tumble particle. It includes the mean tumble rate in a chemical field, for which we derive a Markovian response theory. Using a multipole expansion and a reaction-diffusion equation for…
Self-generated gradients have atttracted a lot of attention in the recent biological literature. It is considered as a robust strategy for a group of cells to find its way during a long journey. This note is intended to discuss various…
We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a nonlinear generalisation of the…
Inspired by Carrillo-Li-Wang's work [Proc. London Math. Soc., 2021] on stationary solutions to the singular Keller-Segel system, this paper presents a novel family of explicit steady-state solutions for the same model on a bounded interval,…
Bacteria can chemotactically migrate up attractant gradients by controlling run-and-tumble motility patterns. In addition to this well-known chemotactic behaviour, several soil and marine bacterial species perform chemokinesis: they adjust…
A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both…
We investigate the behavior of colloidal suspensions with different volume fractions confined between parallel walls under a range of steady shears. We model the particles using molecular dynamics (MD) with full hydrodynamic interactions…
Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of fully-formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting or splitting of existing blood vessels…
It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pathway dynamics. We derive macroscopic models for E.coli…
We consider a stochastic Keller-Segel-Navier-Stokes system in $R^2$ describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by a chemical substance and transported by the ambient fluid…