English
Related papers

Related papers: A stochastic Keller-Segel model of chemotaxis

200 papers

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a…

Biological Physics · Physics 2009-11-13 Pierre-Henri Chavanis , Clement Sire

The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of a generalized nonlinear variant of the Keller-Segel to the degenerate Cahn-Hilliard system. This analysis is made…

Analysis of PDEs · Mathematics 2023-02-13 Charles Elbar , Benoît Perthame , Alexandre Poulain

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and…

Quantitative Methods · Quantitative Biology 2018-06-26 K. J. Painter

The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article clarifies the form of biologically relevant model…

Biological Physics · Physics 2018-04-12 Gissell Estrada-Rodriguez , Heiko Gimperlein , Kevin J. Painter

The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in…

Biological Physics · Physics 2009-11-11 Mark Alber , Nan Chen , Tilmann Glimm , Pavel M. Lushnikov

The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial…

Analysis of PDEs · Mathematics 2026-01-01 Hiroshi Ishii , Hideki Murakawa , Yoshitaro Tanaka

A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between…

Pattern Formation and Solitons · Physics 2010-05-18 Pavel M. Lushnikov

The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and…

Numerical Analysis · Mathematics 2023-10-04 Daniel Acosta-Soba , Francisco Guillén-González , J. Rafael Rodríguez-Galván

In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem are presented and used to derive coupling conditions for the…

Analysis of PDEs · Mathematics 2015-12-29 Raul Borsche , Axel Klar , Ha T. N. Pham

For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…

Condensed Matter · Physics 2015-06-25 S. B. Goryachev

Chemotaxis allows single cells to self-organize at the population level, as classically described by Keller-Segel models. We show that chemotactic aggregation can be understood using a generalized Maxwell construction based on the balance…

Soft Condensed Matter · Physics 2025-11-18 Henrik Weyer , David Muramatsu , Erwin Frey

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…

Analysis of PDEs · Mathematics 2026-05-19 Fanze Kong , Chen-Chih Lai , Krutika Tawri

In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution…

Optimization and Control · Mathematics 2023-09-19 Gianni Gilardi , Andrea Signori , Jürgen Sprekels

We study the existence of steady states to the Keller-Segel system with linear chemotactical sensitivity function on a smooth bounded domain in $\mathbb R^N,$ $N\ge3,$ having rotational symmetry. We find three different types of…

Analysis of PDEs · Mathematics 2016-03-22 Oscar Agudelo , Angela Pistoia

In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented here has broad applications in determining large time…

Analysis of PDEs · Mathematics 2024-06-13 Mengyao Ding , Yuzhou Fang , Chao Zhang

We consider the singular limit of a chemotaxis model of bacterial collective motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models aggregation-diffusion phenomena with advection that is discontinuous and depends…

Analysis of PDEs · Mathematics 2025-08-28 Maria Gualdani , Mikel Ispizua , Nicola Zamponi

The Keller-Segel-Navier-Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial cell…

Numerical Analysis · Mathematics 2023-02-02 Jesús Bonilla , Juan Vicente Gutiérrez-Santacreu

Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely…

Biological Physics · Physics 2011-11-14 S. Banerjee , A. P. Misra , L. Rondoni

The goal of this paper is to exhibit a critical mass phenomenon occuring in a model for cell self-organization via chemotaxis. The very well known dichotomy arising in the behavior of the macroscopic Keller-Segel system is derived at the…

Analysis of PDEs · Mathematics 2015-05-13 Nikolaos Bournaveas , Vincent Calvez

The Keller-Segel partial differential equation is a two-dimensional model for chemotaxis. When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity $\chi$ of bacteria to the…

Probability · Mathematics 2015-07-07 Nicolas Fournier , Benjamin Jourdain