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Related papers: A stochastic Keller-Segel model of chemotaxis

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We introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for…

Probability · Mathematics 2016-02-01 Patrick Cattiaux , Laure Pédèches

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…

Soft Condensed Matter · Physics 2007-05-23 Erkan Tuzel , Thomas Ihle , Daniel M. Kroll

Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching rate increases to infinity, thereby providing a rigorous…

Analysis of PDEs · Mathematics 2024-10-10 Philippe Laurençot , Christian Stinner

We investigate the point spectrum associated with travelling wave solutions in a Keller-Segel model for bacterial chemotaxis with small diffusivity of the chemoattractant, a logarithmic chemosensitivity function and a constant, sublinear or…

Spectral Theory · Mathematics 2017-12-01 P. N. Davis , P. van Heijster , R. Marangell

The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…

Physics and Society · Physics 2021-04-01 Michael Schultz

Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive…

Soft Condensed Matter · Physics 2018-06-07 Markus Gross , Fathollah Varnik

Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and…

Analysis of PDEs · Mathematics 2015-01-08 Herbert Egger , Jan-Frederik Pietschmann , Matthias Schlottbom

Bacterial chemotaxis in Escherichia coli is a canonical system for the study of signal transduction. A remarkable feature of this system is the coexistence of precise adaptation in population with large fluctuating cellular behavior in…

Molecular Networks · Quantitative Biology 2019-08-19 Thierry Emonet , Philippe Cluzel

The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses,…

Soft Condensed Matter · Physics 2024-01-17 Ana Carpio , Elena Cebrian

We present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models for chemosensitive movements set in an arbitrary geometry. We investigate the influence of the geometry on the collective behavior of…

Numerical Analysis · Mathematics 2013-03-12 Francis Filbet , Chang Yang

We present a principled data-driven strategy for learning deterministic hydrodynamic models directly from stochastic non-equilibrium active particle trajectories. We apply our method to learning a hydrodynamic model for the propagating…

Soft Condensed Matter · Physics 2022-01-24 Suryanarayana Maddu , Quentin Vagne , Ivo F. Sbalzarini

We investigate nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. Given any general perturbation of magnitude $\delta$, we prove that its nonlinear evolution is dominated by the corresponding…

Analysis of PDEs · Mathematics 2007-05-23 Yan Guo , Hyung Ju Hwang

This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility…

Analysis of PDEs · Mathematics 2020-05-14 Hai-Yang Jin , Zhi-An Wang

In this paper we present a Keller--Segel model with logistic growth dynamics arising in the study of chemotactic pattern formation. We prove the existence of a minimum wave speed for which the model exhibits nonnegative travelling wave…

Dynamical Systems · Mathematics 2020-09-24 Jason J. Bramburger

We study a version of the Keller-Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct…

Dynamical Systems · Mathematics 2014-03-12 Kristen Harley , Peter van Heijster , Graeme Pettet

Chemotaxis and reactions are fundamental processes in biology, often intricately intertwined. Chemotaxis, in particular, can be crucial in maintaining and accelerating a reaction. In this work, we extend the investigation initiated by…

Analysis of PDEs · Mathematics 2024-12-31 Crystianne L. De Andrade , Alexander A. Kiselev

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,…

Analysis of PDEs · Mathematics 2025-12-29 Yue Huang , Ling Xue , Kun Zhao , Xiaoming Zheng

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional…

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

Chemotaxis plays a crucial role in a variety of processes in biology and ecology. In many instances, processes involving chemical attraction take place in fluids. One of the most studied PDE models of chemotaxis is given by Keller-Segel…

Analysis of PDEs · Mathematics 2016-06-29 Alexander Kiselev , Xiaoqian Xu

Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation, and vascular tumors provide a focus on optimization strategies. Experiments can characterize…

Optimization and Control · Mathematics 2007-07-18 K. Renee Fister , Maeve L. McCarthy