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In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

Numerical Analysis · Mathematics 2017-01-19 Anaïs Crestetto , Nicolas Crouseilles , Mohammed Lemou

Metabolic models condense biochemical knowledge about organisms in a structured and standardised way. As large-scale network reconstructions are readily available for many organisms, genome-scale models are being widely used among modellers…

Molecular Networks · Quantitative Biology 2025-10-15 Marco Corrao , Hai He , Wolfram Liebermeister , Elad Noor , Arren Bar-Even

We are concerned with the hyperbolic Keller-Segel model with quorum sensing, a model describing the collective cell movement due to chemical signalling with a flux limitation for high cell densities. This is a first order quasilinear…

Analysis of PDEs · Mathematics 2007-05-23 Benoit Perthame , Anne-Laure Dalibard

In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting…

Fluid Dynamics · Physics 2019-11-20 Benjamin Anwasia , Patrícia Gonçalves , Ana Jacinta Soares

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…

Tissues and Organs · Quantitative Biology 2019-07-15 Mark AJ Chaplain , Tommaso Lorenzi , Fiona R Macfarlane

A large number of biological systems - from bacteria to sheep - can be described as ensembles of self-propelled agents (active particles) with a complex internal dynamic that controls the agent's behavior: resting, moving slow, moving fast,…

Biological Physics · Physics 2021-09-03 L. Gómez-Nava , T. Goudon , F. Peruani

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

We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…

Analysis of PDEs · Mathematics 2025-01-24 Daniel Acosta Soba , Alessandro Columbu , Giuseppe Viglialoro

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…

Numerical Analysis · Mathematics 2015-03-18 Julien Dambrine , Nicolas Meunier , Bertrand Maury , Aude Roudneff-Chupin

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 movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable,…

Biological Physics · Physics 2009-11-11 Radek Erban , Ioannis G. Kevrekidis , Hans G. Othmer

Bacteria can adjust their swimming behaviour in response to chemical variations, a phenomenon known as chemotaxis. This process is characterised by a drift velocity that depends non-linearly on the concentration of chemical species and its…

Fluid Dynamics · Physics 2026-05-07 Adam Gargasson , Julien Bouvard , Carine Douarche , Peter Mergaert , Harold Auradou

Many eukaryotic cells are able to sense chemical gradients by directly measuring spatial concentration differences. The precision of such gradient sensing is limited by fluctuations in the binding of diffusing particles to specific…

Cell Behavior · Quantitative Biology 2010-06-04 Bo Hu , Wen Chen , Wouter-Jan Rappel , Herbert Levine

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

In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…

Quantitative Methods · Quantitative Biology 2026-01-07 Marzia Bisi , Maria Groppi , Giorgio Martalò , Romina Travaglini

We consider the diffusion and spreading of chainlike molecules on solid surfaces. We first show that the steep spherical cap shape density profiles, observed in some submonolayer experiments on spreading polymer films, imply that the…

Soft Condensed Matter · Physics 2009-10-31 T. Hjelt , S. Herminghaus , T. Ala-Nissila , S. C. Ying

Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic…

Mathematical Physics · Physics 2021-08-10 Clément Erignoux

In response to a concentration gradient of nutrient, E. coli bacterium modulates the rotational bias of flagellar motors which control its run-and-tumble motion, to migrate towards regions of high nutrient concentration. Presence of…

Cell Behavior · Quantitative Biology 2018-04-04 Subrata Dev , Sakuntala Chatterjee

Many chemotactic bacteria inhabit environments in which chemicals appear as localized pulses and evolve by processes such as diffusion and mixing. We show that, in such environments, physical limits on the accuracy of temporal gradient…

Biological Physics · Physics 2016-01-19 Andrew M. Hein , Douglas R. Brumley , Francesco Carrara , Roman Stocker , Simon A. Levin

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…

Quantitative Methods · Quantitative Biology 2016-02-17 Atiyo Ghosh , Tatiana T. Marquez-Lago