相关论文: Kinetic and hydrodynamic models of chemotactic agg…
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it…
The existence of global weak solutions to the compressible Navier-Stokes equations for the density of endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, is…
In this review, a theoretical description is provided for the solid (granular) phase of the gas-solid flows that are the focus of this book. Emphasis is placed on the fundamental concepts involved in deriving a macroscopic hydrodynamic…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
We discuss recent progress in the theoretical description of chemotaxis by coupling the diffusion equation of a chemical species to equations describing the motion of sensing microorganisms. In particular, we discuss models for…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
We develop a causal hydrodynamic model that provides an effective macroscopic description of the field-theoretic dynamics during the early stages of reheating. The inflaton condensate is treated as a homogeneous background coupled to a…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
We consider self-propelled rigid-bodies interacting through local body-attitude alignment modelled by stochastic differential equations. We derive a hydrodynamic model of this system at large spatio-temporal scales and particle numbers in…
This Article presents a nonequilibrium thermodynamic theory for the mean-field precipitation, aggregation and pattern formation of colloidal clusters. A variable gradient energy coefficient and the arrest of particle diffusion upon…
The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually applied for the…
Advection of entities induced by gradients in attractant concentration fields is observed via diffusiophoresis in colloids and via chemotaxis in microorganisms. Mathematically, both diffusiophoresis and chemotaxis follow similar…
We derive from the first principles new hydrodynamic equations -- Smoluchowski-Euler equations for aggregation kinetics in space-inhomogeneous fluids with fluxes. Starting from Boltzmann equations, we obtain microscopic expressions for…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…
Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical…
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller-Segel equation and a…
We consider systems of interacting particles which are described by a second order Langevin equation. The class of equations considered includes the situation where the particle evolution is governed by Hamiltonian dynamics with additional…
Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial…
It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport…
We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The…