410 research outputs found
Analysis of a chemotaxis system modeling ant foraging
In this paper we analyze a system of PDEs recently introduced in [P. Amorim,
{\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail
formation}], in order to describe the dynamics of ant foraging. The system is
made of convection-diffusion-reaction equations, and the coupling is driven by
chemotaxis mechanisms. We establish the well-posedness for the model, and
investigate the regularity issue for a large class of integrable data. Our main
focus is on the (physically relevant) two-dimensional case with boundary
conditions, where we prove that the solutions remain bounded for all times. The
proof involves a series of fine \emph{a priori} estimates in Lebesgue spaces.Comment: 39 page
From Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck Systems to Incompressible Euler Equations: the case with finite charge
We study the asymptotic regime of strong electric fields that leads from the
Vlasov-Poisson system to the Incompressible Euler equations. We also deal with
the Vlasov-Poisson-Fokker-Planck system which induces dissipative effects. The
originality consists in considering a situation with a finite total charge
confined by a strong external field. In turn, the limiting equation is set in a
bounded domain, the shape of which is determined by the external confining
potential. The analysis extends to the situation where the limiting density is
non-homogeneous and where the Euler equation is replaced by the Lake Equation,
also called Anelastic Equation.Comment: 39 pages, 3 figure
Low Field Regime for the Relativistic Vlasov-Maxwell-Fokker-Planck System; the One and One Half Dimensional Case
International audienceWe study the asymptotic regime for the relativistic Vlasov-Maxwell-Fokker-Planck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in the one and one half dimensional case and the proof combines dissipation mechanisms and finite speed of propagation properties
Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations
In this paper we study the diffusion approximation of a swarming model given
by a system of interacting Langevin equations with nonlinear friction. The
diffusion approximation requires the calculation of the drift and diffusion
coefficients that are given as averages of solutions to appropriate Poisson
equations. We present a new numerical method for computing these coefficients
that is based on the calculation of the eigenvalues and eigenfunctions of a
Schr\"odinger operator. These theoretical results are supported by numerical
simulations showcasing the efficiency of the method
Shock Profiles for Non Equilibrium Radiating Gases
We study a model of radiating gases that describes the interaction of an
inviscid gas with photons. We show the existence of smooth traveling waves
called 'shock profiles', when the strength of the shock is small. Moreover, we
prove that the regularity of the traveling wave increases when the strength of
the shock tends to zero
A Numerical Study on Large-Time Asymptotics of the Lifshitz-Slyozov System
We numerically investigate the behaviour for long time of solutions of the Lifshitz-Slyozov system. In particular, we find this behaviour to crucially depend on the distribution of largest aggregates present in the solution
Stochastic and deterministic models for age-structured populations with genetically variable traits
Understanding how stochastic and non-linear deterministic processes interact
is a major challenge in population dynamics theory. After a short review, we
introduce a stochastic individual-centered particle model to describe the
evolution in continuous time of a population with (continuous) age and trait
structures. The individuals reproduce asexually, age, interact and die. The
'trait' is an individual heritable property (d-dimensional vector) that may
influence birth and death rates and interactions between individuals, and vary
by mutation. In a large population limit, the random process converges to the
solution of a Gurtin-McCamy type PDE. We show that the random model has a long
time behavior that differs from its deterministic limit. However, the results
on the limiting PDE and large deviation techniques \textit{\`a la}
Freidlin-Wentzell provide estimates of the extinction time and a better
understanding of the long time behavior of the stochastic process. This has
applications to the theory of adaptive dynamics used in evolutionary biology.
We present simulations for two biological problems involving life-history trait
evolution when body size is plastic and individual growth is taken into
account.Comment: This work is a proceeding of the CANUM 2008 conferenc
Discrete Version of the She Asymptotics: Multigroup Neutron Transport Equations
This paper is devoted to the derivation of multigroup diffusion equations from the Boltzmann equation. The limit system couples the energy levels from both zeroth order term and diffusion currents
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