A simple particle model for a system of coupled equations with absorbing collision term

Valeria Ricci, Cédric Bernardin

Risultato della ricerca: Article

1 Citazione (Scopus)

Abstract

We study a particle model for a simple system of partial differential equations describing, in dimension d ≥ 2, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a transport and a reaction equation coupled through pure absorption collision terms. We consider a particle system where the obstacles, of radius ε, become inactive at a rate related to the number of light particles travelling in their range of influence at a given time and the light particles are instantaneously absorbed at the first time they meet the physical boundary of an obstacle; elements belonging to the same species do not interact among themselves. We prove the convergence (a.s. w.r.t. the product measure associated to the initial datum for the light particle component) of the densities describing the particle system to the solution of the system of partial differential equations in the asymptotics a^d_n−κ → 0 n 11 and ad εζ → 0, for κ ∈ (0, 1/2) and ζ ∈ (0, 2 − 2d ), where a^d_n is the effective range of the obstacles and n is the total number of light particles.
Lingua originaleEnglish
pagine (da-a)633-668
Numero di pagine36
RivistaKinetic and Related Models
Volume4
Stato di pubblicazionePublished - 2011

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Term
Model
Partial differential equations
Related rates
Product Measure
Particle System
Systems of Partial Differential Equations
Absorbing
Range of data
Absorption
Collision
Radius
Partial

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation

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A simple particle model for a system of coupled equations with absorbing collision term. / Ricci, Valeria; Bernardin, Cédric.

In: Kinetic and Related Models, Vol. 4, 2011, pag. 633-668.

Risultato della ricerca: Article

Ricci, V & Bernardin, C 2011, 'A simple particle model for a system of coupled equations with absorbing collision term', Kinetic and Related Models, vol. 4, pagg. 633-668.
Ricci V, Bernardin C. A simple particle model for a system of coupled equations with absorbing collision term. Kinetic and Related Models. 2011;4:633-668.
Ricci, Valeria ; Bernardin, Cédric. / A simple particle model for a system of coupled equations with absorbing collision term. In: Kinetic and Related Models. 2011 ; Vol. 4. pagg. 633-668.
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AB - We study a particle model for a simple system of partial differential equations describing, in dimension d ≥ 2, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a transport and a reaction equation coupled through pure absorption collision terms. We consider a particle system where the obstacles, of radius ε, become inactive at a rate related to the number of light particles travelling in their range of influence at a given time and the light particles are instantaneously absorbed at the first time they meet the physical boundary of an obstacle; elements belonging to the same species do not interact among themselves. We prove the convergence (a.s. w.r.t. the product measure associated to the initial datum for the light particle component) of the densities describing the particle system to the solution of the system of partial differential equations in the asymptotics a^d_n−κ → 0 n 11 and ad εζ → 0, for κ ∈ (0, 1/2) and ζ ∈ (0, 2 − 2d ), where a^d_n is the effective range of the obstacles and n is the total number of light particles.

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EP - 668

JO - Kinetic and Related Models

JF - Kinetic and Related Models

SN - 1937-5093

ER -

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