An Asymptotic Analysis of the Spatially Inhomogeneous Velocity-Jump Process

2011 ◽  
Vol 9 (2) ◽  
pp. 735-765 ◽  
Author(s):  
Jay M. Newby ◽  
James P. Keener
Keyword(s):  
Asymptotic Analysis ◽  
Jump Process ◽  
Velocity Jump Process ◽  
Spatially Inhomogeneous ◽  
Velocity Jump

scholarly journals Spreading in kinetic reaction–transport equations in higher velocity dimensions

2018 ◽  
Vol 30 (2) ◽  
pp. 219-247
Author(s):  
EMERIC BOUIN ◽  
NILS CAILLERIE
Keyword(s):  
Large Scale ◽  
Jump Process ◽  
Travelling Wave ◽  
Transport Equations ◽  
Kinetic Reaction ◽  
Velocity Jump Process ◽  
Minimal Speed ◽  
Crucial Difference ◽  
Velocity Jump ◽  
Reaction Transport

In this paper, we extend and complement previous works about propagation in kinetic reaction–transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction term of monostable type. We focus on the case of bounded velocities, having dimension higher than one. We extend previous results obtained by the first author with Calvez and Nadin in dimension one. We study the large time/large-scale hyperbolic limit via an Hamilton–Jacobi framework together with the half-relaxed limits method. We deduce spreading results and the existence of travelling wave solutions. A crucial difference with the mono-dimensional case is the resolution of the spectral problem at the edge of the front, that yields potential singular velocity distributions. As a consequence, the minimal speed of propagation may not be determined by a first-order condition.

scholarly journals Boltzmann-type equations for multi-agent systems with label switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nadia Loy ◽  
Andrea Tosin
Keyword(s):  
Simple Model ◽  
Infectious Diseases ◽  
Asymptotic Analysis ◽  
Kinetic Equations ◽  
Jump Process ◽  
Multi Agent Systems ◽  
Kinetic Description ◽  
Agent Systems ◽  
State Dependent ◽  
Multi Agent

<p style='text-indent:20px;'>In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump process. We derive general kinetic equations for the joint interaction/label switch processes in each group. For prototypical birth/death dynamics, we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Then we introduce and analyse a simple model for the contagion of infectious diseases, which takes advantage of the joint interaction/label switch processes to describe quarantine measures.</p>

Calculation of spatially inhomogeneous electron distribution functions

1998 ◽  
Vol 08 (PR7) ◽  
pp. Pr7-33-Pr7-42
Author(s):  
L. L. Alves ◽  
G. Gousset ◽  
C. M. Ferreira
Keyword(s):  
Electron Distribution ◽  
Distribution Functions ◽  
Spatially Inhomogeneous
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