The Library
Validity and failure of the Boltzmann approximation of kinetic annihilation
Tools
Matthies, Karsten and Theil, Florian. (2010) Validity and failure of the Boltzmann approximation of kinetic annihilation. Journal of Nonlinear Science, Vol.20 (No.1). pp. 146. ISSN 09388974

PDF
WRAP_Mathies_1070268lb130611wrap_theil_longtime_validity_gainless.pdf  Accepted Version  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (353Kb) 
Official URL: http://dx.doi.org/10.1007/s003320099049y
Abstract
This paper introduces a new method to show the validity of a continuum description for the deterministic dynamics of many interacting particles. Here the manyparticle evolution is analyzed for a hard sphere flow with the addition that after a collision the collided particles are removed from the system. We consider random initial configurations which are drawn from a Poisson point process with spatially homogeneous velocity density f (0)(v). Assuming that the moments of order less than three of f (0) are finite and no mass is concentrated on lines, the homogeneous Boltzmann equation without gain term is derived for arbitrary long times in the BoltzmannGrad scaling. A key element is a characterization of the manyparticle flow by a hierarchy of trees which encode the possible collisions. The occurring trees are shown to have favorable properties with a high probability, allowing us to restrict the analysis to a finite number of interacting particles and enabling us to extract a singlebody distribution. A counterexample is given for a concentrated initial density f (0) even to shortterm validity.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Field theory (Physics), Particles  Mathematical models, Kinetic theory of matter  
Journal or Publication Title:  Journal of Nonlinear Science  
Publisher:  Springer  
ISSN:  09388974  
Official Date:  February 2010  
Dates: 


Volume:  Vol.20  
Number:  No.1  
Number of Pages:  46  
Page Range:  pp. 146  
Identification Number:  10.1007/s003320099049y  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Open Access  
References:  [BBS83] C. Boldrighini, L.A. Bunimovich, Y.G. Sinai. On the Boltzmann equation for the Lorentz gas.J. 

URI:  http://wrap.warwick.ac.uk/id/eprint/6546 
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Actions (login required)
View Item 
Downloads
Downloads per month over past year