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https://hdl.handle.net/1822/11842
Título: | A hyperbolic conservation law and particle systems |
Autor(es): | Gonçalves, Patrícia |
Palavras-chave: | Hyperbolic conservation law Hydrodynamic limit Asymmetric simple exclusion Asymmetric zero-range Equilibrium fluctuations |
Data: | 2010 |
Editora: | Taylor and Francis |
Revista: | Journal of Difference equations and applications |
Citação: | GONÇALVES, Patricia – A hyperbolic conservation law and Particle Systems. “Journal of Difference Equations and Applications” [Em linha]. [Consult. 11 Jan. 2011]. Disponível em WWW:<URL: http://www.informaworld.com/smpp/section?content=a930792520&fulltext=713240928>. ISSN 1563-5120. |
Resumo(s): | In these notes we consider two particle systems: the totally asymmetric simple exclusion process and the totally asymmetric zero-range process. We introduce the notion of hydrodynamic limit and describe the partial differential equation that governs the evolution of the conserved quantity – the density of particles p(t,.). This equation is a hyperbolic conservation law of type ətp(p, u) + vF(p(t, u)) = 0, where the flux F is a concave function. Taking these systems evolving on the Euler time scale tN, a central limit theorem for the empirical measure holds and the temporal evolution of the limit density field is deterministic. By taking the system in a reference frame with constant velocity, the limit density field does not evolve in time. In order to have a non-trivial limit, time needs to be speeded up and for time scales smaller than tN 4=3, there is still no temporal evolution. As a consequence, the current across a characteristic vanishes up to this longer time scale. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/11842 |
ISSN: | 1023-6198 1563-5120 |
Versão da editora: | http://dx.doi.org/10.1080/10236190903382657 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |