Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/16877
Título: | A hyperbolic conservation law and Particle Systems |
Autor(es): | Gonçalves, Patrícia |
Palavras-chave: | Hyperbolic conservation law Asymmetric zero-range and exclusion hydrodynamic limit asymmetric simple exclusion asymmetric zero-range equilibrium fluctuations |
Data: | 2011 |
Editora: | Taylor & Francis |
Revista: | Journal of Difference Equations and Applications |
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 $\rho(t,\cdot)$. This equation is a hyperbolic conservation law of type $\partial_{t}\rho(t,u)+\nabla F(\rho(t,u))=0$, 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 on 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/1822/16877 |
DOI: | 10.1080/10236190903382657 |
ISSN: | 1023-6198 (Print) 1563-5120 (Online) |
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 ED/DH-CII - Comunicações e conferências |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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TASEP repositorium.pdf | Documento principal | 198,33 kB | Adobe PDF | Ver/Abrir |