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 Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/16881

 Title: Hydrodynamical behavior of symmetric exclusion with slow bonds Authors: Franco, TertulianoGonçalves, PatríciaNeumann, Adriana Keywords: Exclusion with slow bondsHydrodynamical behaviorDynamical phase transition Issue date: 7-Feb-2012 Publisher: Elsevier Abstract: We consider the exclusion process in the one-dimensional discrete torus with $N$ points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter $\beta$. If $\beta\in [0,1)$, the hydrodynamic limit is given by the usual heat equation. If $\beta=1$, it is given by a parabolic equation involving an operator $\frac{d}{dx}\frac{d}{dW}$, where $W$ is the Lebesgue measure on the torus plus the sum of the Dirac measure supported on each macroscopic point related to the slow bond. If $\beta\in(1,\infty)$, it is given by the heat equation with Neumann's boundary conditions, meaning no passage through the slow bonds in the continuum. Type: article URI: http://hdl.handle.net/1822/16881 ISSN: 0246-0203 Publisher version: http://www.e-publications.org/ims/submission/index.php/AIHP/user/submissionFile/9315?confirm=1e8d3afe Peer-Reviewed: yes Appears in Collections: CMAT - Artigos com arbitragem/Papers with refereeing

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