caa a22 4500 445391006 CHVBK 20180317143046.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10955-011-0326-4 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0326-4 Current Reservoirs in the Simple Exclusion Process [Elektronische Daten] [A. De Masi, E. Presutti, D. Tsagkarogiannis, M. Vares] We consider the symmetric simple exclusion process in the interval [−N,N] with additional birth and death processes respectively on (N−K,N], K>0, and [−N,−N+K). The exclusion is speeded up by a factor N 2, births and deaths by a factorN. Assuming propagation of chaos (a property proved in a companion paper, De Masi et al., http://arxiv.org/abs/1104.3447 ) we prove convergence in the limit N→∞ to the linear heat equation with Dirichlet condition on the boundaries; the boundary conditions however are not known a priori, they are obtained by solving a non-linear equation. The model simulates mass transport with current reservoirs at the boundaries and the Fourier law is proved to hold. Springer Science+Business Media, LLC, 2011 Hydrodynamic limits nationallicence Fourier law nationallicence Non-linear boundary processes nationallicence De Masi A. Dipartimento di Matematica, Università di L'Aquila, 67100, L'Aquila, Italy aut Presutti E. Dipartimento di Matematica, Università di Roma Tor Vergata, 00133, Roma, Italy aut Tsagkarogiannis D. Dipartimento di Matematica, Università di Roma Tor Vergata, 00133, Roma, Italy aut Vares M. Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ, Brazil aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/6(2011-09-01), 1151-1170 0022-4715 144:6<1151 2011 144 10955 https://doi.org/10.1007/s10955-011-0326-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0326-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- De Masi A. Dipartimento di Matematica, Università di L'Aquila, 67100, L'Aquila, Italy aut NATIONALLICENCE 700 1- Presutti E. Dipartimento di Matematica, Università di Roma Tor Vergata, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Tsagkarogiannis D. Dipartimento di Matematica, Università di Roma Tor Vergata, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Vares M. Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ, Brazil aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/6(2011-09-01), 1151-1170 0022-4715 144:6<1151 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer