SPMES: Exclusion processes with non-reversible boundary dynamics... - Beatriz Salvador Costa

Seminário de Probabilidade e Mecânica Estatística Título: Exclusion processes with non-reversible boundary dynamics: hydrodynamics and stationary solutions Palestrante: Beatriz Salvador Costa, IST, Lisbon Playlist dos videos:    • Seminário de Probabilidade e Mecânica Esta...   Resumo: Exclusion processes with non-reversible boundary dynamics are one-dimensional interacting particle systems evolving on a finite lattice. These systems arise from the superposition of two different types of dynamics. In the bulk, particles evolve according to the usual symmetric simple exclusion dynamics, that is, at most one particle is allowed per site and jumps occur through nearest-neighbor interactions. Near the boundary, within a window of fixed size $l\geq 1$, particles may be created or annihilated according to rates depending on the local configuration in a finite neighborhood of the boundary. This choice of boundary dynamics is non-conservative and is considered under very general rates, allowing, in particular, the simultaneous creation of more than one particle. This flexibility creates a crucial distinction between our model and the simplified version first introduced in 2011 to describe boundary current fluctuations, where a very specific choice of boundary rates was considered. In this sense, our model generalizes earlier works by capturing not only non-linear evolutions of the particle density, but also, and more importantly, the surprising emergence of multiple stationary solutions to the hydrodynamic equation describing the density profile. In this talk, we define the model, discuss its hydrodynamic limit, and analyze several properties of the stationary solutions of the associated hydrodynamic equation. This presentation is based on joint works with Claudio Landim and João Pedro Mangi. Apoio: IMPA Instituto Superior Técnico de Lisboa UFBA UFMG UFRGS UFRJ Unicamp Universidade do Porto USP Comitê científico: Luiz Renato Fontes (USP) Tertuliano Franco (UFBA) Nancy Lopes Garcia (Unicamp) Patrícia Gonçalves (IST, Lisboa) Marcelo Hilário (UFMG) Roberto Imbuzeiro (Coordenador, IMPA) Claudio Landim (Coordenador, IMPA) Adriana Neumann (UFRGS) Serguei Popov (UP, Porto) Glauco Valle (UFRJ) Redes Sociais do IMPA: https://linktr.ee/impabr IMPA - Instituto de Matemática Pura e Aplicada © http://www.impa.br | http://impa.br/videos #spmes Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.