In this work, we study the porous medium model (PMM), an interacting particle system with nearest neighbor interactions of particles under some constraints. First, we consider the discrete space { 1, …, n- 1 } with additional Glauber dynamics acting respectively on sites 0 and n. We assume the hydrodynamic limit (proved in a companion paper [4]) and we prove that the Fick’s law holds. Moreover, we review how to construct a self-duality relation starting from the reversible measure of the process. Following this method, we show a self-duality result for the process without reservoirs, which is found inspired by its description via the Lie algebra su(2 ).
Porous Medium Model: An Algebraic Perspective and the Fick’s Law / De Paula, R.; Franceschini, C.. - 352:(2021), pp. 195-225. (Intervento presentato al convegno International Conference on Particle Systems and PDEs VI, VII and VIII, 2017-2019 tenutosi a prt nel 2019) [10.1007/978-3-030-69784-6_10].
Porous Medium Model: An Algebraic Perspective and the Fick’s Law
Franceschini C.
2021
Abstract
In this work, we study the porous medium model (PMM), an interacting particle system with nearest neighbor interactions of particles under some constraints. First, we consider the discrete space { 1, …, n- 1 } with additional Glauber dynamics acting respectively on sites 0 and n. We assume the hydrodynamic limit (proved in a companion paper [4]) and we prove that the Fick’s law holds. Moreover, we review how to construct a self-duality relation starting from the reversible measure of the process. Following this method, we show a self-duality result for the process without reservoirs, which is found inspired by its description via the Lie algebra su(2 ).
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