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Mean curvature interface limit from Glauber+Zero-range interacting particles | | Perla El Kettani
; Tadahisa Funaki
; Danielle Hilhorst
; Hyunjoon Park
; Sunder Sethuraman
; | | Date: |
11 Apr 2020 | | Abstract: | We derive a continuum mean-curvature flow as a certain hydrodynamic scaling
limit of a class of Glauber+Zero-range particle systems. The Zero-range part
moves particles while preserving particle numbers, and the Glauber part governs
the creation and annihilation of particles and is set to favor two levels of
particle density. When the two parts are simultaneously seen in certain
different time-scales, the Zero-range part being diffusively scaled while the
Glauber part is speeded up at a lesser rate, a mean-curvature interface flow
emerges, with a homogenized ’surface tension-mobility’ parameter reflecting
microscopic rates, between the two levels of particle density. We use relative
entropy methods, along with a suitable ’Boltzmann-Gibbs’ principle, to show
that the random microscopic system may be approximated by a ’discretized’
Allen-Cahn PDE with nonlinear diffusion. In turn, we show the behavior of this
’discretized’ PDE is close to that of a continuum Allen-Cahn equation, whose
generation and propagation interface properties we also derive. | | Source: | arXiv, 2004.5276 | | Services: | Forum | Review | PDF | Favorites | |
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