TY - JOUR

T1 - Mean Curvature Interface Limit from Glauber+Zero-Range Interacting Particles

AU - El Kettani, Perla

AU - Funaki, Tadahisa

AU - Hilhorst, Danielle

AU - Park, Hyunjoon

AU - Sethuraman, Sunder

N1 - Funding Information:
P. El Kettani, D. Hilhorst and H.J. Park thank IRN ReaDiNet as well as the French-Korean project STAR. T. Funaki was supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Researches (A) 18H03672 and (S) 16H06338, and also thanks IRN ReaDiNet. S. Sethuraman was supported by grant ARO W911NF-181-0311, a Simons Foundation Sabbatical grant, and by a JSPS Fellowship, and thanks Waseda U. for the kind hospitality during a sabbatical visit.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/9

Y1 - 2022/9

N2 - 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, especially generation and propagation of interface properties, of this ‘discretized’ PDE.

AB - 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, especially generation and propagation of interface properties, of this ‘discretized’ PDE.

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U2 - 10.1007/s00220-022-04424-8

DO - 10.1007/s00220-022-04424-8

M3 - Article

AN - SCOPUS:85132973788

SN - 0010-3616

VL - 394

SP - 1173

EP - 1223

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -