Abstract
We study the hydrodynamic scaling limit for the Glauber–Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen–Cahn equation which is a kind of the reaction–diffusion equation in the limit. This paper concerns the scaling that the Glauber part, which governs the creation and annihilation of particles, is also speeded up but slower than the Kawasaki part. Under such scaling, we derive directly from the particle system the motion by mean curvature for the interfaces separating sparse and dense regions of particles as a combination of the hydrodynamic and sharp interface limits.
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Communicated by Abhishek Dhar.
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Tadahisa Funaki is supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Researches (S) 16H06338, (A) 18H03672, 17H01093, 17H01097 and (B) 16KT0024, 26287014. Kenkichi Tsunoda is supported in part by JSPS KAKENHI, Grant-in-Aid for Early-Career Scientists 18K13426.
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Funaki, T., Tsunoda, K. Motion by Mean Curvature from Glauber–Kawasaki Dynamics. J Stat Phys 177, 183–208 (2019). https://doi.org/10.1007/s10955-019-02364-7
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DOI: https://doi.org/10.1007/s10955-019-02364-7
Keywords
- Hydrodynamic limit
- Motion by mean curvature
- Glauber–Kawasaki dynamics
- Allen–Cahn equation
- Sharp interface limit