Continuum limits of particles interacting via diffusion
We consider a two-phase system mainly in three dimensions and we examine the coarsening of the spatial distribution, driven by the reduction of interface energy and limited by diffusion as described by the quasistatic Stefan free boundary problem. Under the appropriate scaling we pass rigorously to...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337504310080 |
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| Summary: | We consider a two-phase system mainly in three dimensions and we
examine the coarsening of the spatial distribution, driven by the
reduction of interface energy and limited by diffusion as
described by the quasistatic Stefan free boundary problem. Under
the appropriate scaling we pass rigorously to the limit by taking
into account the motion of the centers and the deformation of the
spherical shape. We distinguish between two different cases and we
derive the classical mean-field model and another continuum limit
corresponding to critical density which can be related to a
continuity equation obtained recently by Niethammer andOtto.
So, the theory of Lifshitz, Slyozov, and Wagner is improved by taking
into account the geometry of the spatial distribution. |
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| ISSN: | 1085-3375 1687-0409 |