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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| Format: | Article |
| Language: | English |
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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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| author | Nicholas D. Alikakos Giorgio Fusco Georgia Karali |
| author_facet | Nicholas D. Alikakos Giorgio Fusco Georgia Karali |
| author_sort | Nicholas D. Alikakos |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3541045153774833868da5e741de4256 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3541045153774833868da5e741de42562025-02-03T06:04:59ZengWileyAbstract and Applied Analysis1085-33751687-04092004-01-012004321523710.1155/S1085337504310080Continuum limits of particles interacting via diffusionNicholas D. Alikakos0Giorgio Fusco1Georgia Karali2Department of Mathematics, University of Athens, Athens 15784, GreeceDipartimento di Mathematica, Universita di L'Aquila, L'Aquila 67010, ItalyDepartment of Mathematics, University of Toronto, Toronto M5S 3G3, CanadaWe 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.http://dx.doi.org/10.1155/S1085337504310080 |
| spellingShingle | Nicholas D. Alikakos Giorgio Fusco Georgia Karali Continuum limits of particles interacting via diffusion Abstract and Applied Analysis |
| title | Continuum limits of particles interacting via diffusion |
| title_full | Continuum limits of particles interacting via diffusion |
| title_fullStr | Continuum limits of particles interacting via diffusion |
| title_full_unstemmed | Continuum limits of particles interacting via diffusion |
| title_short | Continuum limits of particles interacting via diffusion |
| title_sort | continuum limits of particles interacting via diffusion |
| url | http://dx.doi.org/10.1155/S1085337504310080 |
| work_keys_str_mv | AT nicholasdalikakos continuumlimitsofparticlesinteractingviadiffusion AT giorgiofusco continuumlimitsofparticlesinteractingviadiffusion AT georgiakarali continuumlimitsofparticlesinteractingviadiffusion |