Hydrodynamic scaling limit of continuum solid-on-solid model
A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of the hydrodynamic scaling limit of nongradient models. What distinguishes our model from ot...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/JAM/2006/69101 |
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| _version_ | 1832559858950340608 |
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| author | Anamaria Savu |
| author_facet | Anamaria Savu |
| author_sort | Anamaria Savu |
| collection | DOAJ |
| description | A fourth-order nonlinear evolution equation is derived from a
microscopic model for surface diffusion, namely, the continuum
solid-on-solid model. We use the method developed by Varadhan for
the computation of the hydrodynamic scaling limit of nongradient
models. What distinguishes our model from other models discussed
so far is the presence of two conservation laws for the dynamics
in a nonperiodic box and the complex dynamics that is not
nearest-neighbor interaction. Along the way, a few steps have to
be adapted to our new context. As a byproduct of our main result,
we also derive the hydrodynamic scaling limit of a perturbation of
the continuum solid-on-solid model, a model that incorporates both
surface diffusion and surface electromigration. |
| format | Article |
| id | doaj-art-c02ee843a5e44ff596f56dbff5f5fa3a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c02ee843a5e44ff596f56dbff5f5fa3a2025-02-03T01:29:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422006-01-01200610.1155/JAM/2006/6910169101Hydrodynamic scaling limit of continuum solid-on-solid modelAnamaria Savu0Department of Mathematics, University of Northern British Columbia, Prince George V2N 4Z9, BC, CanadaA fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of the hydrodynamic scaling limit of nongradient models. What distinguishes our model from other models discussed so far is the presence of two conservation laws for the dynamics in a nonperiodic box and the complex dynamics that is not nearest-neighbor interaction. Along the way, a few steps have to be adapted to our new context. As a byproduct of our main result, we also derive the hydrodynamic scaling limit of a perturbation of the continuum solid-on-solid model, a model that incorporates both surface diffusion and surface electromigration.http://dx.doi.org/10.1155/JAM/2006/69101 |
| spellingShingle | Anamaria Savu Hydrodynamic scaling limit of continuum solid-on-solid model Journal of Applied Mathematics |
| title | Hydrodynamic scaling limit of continuum solid-on-solid model |
| title_full | Hydrodynamic scaling limit of continuum solid-on-solid model |
| title_fullStr | Hydrodynamic scaling limit of continuum solid-on-solid model |
| title_full_unstemmed | Hydrodynamic scaling limit of continuum solid-on-solid model |
| title_short | Hydrodynamic scaling limit of continuum solid-on-solid model |
| title_sort | hydrodynamic scaling limit of continuum solid on solid model |
| url | http://dx.doi.org/10.1155/JAM/2006/69101 |
| work_keys_str_mv | AT anamariasavu hydrodynamicscalinglimitofcontinuumsolidonsolidmodel |