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An analysis of surface relaxation in the surface cauchy-born model
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Jayawardana, K., Mordacq, C., Ortner, Christoph and Park, H. S. (2011) An analysis of surface relaxation in the surface cauchy-born model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.0683v1).
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Official URL: http://arxiv.org/pdf/1112.0683v1.pdf
Abstract
The Surface Cauchy{Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is O(1) in the mesh size; however, we are able to identify an alternative \approximation parameter" | the sti�ness of the interaction potential | with respect to which the error in the mean strain is exponentially small. Our analysis naturally suggests an improvement of the SCB model by enforcing atomistic mesh spacing in the normal direction at the free boundary.
| Item Type: | Working or Discussion Paper (Working Paper) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Series Name: | ArXiv e-prints | ||||
| Publisher: | ArXiv e-prints | ||||
| Official Date: | 3 December 2011 | ||||
| Dates: |
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| Number: | No.1112.0683v1 | ||||
| Number of Pages: | 17 | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access | ||||
| Funder: | EPSRC, NSF | ||||
| Grant number: | EP/H003096, CMMI-0750395, CMMI-1036460 | ||||
| Related URLs: |
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