Local minimizers and low energy paths in a model of material microstructure with a surface energy term
| dc.creator | Bevan, J. J. | |
| dc.date | 2008-09-22 | |
| dc.date.accessioned | 2026-07-07T10:04:36Z | |
| dc.date.available | 2026-07-07T10:04:36Z | |
| dc.description | A family of integral functionals F which, in a simplified way, model material microstructure occupying a two-dimensional domain D and which take account of surface energy and a variable well-depth is studied. It is shown that there is a critical well-depth, whose scaling with the surface energy density and domain dimensions is given, below which the state u=0 is the global minimizer of a typical f in the class F. It is also shown that u=0 is a strict local minimizer of f in the sense that if a non-zero v is admissible and either its L2 norm or the meaure of the subset of D where |v_{y}| exceeds 1 is sufficiently small (with quantitative bounds given in terms of the parameters appearing in the energy functional f) then f(v) > f(0). Low energy paths between u=0 and the global minimizer (in the case of a sufficiently large well-depth) are given such that the cost of introducing small regions where |v_{y}| is larger 1 (analogous to nucleation of martensite in austenite) into the domain D can be made arbitrarily small. | |
| dc.description | 32 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0809.3828 | |
| dc.identifier | http://arxiv.org/abs/0809.3828 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169737 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 49J40; 49J45; 74N15 | |
| dc.title | Local minimizers and low energy paths in a model of material microstructure with a surface energy term | |
| dc.type | text |