Partial Localization, Lipid Bilayers, and the Elastica Functional
| dc.creator | Peletier, Mark A. | |
| dc.creator | Roeger, Matthias | |
| dc.date | 2006-07-12 | |
| dc.date.accessioned | 2026-07-07T07:20:32Z | |
| dc.date.available | 2026-07-07T07:20:32Z | |
| dc.description | Partial localization is the phenomenon of self-aggregation of mass into high-density structures that are thin in one direction and extended in the others. We give a detailed study of an energy functional that arises in a simplified model for lipid bilayer membranes. We demonstrate that this functional, defined on a class of two-dimensional spatial mass densities, exhibits partial localization and displays the `solid-like' behavior of cell membranes. Specifically, we show that density fields of moderate energy are partially localized, i.e. resemble thin structures. Deviation from a specific uniform thickness, creation of `ends', and the bending of such structures all carry an energy penalty, of different orders in terms of the thickness of the structure. These findings are made precise in a Gamma-convergence result. We prove that a rescaled version of the energy functional converges in the zero-thickness limit to a functional that is defined on a class of planar curves. Finiteness of the limit enforces both optimal thickness and non-fracture; if these conditions are met, then the limit value is given by the classical Elastica (bending) energy of the curve. | |
| dc.description | 56 pages, latex with figures included with \includegraphics and geompsfi.sty | |
| dc.identifier | https://arxiv.org/abs/math-ph/0607024 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0607024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114983 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 74Q99,49Q15, 49Q20, 49Q10 | |
| dc.title | Partial Localization, Lipid Bilayers, and the Elastica Functional | |
| dc.type | text |