Emergent singular solutions of non-local density-magnetization equations in one dimension
| dc.creator | Holm, Darryl D. | |
| dc.creator | Naraigh, Lennon O. | |
| dc.creator | Tronci, Cesare | |
| dc.date | 2007-11-14 | |
| dc.date.accessioned | 2026-07-07T09:34:48Z | |
| dc.date.available | 2026-07-07T09:34:48Z | |
| dc.description | We investigate the emergence of singular solutions in a non-local model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that the evolution depends strongly on the length scales of the non-local effects. We pass to a coupled density-magnetization model and perform a linear stability analysis, noting the effect of the length scales of non-locality on the system's stability properties. We carry out numerical simulations of the coupled system and find that singular solutions emerge from smooth initial data. The singular solutions represent a collection of interacting particles (clumpons). By restricting ourselves to the two-clumpon case, we are reduced to a two-dimensional dynamical system that is readily analyzed, and thus we classify the different clumpon interactions possible. | |
| dc.description | 19 pages, 13 figures. Submitted to Phys. Rev. E | |
| dc.identifier | https://arxiv.org/abs/0711.2177 | |
| dc.identifier | http://arxiv.org/abs/0711.2177 | |
| dc.identifier | doi:10.1103/PhysRevE.77.036211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159624 | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.title | Emergent singular solutions of non-local density-magnetization equations in one dimension | |
| dc.type | text |