Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2007-11-14
Nonlinear Sciences
Adaptation and Self-Organizing Systems
19 pages, 13 figures. Submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.77.036211
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.
Holm Darryl D.
Naraigh Lennon O.
Tronci Cesare
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