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The dynamics of line singularities in three different physical systems are considered, namely vortices in an inviscid fluid, vortices in a type-II superconductor, and dislocations in an elastic crystal. When the core of the singularity can be re[...]texto impreso
A model for the interaction of dislocations in a honeycomb-type configuration is proposed. Formation of complex structures is expected when the two populations involved interact. Our system of conservation laws turns out to degenerate into an el[...]texto impreso
Carpio, Ana ; Chapman, S.J. ; Velázquez, J.J. L. | Society for Industrial and Applied Mathematics | 2001Some continuum models for dislocation interactions in a simple crystal geometry are studied. The simplest models are mixed systems ofconservation laws which are shown to exhibit singularities and instabilities. These are then regularized, leadin[...]texto impreso
Motivated by models from fracture mechanics and from biology, we study the infinite system of differential equations u'(n) = u(n-1) - 2u(n) + u(n+1) - A sin u(n) + F, ' = d/dt, where A and F are positive parameters. For fixed A > 0 we show that[...]
