Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2004-12-23
Physics
Condensed Matter
Other Condensed Matter
Submitted to 22nd IFIP TC 7 Conference on System Modeling and Optimization Turin, Italy, July 18-22, 2005
Scientific paper
Similar evolutionary variational inequalities appear as convenient formulations for continuous models for sandpile growth, magnetization of type-II superconductors, and evolution of some other dissipative systems characterized by the multiplicity of metastable states, long-range interactions, avalanches, and hysteresis. The origin of this similarity is that these are quasistationary models of equilibrium in which the multiplicity of metastable states is a consequence of a unilateral condition of equilibrium (critical-state constraint). Existing variational formulations for critical-state models of sandpiles and superconductors are convenient for modelling only the "primary" variables (evolving pile shape and magnetic field, respectively). The conjugate variables (the surface sand flux and the electric field) are also of interest in various applications. Here we derive dual variational formulations, similar to mixed variational inequalities in plasticity, for the sandpile and superconductor models. These formulations are used in numerical simulations and allow us to approximate simultaneously both the primary and dual variables.
Barrett John W.
Prigozhin Leonid
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