2004/12/23 by John W. Barrett, Barrett, John W., Leonid Prigozhin +1
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Geological and Geochemical Analysis #Geological formations and processes #Other Condensed Matter (cond-mat.other) #Superconductivity (cond-mat.supr-con) #Theoretical and Computational Physics #cond-mat.other #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.cond-mat/0412648
Submitted to 22nd IFIP TC 7 Conference on System Modeling and Optimization Turin, Italy, July 18-22, 2005
arxiv created 2004/12/23 · openalex publication_date 2004/12/23 · arxiv updated 2009/12/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Similar evolutionary variational inequalities appear as convenient\nformulations for continuous models for sandpile growth, magnetization of\ntype-II superconductors, and evolution of some other dissipative systems\ncharacterized by the multiplicity of metastable states, long-range\ninteractions, avalanches, and hysteresis. The origin of this similarity is that\nthese are quasistationary models of equilibrium in which the multiplicity of\nmetastable states is a consequence of a unilateral condition of equilibrium\n(critical-state constraint). Existing variational formulations for\ncritical-state models of sandpiles and superconductors are convenient for\nmodelling only the "primary" variables (evolving pile shape and magnetic field,\nrespectively). The conjugate variables (the surface sand flux and the electric\nfield) are also of interest in various applications. Here we derive dual\nvariational formulations, similar to mixed variational inequalities in\nplasticity, for the sandpile and superconductor models. These formulations are\nused in numerical simulations and allow us to approximate simultaneously both\nthe primary and dual variables.\n