Advertisement

Sandpiles and Superconductors: Dual Variational Formulations for Critical-State Problems

  • J. W. Barrett
  • L. Prigozhin
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)

Abstract

Similar evolutionary variational inequalities appear as variational formulations of 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. Such formulations for sandpile and superconductor models are, however, convenient for modeling only some of the variables (evolving pile shape and magnetic field for sandpile and superconductor models, 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.

keywords

variational inequalities critical-state problems duality numerical solution 

References

  1. [1]
    L. Prigozhin. Variational inequalities in critical-state problems. Physica D 167:197–210, 2004.MathSciNetCrossRefGoogle Scholar
  2. [2]
    P. Cannarsa, P. Cardaliaguet. Representation of equilibrium solutions to the table problem for growing sandpiles. J. Eur. Math. Soc. 6:435–464, 2004.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    J. W. Barrett, L. Prigozhin. Dual formulations in critical-state problems. In preparation.Google Scholar
  4. [4]
    A. Badía-Majós, C. López. Electric field in hard superconductors with arbitrary cross section and general critical current law. J. Appl Phys. 95:8035–8040, 2004.CrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • J. W. Barrett
    • 1
  • L. Prigozhin
    • 2
  1. 1.Dept. of MathematicsImperial CollegeLondonUK
  2. 2.Blaustein Institute for Desert ResearchBen-Gurion UniversityIsrael

Personalised recommendations