TY - GEN
T1 - Sandpiles and superconductors
T2 - Dual variational formulations for critical-state problems
AU - Barrett, J. W.
AU - Prigozhin, Leo
PY - 2006/11/6
Y1 - 2006/11/6
N2 - 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.
AB - 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.
KW - Critical-state problems
KW - Duality
KW - Numerical solution
KW - Variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=33750438794&partnerID=8YFLogxK
U2 - 10.1007/0-387-33882-9_3
DO - 10.1007/0-387-33882-9_3
M3 - Conference contribution
AN - SCOPUS:33750438794
SN - 0387338810
SN - 9780387338811
T3 - IFIP International Federation for Information Processing
SP - 25
EP - 29
BT - Systems Control, Modeling and Optimization
A2 - Ceragioli, F.
A2 - Pandolfi, L.
A2 - Dontchev, A.
A2 - Furuta, H.
A2 - Marti, K.
ER -