Critical state problems which incorporate more than one component for the magnetization vector of hard superconductors are investigated. The theory is based on the minimization of a cost functional ${\cal C}[\vec{H}(\vec{x})]$ which weighs the changes of the magnetic field vector within the sample. We show that Bean's simplest prescription of choosing the correct sign for the critical current density $J_c$ in one dimensional problems is just a particular case of finding the components of the vector $\vec{J}_c$. $\vec{J}_c$ is determined by minimizing ${\cal C}$ under the constraint $\vec{J}\in\Delta (\vec{H},\vec{x})$, with $\Delta$ a bounded set. Upon the selection of different sets $\Delta$ we discuss existing crossed field measurements and predict new observable features. It is shown that a complex behavior in the magnetization curves may be controlled by a single external parameter, i.e.: the maximum value of the applied magnetic field $H_m$.Comment: 10 pages, 9 figures, accepted in Phys. Rev.

Coarse-grained flux density profiles in type-II superconductors with nonparallel vortex configurations are obtained by a proposed phenomenological least action principle. We introduce a functional C[ H] which is minimized under a constraint of the kind J ∈ ∆( H, x), where ∆ is a bounded set.In particular, we choose the isotropic case | J | ≤ J c (H), for which the field penetration profiles H( x, t) are derived when a changing external excitation is applied. Faraday's law, and the principle of minimum entropy production rate for stationary thermodynamic processes dictate the evolution of the system.Calculations based on the model can reproduce the physical phenomena of flux transport and consumption, and the striking effect of magnetization collapse in crossed field measurements. PACS number(s): 41.20. Gz,74.60.Jg, 74.60.Ge, 02.30.Xx Typeset using REVT E X 1

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