Hydromagnetic equilibrium configurations.

Equilibrium configurations of defective crystals

Equilibrium configurations of tripolar charges

It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic moleculelike structures. The basic combinatoric rule remains essentially the same on different levels of the hierarchy, thus leading to a pattern of resemblance between different levels. The number of pri...

Hydromagnetic Equilibrium Ii. Stability in the Variational Formulation.

In a few recent papers (Woltjer," 2 Chandrasekhar3) a beginning has been made with a variational formulation of the problems of hydromagnetic equilibrium. A similar approach was followed by Kruskal and Kulsrud4 who examined the static equilibrium in a toroid from the variational point of view, making largely use of topological arguments. It seems somewhat doubtful whether this approach can be g...

Equilibrium Vortex Configurations in Domains with Boundary

Given a stable configuration of point vortices for steady two-dimensional inviscid, incompressible fluid flow in a domain D, it is shown that there is another stable configuration of stationary vortices in D with vortices near the original vortices plus additional vortices near any points on the boundary where the speed of the original flow is a nonzero relative minimum.

Uniqueness of Equilibrium Configurations in Solid Crystals

In this article, under suitable assumptions, it is proved that infu∈UΛ E[u] is dual to sup(a,b){ ∫ Ω a(F(x))dx + ∫ Λ b(y)dy}, where, E[u] := ∫ Ω(h(detDu) − F · u)dx. Here, the infimum is performed over UΛ, the set of all orientation-preserving deformations u ∈ C1(Ω)d that are homeomorphisms from Ω̄ onto Λ̄, and the supremum is performed over the set of all upper semicontinuous functions a, b such...