Surface Coulomb problem

Locally Stable States of the Surface Coulomb Problem... 

The locally stable equilibrium configurations of the surface Coulomb problem satisfy the additional constraint that the associated energies are local minima. Specifically, if the charge positions are described by spherical coordinates—the co-latitudes 0 s d>. < tt, and longitudes -7T < 0, TT—then the Coulomb energy (2.1) is E(i, 0,), 1 < j < N and the equilibrium condition (2.2) is equivalent to... 

Most of the numerical work was carried out with the ACPMAPS supercomputer at Fermilab. This is a parallel processing machine utilizing 600 double precision nodes. The computer searches for the locally stable states of the surface Coulomb problem were started from sets of points randomly distributed over the surface of the sphere—specifically, 10 random starts for every value of N in the range 2 A < 64 2000 starts for each successive N in the interval 65 108, 111 and 1000 starts for... 

The electrostatic energy of the 7V-particle surface Coulomb problem, Eq. (2.1), is given explicitly by... 

The locally stable solutions of the TV-charge surface Coulomb problem are constrained solely by spherical boundary conditions and the 0(4) symmetry of the Coulomb interaction. The exponential growth of the multiplicity of solutions—M(N) e Eq. (3.2a)—shows that these restrictions are compatible with a great variety of geometric structures. Only in the simplest systems is there an overlap with the criteria of strict regularity... 

The locally stable equilibrium states of the surface Coulomb problem share many of the characteristics of planar magnetic dipole configura-... 

The surface Coulomb problem is a special type of gradient system with Its extremals are determined by the simultaneous solutions... 

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