13 research outputs found
Exact solutions for a mean-field Abelian sandpile
We introduce a model for a sandpile, with N sites, critical height N and each
site connected to every other site. It is thus a mean-field model in the
spin-glass sense. We find an exact solution for the steady state probability
distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe
Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices
We show that negative of the number of floppy modes behaves as a free energy
for both connectivity and rigidity percolation, and we illustrate this result
using Bethe lattices. The rigidity transition on Bethe lattices is found to be
first order at a bond concentration close to that predicted by Maxwell
constraint counting. We calculate the probability of a bond being on the
infinite cluster and also on the overconstrained part of the infinite cluster,
and show how a specific heat can be defined as the second derivative of the
free energy. We demonstrate that the Bethe lattice solution is equivalent to
that of the random bond model, where points are joined randomly (with equal
probability at all length scales) to have a given coordination, and then
subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.
Crossover from directed percolation to compact directed percolation
We study critical spreading in a surface-modified directed percolation model
in which the left- and right-most sites have different occupation probabilities
than in the bulk. As we vary the probability for growth at an edge, the
critical exponents switch from the compact directed percolation class to
ordinary directed percolation. We conclude that the nonuniversality observed in
models with multiple absorbing configurations cannot be explained as a simple
surface effect.Comment: 4 pages, Revtex, 5 figures postscrip
A spin polarized disc
We present a solution to the gravitational field equations in a Riemann-Cartan spacetime. The solution describes a disc of infinite radius and finite thickness. The solution has three forms which depend on the size of the acceleration. The matter content of the disc is a rotating spin fluid with a constant z acceleration and a spin density polarized along the axis of rotation. The fluid has zero axial and tangential pressures. There is a radial pressure. The energy density and pressure are finite within the disc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44467/1/10714_2005_Article_BF02109124.pd