41,609 research outputs found
Analytical study of tunneling times in flat histogram Monte Carlo
We present a model for the dynamics in energy space of multicanonical
simulation methods that lends itself to a rather complete analytic
characterization. The dynamics is completely determined by the density of
states. In the \pm J 2D spin glass the transitions between the ground state
level and the first excited one control the long time dynamics. We are able to
calculate the distribution of tunneling times and relate it to the
equilibration time of a starting probability distribution. In this model, and
possibly in any model in which entering and exiting regions with low density of
states are the slowest processes in the simulations, tunneling time can be much
larger (by a factor of O(N)) than the equilibration time of the probability
distribution. We find that these features also hold for the energy projection
of single spin flip dynamics.Comment: 7 pages, 4 figures, published in Europhysics Letters (2005
Large time behavior for vortex evolution in the half-plane
In this article we study the long-time behavior of incompressible ideal flow
in a half plane from the point of view of vortex scattering. Our main result is
that certain asymptotic states for half-plane vortex dynamics decompose
naturally into a nonlinear superposition of soliton-like states. Our approach
is to combine techniques developed in the study of vortex confinement with weak
convergence tools in order to study the asymptotic behavior of a self-similar
rescaling of a solution of the incompressible 2D Euler equations on a half
plane with compactly supported, nonnegative initial vorticity.Comment: 30 pages, no figure
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