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

Propagation velocity of epileptiform activity in the hippocampus

The propagation of epileptiform burst activity was investigated in the CA1 area of the in-vitro hippocampal slice preparation of the guinea pig. This activity was provoked by 0.1 mM 4-aminopyridine in the bathing medium and was recorded in the pyramidal layer with an array of eight electrodes. The delay between the first population spike of a burst recorded with different electrodes was calculated using the cross-correlation function. The propagation velocity was estimated from the delays and the electrode intervals. It was found that the velocity of spontaneous and evoked epileptiform bursts varies between 0.15 and 5 m/s and is not confined to the range of conduction velocities of the fibre systems in CA1 (0.3–0.55 and 1.0–1.8 m/s). Different velocities can be present in different parts of the CA1 area and the initiation of spontaneous bursts is not confined to the CA2–3 areas, but can also occur in CA1. Burst activity also propagated in a low calcium-high magnesium medium. Different mechanisms of propagation are discussed and it is argued that the propagation velocity due to ephaptic interaction may vary largely. It is concluded that epileptiform activity can be propagated not only by synaptic connections at or near the pyramidal layer, but also by way of electrical field effects of population spikes