Shift in critical temperature for random spatial permutations with cycle weights

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of permutations. The critical temperature of the transition to long cycles depends on an interaction-strength parameter $\alpha$. For weak interactions, the shift in critical temperature is expected to be linear in $\alpha$ with constant of linearity $c$. Using Markov chain Monte Carlo methods and finite-size scaling, we find $c = 0.618 \pm 0.086$. This finding matches a similar analytical result of Ueltschi and Betz. We also examine the mean longest cycle length as a fraction of the number of sites in long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures which appeared at the end of the PDF

High-speed video recordings of lightning, electric fields and high-energy detections during thunderstorms in Catalonia Spain

High-speed video recordings of natural lightning flashes show amazing details of this phenomenon. The paper summarizes the results of the 2009 measurement campaign where the combination of electric fields, total lightning, high-energy detections and high-speed videos provided a valuable data. The paper describes the visible differences between the recorded negative, positive and upward cloudto- ground flashes. Thanks to the precise time synchronization of each video frame we investigated which processes are detected by the lightning location networks (VHF and VLF). We suggest that the VHF interferometer network detects mostly those processes of intra-cloud flashes where substantial charge is transferred during few milliseconds. The study of the detections of intra-cloud events provided by the VLF network were related to high and fast (less than a millisecond) charge transfers within the cloud that saturated the camera in the same manner as return strokes in cloud-to-ground flashes. In other hand, the paper discusses the high-energy detections related to a very close cloud-to-ground lightning flash.Preprin