133 research outputs found
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
. For weak interactions, the shift in critical temperature is expected
to be linear in with constant of linearity . Using Markov chain
Monte Carlo methods and finite-size scaling, we find .
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
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