6,920 research outputs found
Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures
We consider Ising-spin systems starting from an initial Gibbs measure
and evolving under a spin-flip dynamics towards a reversible Gibbs measure
. Both and are assumed to have a finite-range
interaction. We study the Gibbsian character of the measure at time
and show the following: (1) For all and , is Gibbs
for small . (2) If both and have a high or infinite temperature,
then is Gibbs for all . (3) If has a low non-zero
temperature and a zero magnetic field and has a high or infinite
temperature, then is Gibbs for small and non-Gibbs for large
. (4) If has a low non-zero temperature and a non-zero magnetic field
and has a high or infinite temperature, then is Gibbs for
small , non-Gibbs for intermediate , and Gibbs for large . The regime
where has a low or zero temperature and is not small remains open.
This regime presumably allows for many different scenarios
Large deviations principle for Curie-Weiss models with random fields
In this article we consider an extension of the classical Curie-Weiss model
in which the global and deterministic external magnetic field is replaced by
local and random external fields which interact with each spin of the system.
We prove a Large Deviations Principle for the so-called {\it magnetization per
spin} with respect to the associated Gibbs measure, where is
the scaled partial sum of spins. In particular, we obtain an explicit
expression for the LDP rate function, which enables an extensive study of the
phase diagram in some examples. It is worth mentioning that the model
considered in this article covers, in particular, both the case of i.\,i.\,d.\
random external fields (also known under the name of random field Curie-Weiss
models) and the case of dependent random external fields generated by e.\,g.\
Markov chains or dynamical systems.Comment: 11 page
Laboratory Investigations of the Mechanism of Cavitation
The paper describes some experimental investigations of
the formation and collapse of cavitation bubbles. The
experiments were carried on in the high-speed water tunnel
of the Hydrodynamics Laboratory of the California
Institute of Technology under the sponsorship of the Research and Development Division of the Bureau of Ordnance of the U. S. Navy and the Fluid Mechanics Section
of the Office of Naval Research. A detailed study of
the formation and collapse of the individual bubbles has
been carried on by the use of high-speed motion pictures
taken at rates up to 20,000 per sec. From these records
calculations have been made of rate of formation and collapse of the bubbles. Deductions have been drawn from
these results concerning the physical mechanism of the
cavitation phenomenon
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