345 research outputs found
Static- and dynamical-phase transition in multidimensional voting models on continua
A voting model (or a generalization of the Glauber model at zero temperature)
on a multidimensional lattice is defined as a system composed of a lattice each
site of which is either empty or occupied by a single particle. The reactions
of the system are such that two adjacent sites, one empty the other occupied,
may evolve to a state where both of these sites are either empty or occupied.
The continuum version of this model in a Ddimensional region with boundary is
studied, and two general behaviors of such systems are investigated. The
stationary behavior of the system, and the dominant way of the relaxation of
the system toward its stationary state. Based on the first behavior, the static
phase transition (discontinuous changes in the stationary profiles of the
system) is studied. Based on the second behavior, the dynamical phase
transition (discontinuous changes in the relaxation-times of the system) is
studied. It is shown that the static phase transition is induced by the bulk
reactions only, while the dynamical phase transition is a result of both bulk
reactions and boundary conditions.Comment: 10 pages, LaTeX2
Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pad\'e approximation
Complex analytical structure of Stokes wave for two-dimensional potential
flow of the ideal incompressible fluid with free surface and infinite depth is
analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating
with the constant velocity. Simulations with the quadruple and variable
precisions are performed to find Stokes wave with high accuracy and study the
Stokes wave approaching its limiting form with radians angle on the
crest. A conformal map is used which maps a free fluid surface of Stokes wave
into the real line with fluid domain mapped into the lower complex half-plane.
The Stokes wave is fully characterized by the complex singularities in the
upper complex half-plane. These singularities are addressed by rational
(Pad\'e) interpolation of Stokes wave in the complex plane. Convergence of
Pad\'e approximation to the density of complex poles with the increase of the
numerical precision and subsequent increase of the number of approximating
poles reveals that the only singularities of Stokes wave are branch points
connected by branch cuts. The converging densities are the jumps across the
branch cuts. There is one branch cut per horizontal spatial period of
Stokes wave. Each branch cut extends strictly vertically above the
corresponding crest of Stokes wave up to complex infinity. The lower end of
branch cut is the square-root branch point located at the distance from
the real line corresponding to the fluid surface in conformal variables. The
limiting Stokes wave emerges as the singularity reaches the fluid surface.
Tables of Pad\'e approximation for Stokes waves of different heights are
provided. These tables allow to recover the Stokes wave with the relative
accuracy of at least . The tables use from several poles to about
hundred poles for highly nonlinear Stokes wave with Comment: 38 pages, 9 figures, 4 tables, supplementary material
Beyond the random phase approximation: Stimulated Brillouin backscatter for finite laser coherence times
We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of
a spatially and temporally partially incoherent laser beam for laser fusion
relevant plasma. We find a new collective regime of BSBS (CBSBS) with intensity
threshold controlled by diffraction, an insensitive function of the laser
coherence time, , once light travel time during exceeds a laser
speckle length. The BSBS spatial gain rate is approximately the sum of that due
to CBSBS, and a part which is independent of diffraction and varies linearly
with . We find that the bandwidth of KrF-laser-based fusion systems would
be large enough to allow additional suppression of BSBS.Comment: 8 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1105.209
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