59,286 research outputs found
On the time evolution of Bernstein processes associated with a class of parabolic equations
In this article dedicated to the memory of Igor D. Chueshov, I first
summarize in a few words the joint results that we obtained over a period of
six years regarding the long-time behavior of solutions to a class of
semilinear stochastic parabolic partial differential equations. Then, as the
beautiful interplay between partial differential equations and probability
theory always was close to Igor's heart, I present some new results concerning
the time evolution of certain Markovian Bernstein processes naturally
associated with a class of deterministic linear parabolic partial differential
equations. Particular instances of such processes are certain conditioned
Ornstein-Uhlenbeck processes, generalizations of Bernstein bridges and
Bernstein loops, whose laws may evolve in space in a non trivial way.
Specifically, I examine in detail the time development of the probability of
finding such processes within two-dimensional geometric shapes exhibiting
spherical symmetry. I also define a Faedo-Galerkin scheme whose ultimate goal
is to allow approximate computations with controlled error terms of the various
probability distributions involved
On the Magnetic Prandtl Number Behavior of Accretion Disks
We investigate the behavior of the magnetic Prandtl number (ratio of
microscopic viscosity to resistivity) for accretion sources. Generally this
number is very small in standard accretion disk models, but can become larger
than unity within Schwarzschild radii of the central mass. Recent
numerical investigations suggest a marked dependence of the level of MHD
turbulence on the value of the Prandtl number. Hence, black hole and neutron
star accretors, i.e. compact X-ray sources, are affected. The astrophysical
consequences of this could be significant, including a possible route to
understanding the mysterious state changes that have long characterized these
sources.Comment: 15 pages, 6 figures. Accepted for publication in the Astrophysical
Journal (February 10, 2008 issue.) Minor changes from original submissio
Dewetting of solid films with substrate mediated evaporation
The dewetting dynamics of an ultrathin film is studied in the presence of
evaporation - or reaction - of adatoms on the substrate. KMC simulations are in
good agreement with an analytical model with diffusion, rim facetting, and
substrate sublimation. As sublimation is increased, we find a transition from
the usual dewetting regime where the front slows down with time, to a
sublimation-controlled regime where the front velocity is approximately
constant. The rim width exhibits an unexpected non-monotonous behavior, with a
maximum in time.Comment: 6 pages, 6 figure
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