11,060 research outputs found
Regularization of subsolutions in discrete weak KAM theory
We expose different methods of regularizations of subsolutions in the context
of discrete weak KAM theory. They allow to prove the existence and the density
of subsolutions. Moreover, these subsolutions can be made strict and
smooth outside of the Aubry set.Comment: 15 pages, second version. Modified according to the referee's
suggestions. The hypotheses are now uniform throughout the paper, which
allows a simpler and more general statement of the main result
A two-scale approach to the hydrodynamic limit, part II: local Gibbs behavior
This work is a follow-up on [GOVW]. In that previous work a two-scale
approach was used to prove the logarithmic Sobolev inequality for a system of
spins with fixed mean whose potential is a bounded perturbation of a Gaussian,
and to derive an abstract theorem for the convergence to the hydrodynamic
limit. This strategy was then successfully applied to Kawasaki dynamics. Here
we shall use again this two-scale approach to show that the microscopic
variable in such a model behaves according to a local Gibbs state. As a
consequence, we shall prove the convergence of the microscopic entropy to the
hydrodynamic entropy.Comment: 31 pages, 2nd version. The proof of Theorem 1.15 has been simplifie
Origin theories for the eccentricities of extrasolar planets
Half the known extrasolar planets have orbital eccentricities in excess of
0.3. Such large eccentricities are surprising as it is thought that planets
form in a protoplanetary disk on nearly circular orbits much like the current
states of the solar system planets. Possible explanations for the large
planetary eccentricities include the perturbations that accompany planet-planet
scattering, the tidal interaction between the gas disk and the planets, Kozai's
secular eccentricity cycles, the eccentricity excitation during planetary pair
migration in mean motion resonance, the perturbations by stellar encounters,
stellar-like relaxation that occurs if planets formed through gravitational
instability, and the relative acceleration by the stellar jet system of the
host star with respect to the companion. In this chapter, we comment on the
relevance and characteristics of the various eccentricity origin theories.Comment: 23 pages, 8 figures. Review lecture at the 2006 Aussois Winter School
"Open Problems in Celestial Mechanics". To appear in Lecture Notes in
Physics, Springe
On dynamical friction in a gaseous medium with a boundary
Dynamical friction arises from the interaction of a perturber and the
gravitational wake it excites in the ambient medium. We study the effects of
the presence of a boundary on dynamical friction by studying analytically the
interaction of perturber with uniform rectilinear motion in a uniform
homogeneous medium with a reflecting planar boundary. Wake reflection at a
medium's boundary may occur at the edges of truncated disks perturbed by
planetary or stellar companions as well as in numerical simulations of
planet-disk interaction with no-outflow boundary conditions. In this paper, we
show that the presence of the boundary modifies the behaviour of dynamical
friction significantly. We find that perturbers are invariably pushed away from
the boundary and reach a terminal subsonic velocity near Mach 0.37 regardless
of initial velocity. Dynamical friction may even be reversed for Mach numbers
less than 0.37 thereby accelerating instead of decelerating the perturber.
Perturbers moving parallel to the boundary feel additional friction orthogonal
to the direction of motion that is much stronger than the standard friction
along the direction of motion. These results indicate that the common use of
the standard Chandrasekhar formula as a short hand estimate of dynamical
friction may be inadequate as observed in various numerical simulations.Comment: Revised version, 28 pages, 10 figures, Accepted for publication in
Astrophysics & Space Scienc
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