397 research outputs found
The dissipative linear Boltzmann equation for hard spheres
We prove the existence and uniqueness of an equilibrium state with unit mass
to the dissipative linear Boltzmann equation with hard--spheres collision
kernel describing inelastic interactions of a gas particles with a fixed
background. The equilibrium state is a universal Maxwellian distribution
function with the same velocity as field particles and with a non--zero
temperature lower than the background one, which depends on the details of the
binary collision. Thanks to the H--theorem we then prove strong convergence of
the solution to the Boltzmann equation towards the equilibrium.Comment: 17 pages, submitted to Journal of Statistical Physic
On the speed of approach to equilibrium for a collisionless gas
We investigate the speed of approach to Maxwellian equilibrium for a
collisionless gas enclosed in a vessel whose wall are kept at a uniform,
constant temperature, assuming diffuse reflection of gas molecules on the
vessel wall. We establish lower bounds for potential decay rates assuming
uniform bounds on the initial distribution function. We also obtain a
decay estimate in the spherically symmetric case. We discuss with particular
care the influence of low-speed particles on thermalization by the wall.Comment: 22 pages, 1 figure; submitted to Kinetic and Related Model
Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior
We consider the spatially homogeneous Boltzmann equation for inelastic hard
spheres, in the framework of so-called constant normal restitution
coefficients. We prove the existence of self-similar solutions, and we give
pointwise estimates on their tail. We also give general estimates on the tail
and the regularity of generic solutions. In particular we prove Haff 's law on
the rate of decay of temperature, as well as the algebraic decay of
singularities. The proofs are based on the regularity study of a rescaled
problem, with the help of the regularity properties of the gain part of the
Boltzmann collision integral, well-known in the elastic case, and which are
extended here in the context of granular gases.Comment: 41 page
Galactic Rotation Parameters from Data on Open Star Clusters
Currently available data on the field of velocities Vr, Vl, Vb for open star
clusters are used to perform a kinematic analysis of various samples that
differ by heliocentric distance, age, and membership in individual structures
(the Orion, Carina--Sagittarius, and Perseus arms). Based on 375 clusters
located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the
Galactic rotation parameters
Wo =-26.0+-0.3 km/s/kpc,
W'o = 4.18+-0.17 km/s/kpc^2,
W''o=-0.45+-0.06 km/s/kpc^3, the system contraction parameter K = -2.4+-0.1
km/s/kpc, and the parameters of the kinematic center Ro =7.4+-0.3 kpc and lo =
0+-1 degrees. The Galactocentric distance Ro in the model used has been found
to depend significantly on the sample age. Thus, for example, it is 9.5+-0.7
kpc and 5.6+-0.3 kpc for the samples of young (50 Myr)
clusters, respectively. Our study of the kinematics of young open star clusters
in various spiral arms has shown that the kinematic parameters are similar to
the parameters obtained from the entire sample for the Carina-Sagittarius and
Perseus arms and differ significantly from them for the Orion arm. The
contraction effect is shown to be typical of star clusters with various ages.
It is most pronounced for clusters with a mean age of 100 Myr, with the
contraction velocity being Kr = -4.3+-1.0 km/s.Comment: 14 pages, 4 figures, 2 table
Kinetic models with randomly perturbed binary collisions
We introduce a class of Kac-like kinetic equations on the real line, with
general random collisional rules, which include as particular cases models for
wealth redistribution in an agent-based market or models for granular gases
with a background heat bath. Conditions on these collisional rules which
guarantee both the existence and uniqueness of equilibrium profiles and their
main properties are found. We show that the characterization of these
stationary solutions is of independent interest, since the same profiles are
shown to be solutions of different evolution problems, both in the econophysics
context and in the kinetic theory of rarefied gases
Elemental Abundances of Solar Sibling Candidates
Dynamical information along with survey data on metallicity and in some cases
age have been used recently by some authors to search for candidates of stars
that were born in the cluster where the Sun formed. We have acquired high
resolution, high signal-to-noise ratio spectra for 30 of these objects to
determine, using detailed elemental abundance analysis, if they could be true
solar siblings. Only two of the candidates are found to have solar chemical
composition. Updated modeling of the stars' past orbits in a realistic Galactic
potential reveals that one of them, HD162826, satisfies both chemical and
dynamical conditions for being a sibling of the Sun. Measurements of
rare-element abundances for this star further confirm its solar composition,
with the only possible exception of Sm. Analysis of long-term high-precision
radial velocity data rules out the presence of hot Jupiters and confirms that
this star is not in a binary system. We find that chemical tagging does not
necessarily benefit from studying as many elements as possible, but instead
from identifying and carefully measuring the abundances of those elements which
show large star-to-star scatter at a given metallicity. Future searches
employing data products from ongoing massive astrometric and spectroscopic
surveys can be optimized by acknowledging this fact.Comment: ApJ, in press. Tables 2 and 4 are available in full in the "Other
formats: source" downloa
Celebrating Cercignani's conjecture for the Boltzmann equation
Cercignani's conjecture assumes a linear inequality between the entropy and
entropy production functionals for Boltzmann's nonlinear integral operator in
rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities
and spectral gap inequalities, this issue has been at the core of the renewal
of the mathematical theory of convergence to thermodynamical equilibrium for
rarefied gases over the past decade. In this review paper, we survey the
various positive and negative results which were obtained since the conjecture
was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani,
powerful mind and great scientist, one of the founders of the modern theory
of the Boltzmann equation. 24 pages. V2: correction of some typos and one
ref. adde
Astrometric Control of the Inertiality of the Hipparcos Catalog
Based on the most complete list of the results of an individual comparison of
the proper motions for stars of various programs common to the Hipparcos
catalog, each of which is an independent realization of the inertial reference
frame with regard to stellar proper motions, we redetermined the vector
of residual rotation of the ICRS system relative to the extragalactic
reference frame. The equatorial components of this vector were found to be the
following: mas yr,
mas yr, and mas yr.Comment: 8 pages, 1 figur
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