96 research outputs found
Analysis of Jeans instability from the Boltzmann equation
The dynamics of self-gravitating fluids is analyzed within the framework of a
collisionless Boltzmann equation in the presence of gravitational fields and
Poisson equation. Two cases are analyzed: a system with baryonic and dark
matter in a static universe and a single system in an expanding universe. The
amplitudes of the perturbed distribution functions are considered as a linear
combination of the collision invariants of the Boltzmann equation. For the
system of baryonic and dark matter, the Jeans mass of the combined system is
smaller than the one of the single system indicating that a smaller mass is
needed to initiate the collapse. For the single system in an expanding universe
it is not necessary to make use of Jeans "swindle"and it shown that for small
wavelengths the density contrast oscillates while for large wavelengths it
grows with time and the Jeans instability emerges.Comment: 10 pages, 1 figure, new analysi
The Boltzmann equation in special and general relativity
Relativistic field equations for a gas in special and general relativity are
determined from the Boltzmann equation. The constitutive equations are obtained
from the Chapman-Enskog methodology applied to a relativistic model equation
proposed by Anderson and Witting. Two applications in general relativity are
considered: one refers to a gas in a homogeneous and isotropic Universe where
irreversible processes are present during its evolution; in the other it is
analyzed a gas under the influence of a spherically symmetrical non-rotating
and uncharged source of the gravitational field.Comment: 8 pages, contributed paper at the 28th International Symposium on
Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012) correction: eqs.
(40), (42) and (43
Relative Entropy of a Freely Cooling Granular Gas
The time evolution and stationary values of the entropy per particle of a
homogeneous freely cooling granular gas, relative to the maximum entropy
consistent with the instantaneous translational and rotational temperatures, is
analyzed by means of a Sonine approximation involving fourth-degree cumulants.
The results show a rich variety of dependencies of the relative entropy on time
and on the coefficients of normal and tangential restitution, including a
peculiar behavior in the quasi-smooth limit.Comment: 6 pages; 2 figures; contributed paper at the 28th International
Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012
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