Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails

We consider the Boltzmann equations for mixtures ofMaxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that power like tails can appear not just for granular particles (Maxwell models are far from reality in this case), but also in the system of particles interacting in accordance with laws of classical mechanics. In addition, non-existence of positive self-similar solutions with finite moments of any order is proven for a wide class of Maxwell models.Comment: 20 page

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

Flexoelectricity and pattern formation in nematic liquid crystals

We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $\omega$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic which describes the elasticity with respects to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $\omega \to 0$ is highly singular. In distinct contrast to the dc-case, where the patterns are stationary and time-independent, they appear at finite, small $\omega$ periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electro-hydrodynamic instability in nematics, which presents a non-equilibrium dissipative transition. It will be demonstrated that $\omega$ is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes

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

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

Kinematic Control of the Inertiality of the System of Tycho-2 and UCAC2 Stellar Proper Motions

Based on the Ogorodnikov-Milne model, we analyze the proper motions of Tycho-2 and UCAC2 stars. We have established that the model component that describes the rotation of all stars under consideration around the Galactic y axis differs significantly from zero at various magnitudes. We interpret this rotation found using the most distant stars as a residual rotation of the ICRS/Tycho-2 system relative to the inertial reference frame. For the most distant ($d\approx900$ pc) Tycho-2 and UCAC2 stars, the mean rotation around the Galactic y axis has been found to be $M_{13}=-0.37\pm0.04$ mas yr$^{-1}$. The proper motions of UCAC2 stars with magnitudes in the range $12-15^m$ are shown to be distorted appreciably by the magnitude equation in $\mu_\alpha\cos\delta$, which has the strongest effect for northern-sky stars with a coefficient of $-0.60\pm0.05$ mas yr$^{-1}$ mag$^{-1}$. We have detected no significant effect of the magnitude equation in the proper motions of UCAC2 stars brighter than $\approx11^m$.Comment: 15 pages, 6 figure