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

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

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

Velocity Tails for Inelastic Maxwell Models

We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the Boltzmann equation, we find that the velocity distribution function decays algebraically for large velocities, with exponents that are analytically calculated.Comment: 4 pages, 2 figure

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 $\omega$ 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: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

Open Clusters IC 4665 and Cr 359 and a Probable Birthplace of the Pulsar PSR B1929+10

Based on the epicyclic approximation, we have simulated the motion of the young open star clusters IC 4665 and Collinder 359. The separation between the cluster centers is shown to have been minimal 7 Myr ago, 36 pc. We have established a close evolutionary connection between IC 4665 and the Scorpius-Centaurus association -- the separation between the centers of these structures was $\approx200$ pc 15 Myr ago. In addition, the center of IC 4665 at this time was near two well-known regions of coronal gas: the Local Bubble and the North Polar Spur. The star HIP 86768 is shown to be one of the candidates for a binary (in the past) with the pulsar PSR B1929+10. At the model radial velocity of the pulsar $V_r= 2\pm50$ km s$^{-1}$, a close encounter of this pair occurs in the vicinity of IC 4665 at a time of -1.1 Myr. At the same time, using currently available data for the pulsar B1929+10 at its model radial velocity $V_r=200\pm50$ km s$^{-1}$, we show that the hypothesis of Hoogerwerf et al. (2001) about the breakup of the $\zeta$Oph--B1929+10 binary in the vicinity of Upper Scorpius (US) about 0.9 Myr ago is more plausible.Comment: 19 pages, 8 figure

Steady state properties of a mean field model of driven inelastic mixtures

We investigate a Maxwell model of inelastic granular mixture under the influence of a stochastic driving and obtain its steady state properties in the context of classical kinetic theory. The model is studied analytically by computing the moments up to the eighth order and approximating the distributions by means of a Sonine polynomial expansion method. The main findings concern the existence of two different granular temperatures, one for each species, and the characterization of the distribution functions, whose tails are in general more populated than those of an elastic system. These analytical results are tested against Monte Carlo numerical simulations of the model and are in general in good agreement. The simulations, however, reveal the presence of pronounced non-gaussian tails in the case of an infinite temperature bath, which are not well reproduced by the Sonine method.Comment: 23 pages, 10 figures, submitted for publicatio

The OSACA Database and a Kinematic Analysis of Stars in the Solar Neighborhood

We transformed radial velocities compiled from more than 1400 published sources, including the Geneva--Copenhagen survey of the solar neighborhood (CORAVEL-CfA), into a uniform system based on the radial velocities of 854 standard stars in our list. This enabled us to calculate the average weighted radial velocities for more than 25~000 HIPPARCOS stars located in the local Galactic spiral arm (Orion arm) with a median error of +-1 km/s. We use these radial velocities together with the stars' coordinates, parallaxes, and proper motions to determine their Galactic coordinates and space velocities. These quantities, along with other parameters of the stars, are available from the continuously updated Orion Spiral Arm CAtalogue (OSACA) and the associated database. We perform a kinematic analysis of the stars by applying an Ogorodnikov-Milne model to the OSACA data. The kinematics of the nearest single and multiple main-sequence stars differ substantially. We used distant (r\approx 0.2 kpc) stars of mixed spectral composition to estimate the angular velocity of the Galactic rotation -25.7+-1.2 km/s/kpc, and the vertex deviation,l=13+-2 degrees, and detect a negative K effect. This negative K effect is most conspicuous in the motion of A0-A5 giants, and is equal to K=-13.1+-2.0 km/s/kpc.Comment: 16 pages, 8 figure

Subsurface planning: Towards a common understanding of the subsurface as a multifunctional resource

In response to powerful trends in technology, resource and land supply and demand, socioeconomics and geopolitics, cities are likely to increase use of the subsurface in the near future. Indeed, the subsurface and its appropriate use have been put forward as being of crucial importance if we are to achieve resilient and sustainable cities. In recent years, quite apart from being seen primarily as a construction basis to provide physical space for infrastructure and to create a better surface living environment, the subsurface has been recognised as a multifunctional natural resource, one which provides physical space, water, energy, materials, habitats for ecosystems, support for surface life, and a repository for cultural heritage and geological archives. Currently, the subsurface is often utilised according to the “first-come-first-served” principle, which hinders possibilities to take strategic decisions on prioritisation and optimisation of competing subsurface uses, as well as fair inter- and intragenerational distribution of limited natural resources. Taking a broad international perspective, this paper investigates the subsurface as a multifunctional resource from five focal points: (1) what professionals with different backgrounds mean when using different terms related to the subsurface; (2) how professionals describe the subsurface and its multiple resources, functions and services; (3) how planning of subsurface use is supported in policy and regulations; (4) how the subsurface is included in the planning process; and (5) frameworks that can support decision-making on responsible use of the subsurface. The study reveals that the subsurface must be recognised (not only by scientists but also by decision- and policy-makers and other stakeholders) as a precious and multifunctional resource requiring careful planning and sensitive management in accordance with its potential and its value to society. Utilisation of the different subsurface functions to yield services requires careful planning and a framework to support decision-makers in achieving a balance between utilisation and preservation, and between the subsurface functions themselves in the case of outright utilisation. Further, to facilitate the necessary change towards transdisciplinary work settings in the planning process and form a platform for knowledge exchange and capacity building, there is an urgent need for a common language, i.e. mutually understandable terminology, and a common understanding, i.e. an all-inclusive view on the subsurface as a complex multifunctional resource