Poisson structures for reduced non-holonomic systems

Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank two and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of that Poisson structures and extend their domain of definition. We apply the theory to the rolling disk, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder.Comment: 22 page

Modeling of the Vela complex including the Vela supernova remnant, the binary system gamma2 Velorum, and the Gum nebula

We study the geometry and dynamics of the Vela complex including the Vela supernova remnant (SNR), the binary system gamma2 Velorum and the Gum nebula. We show that the Vela SNR belongs to a subclass of non-Sedov adiabatic remnants in a cloudy interstellar medium (ISM), the dynamics of which is determined by the heating and evaporation of ISM clouds. We explain observable characteristics of the Vela SNR with a SN explosion with energy 1.4 x 10^50 ergs near the step-like boundary of the ISM with low intercloud densities (~ 10^{-3} cm^{-3}) and with a volume-averaged density of clouds evaporated by shock in the north-east (NE) part about four times higher than the one in the south-west (SW) part. The observed asymmetry between the NE and SW parts of the Vela SNR could be explained by the presence of a stellar wind bubble (SWB) blown by the nearest-to-the Earth Wolf-Rayet (WR) star in the gamma2 Velorum system. We show that the size and kinematics of gamma2 Velorum SWB agree with predictions of numerical calculations for the evolution of the SWB of M_ini = 35M* star. The low initial mass of the WR star in gamma2 Velorum implies that the luminosity of the nuclear line of 26Al, produced by gamma2 Velorum, is below the sensitivity of existing gamma-ray telescopes.Comment: 8 pages, 2 figures, accepted for publication in A&

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

On the relativistic Lattice Boltzmann method for quark-gluon plasma simulations

In this paper, we investigate the recently developed lattice Boltzmann model for relativistic hydrodynamics. To this purpose, we perform simulations of shock waves in quark-gluon plasma in the low and high viscosities regime, using three different computational models, the relativistic lattice Boltzmann (RLB), the Boltzmann Approach Multi-Parton Scattering (BAMPS), and the viscous sharp and smooth transport algorithm (vSHASTA). From the results, we conclude that the RLB model departs from BAMPS in the case of high speeds and high temperature(viscosities), the departure being due to the fact that the RLB is based on a quadratic approximation of the Maxwell-J\"uttner distribution, which is only valid for sufficiently low temperature and velocity. Furthermore, we have investigated the influence of the lattice speed on the results, and shown that inclusion of quadratic terms in the equilibrium distribution improves the stability of the method within its domain of applicability. Finally, we assess the viability of the RLB model in the various parameter regimes relevant to ultra-relativistic fluid dynamics.Comment: 10 pages, 16 Figure

Oxytocin moderates the association between testosterone-cortisol ratio and trustworthiness:A randomized placebo-controlled study

Oxytocin has been proposed to enhance feelings of trust, however, these findings have been difficult to replicate. Environmental or hormonal factors might influence this association. We studied whether oxytocin moderates the association between the testosterone-cortisol ratio, which is associated with risk taking behavior and aggression, and trustworthiness, while controlling for the general level of trust. A randomized double-blind placebo-controlled study with 53 healthy males was performed in which 32IU oxytocin (n = 27) or placebo (n = 26) was administered intranasally. Participants subsequently played the Trust Game in which they were allocated to the role of trustee. In the third phase of the Trust Game, we found a positive association between the testosterone-cortisol-ratio and the proportion of the amount that is returned to the investor (P=<0.01). However, administration of oxytocin reduced reciprocity in those with a high testosterone-cortisol ratio after reciprocity restoration (a significant interaction effect between administration of oxytocin and the testosterone-cortisol ratio in the third phase of the Trust Game, P = 0.015). The third phase of the Trust Game represents the restoration of reciprocity and trustworthiness, after this is violated in the second phase. Therefore, our data suggest that oxytocin might hinder the restoration of trustworthiness and diminish risk-taking behavior when trust is violated, especially in those who are hormonally prone to risk-taking behavior by a high testosterone-cortisol ratio

Derivation of fluid dynamics from kinetic theory with the 14--moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.Comment: 15 pages, 3 figures, typos fixed and discussions added; EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics

Supernovae from Red Supergiants with Extensive Mass Loss

We calculate multicolor light curves (LCs) of supernovae (SNe) from red supergiants (RSGs) exploded within dense circumstellar medium (CSM). Multicolor LCs are calculated by using a multi-group radiation hydrodynamics code STELLA. If CSM is dense enough, the shock breakout signal is delayed and smeared by CSM and kinetic energy of SN ejecta is efficiently converted to thermal energy which is eventually released as radiation. We find that explosions of RSGs are affected by CSM in early epochs when mass-loss rate just before the explosions is higher than 10^{-4} Msun/yr. Their characteristic features are that the LC has a luminous round peak followed by a flat LC, that multicolor LCs are simultaneously bright in ultraviolet and optical at the peak, and that photospheric velocity is very low at these epochs. We calculate LCs for various CSM conditions and explosion properties, i.e., mass-loss rates, radii of CSM, density slopes of CSM, explosion energies of SN ejecta, and SN progenitors inside, to see their influence on LCs. We compare our model LCs to those of ultraviolet-bright Type IIP SN 2009kf and show that the mass-loss rate of the progenitor of SN 2009kf just before the explosion is likely to be higher than 10^{-4} Msun/yr. Combined with the fact that SN 2009kf is likely to be an energetic explosion and has large 56Ni production, which implies that the progenitor of SN 2009kf is a massive RSG, our results indicate that there could be some mechanism to induce extensive mass loss in massive RSGs just before their explosions.Comment: 16 pages, 17 figures, 3 tables, accepted by Monthly Notices of the Royal Astronomical Society, the unit of Lbol in Table 3 corrected in v

First Stars. II. Evolution with mass loss

The first stars are assumed to be predominantly massive. Although, due to the low initial abundances of heavy elements the line-driven stellar winds are supposed to be inefficient in the first stars, these stars may loose a significant amount of their initial mass by other mechanisms. In this work, we study the evolution with a prescribed mass loss rate of very massive, galactic and pregalactic, Population III stars, with initial metallicities $Z=10^{-6}$ and $Z=10^{-9}$, respectively, and initial masses 100, 120, 150, 200, and 250$\,M_{\odot}$ during the hydrogen and helium burning phases. The evolution of these stars depends on their initial mass, metallicity and the mass loss rate. Low metallicity stars are hotter, compact and luminous, and they are shifted to the blue upper part in the Hertzprung-Russell diagram. With mass loss these stars provide an efficient mixing of nucleosynthetic products, and depending on the He-core mass their final fate could be either pair-instability supernovae or energetic hypernovae. These stars contributed to the reionization of the universe and its enrichment with heavy elements, which influences the subsequent star formation properties.Comment: Accepted for publication in Astrophysics & Space Science. 15 pages, 18 figure

Collisional equilibrium, particle production and the inflationary universe

Particle production processes in the expanding universe are described within a simple kinetic model. The equilibrium conditions for a Maxwell-Boltzmann gas with variable particle number are investigated. We find that radiation and nonrelativistic matter may be in equilibrium at the same temperature provided the matter particles are created at a rate that is half the expansion rate. Using the fact that the creation of particles is dynamically equivalent to a nonvanishing bulk pressure we calculate the backreaction of this process on the cosmological dynamics. It turns out that the `adiabatic' creation of massive particles with an equilibrium distribution for the latter necessarily implies power-law inflation. Exponential inflation in this context is shown to become inconsistent with the second law of thermodynamics after a time interval of the order of the Hubble time.Comment: 19 pages, latex, no figures, to appear in Phys.Rev.

Dynamics of Relativistic Interacting Gases : from a Kinetic to a Fluid Description

Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this equation to obtain an effective macroscopic description. This formalism will be useful to study the cosmic microwave background non-perturbatively in inhomogeneous cosmologies. It should also be useful for the study of the dynamics of the early universe and can be applied, if one considers fluids of galaxies, to the study of structure formation.Comment: Latex file, 28 pages, accepted for publication in Class. Quant. Gra