Delay time distribution of type Ia supernovae: theory vs. observation

Two formation scenarios are investigated for type Ia supernovae in elliptical galaxies: the single degenerate scenario (a white dwarf reaching the Chandrasekhar limit through accretion of matter transferred from its companion star in a binary) and the double degenerate scenario (the inspiraling and merging of two white dwarfs in a binary as a result of the emission of gravitational wave radiation). A population number synthesis code is used, which includes the latest physical results in binary evolution and allows to differentiate between certain physical scenarios (such as the description of common envelope evolution) and evolutionary parameters (such as the mass transfer efficiency during Roche lobe overflow). The thus obtained theoretical distributions of type Ia supernova delay times are compared to those that are observed, both in morphological shape and absolute number of events. The critical influence of certain parameters on these distributions is used to constrain their values. The single degenerate scenario alone is found to be unable in reproducing the morphological shape of the observational delay time distribution, while use of the double degenerate one (or a combination of both) does result in fair agreement. Most double degenerate type Ia supernovae are formed through a normal, quasi-conservative Roche lobe overflow followed by a common envelope phase, not through two successive common envelope phases as is often assumed. This may cast doubt on the determination of delay times by using analytical formalisms, as is sometimes done in other studies. The theoretical absolute number of events in old elliptical galaxies lies a factor of at least three below the rates that are observed. While this may simply be the result of observational uncertainties, a better treatment of the effects of rotation on stellar structure could mitigate the discrepancy.Comment: 5 pages, 4 figures, to appear in proceedings of "Binary Star Evolution: Mass Loss, Accretion, and Mergers

Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.Comment: 93 pages, no figure

A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

We describe a simple family of analytical coordinate systems for the Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are spatially isotropic. Spatial slices of constant coordinate time $t$ feature a trumpet geometry with an asymptotically cylindrical end inside the horizon at a prescribed areal radius $R_0$ (with $0<R_{0}\leq M$) that serves as the free parameter for the family. The slices also have an asymptotically flat end at spatial infinity. In the limit $R_{0}=0$ the spatial slices lose their trumpet geometry and become flat -- in this limit, our coordinates reduce to Painlev\'e-Gullstrand coordinates.Comment: 7 pages, 3 figure

Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general non-equilibrium thermodynamic description of the system when it is out of equilibrium. We then apply it to study the structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.Comment: 20 pages, 1 figur

Effects of CPT and Lorentz Invariance Violation on Pulsar Kicks

The breakdown of Lorentz's and CPT invariance, as described by the Extension of the Standard Model, gives rise to a modification of the dispersion relation of particles. Consequences of such a modification are reviewed in the framework of pulsar kicks induced by neutrino oscillations (active-sterile conversion). A peculiar feature of the modified energy-momentum relations is the occurrence of terms of the form \delta {\bbox \Pi}\cdot {\bf {\hat p}}, where \delta {\bbox \Pi} accounts for the difference of spatial components of flavor depending coefficients which lead to the departure of the Lorentz symmetry, and ${\bf {\hat p}}={\bf p}/p$, being ${\bf p}$ the neutrino momentum. Owing to the relative orientation of ${\bf p}$ with respect to \delta {\bbox \Pi}, the {\it coupling} \delta {\bbox \Pi}\cdot {\bf {\hat p}} may induce the mechanism to generate the observed pulsar velocities. Topics related to the velocity distribution of pulsars are also discussed.Comment: 10 pages, 1 figur

A fluctuation theorem for currents and non-linear response coefficients

We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations

Excision boundary conditions for the conformal metric

Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a freely-specifiable variable, but rather is determined as a solution to the field equations. The new set of freely-specifiable variables includes only time-derivatives of metric quantities, which makes this decomposition very attractive for the construction of quasiequilibrium solutions. To date, this new formalism has only been used for binary neutron stars. Applications involving black holes require new boundary conditions for the conformal metric on the domain boundaries. In this paper we demonstrate how these boundary conditions follow naturally from the conformal geometry of the boundary surfaces and the inherent gauge freedom of the conformal metric.Comment: 10 pages, revtex4, accepted by Physical Review

Thermodynamic Field Theory with the Iso-Entropic Formalism

A new formulation of the thermodynamic field theory (TFT) is presented. In this new version, one of the basic restriction in the old theory, namely a closed-form solution for the thermodynamic field strength, has been removed. In addition, the general covariance principle is replaced by Prigogine's thermodynamic covariance principle (TCP). The introduction of TCP required the application of an appropriate mathematical formalism, which has been referred to as the iso-entropic formalism. The validity of the Glansdorff-Prigogine Universal Criterion of Evolution, via geometrical arguments, is proven. A new set of thermodynamic field equations, able to determine the nonlinear corrections to the linear ("Onsager") transport coefficients, is also derived. The geometry of the thermodynamic space is non-Riemannian tending to be Riemannian for hight values of the entropy production. In this limit, we obtain again the same thermodynamic field equations found by the old theory. Applications of the theory, such as transport in magnetically confined plasmas, materials submitted to temperature and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein.Comment: 35 page

Random paths and current fluctuations in nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems

A model for the degradation of polyimides due to oxidation

Polyimides, due to their superior mechanical behavior at high temperatures, are used in a variety of applications that include aerospace, automobile and electronic packaging industries, as matrices for composites, as adhesives etc. In this paper, we extend our previous model in [S. Karra, K. R. Rajagopal, Modeling the non-linear viscoelastic response of high temperature polyimides, Mechanics of Materials, In press, doi:10.1016/j.mechmat.2010.09.006], to include oxidative degradation of these high temperature polyimides. Appropriate forms for the Helmholtz potential and the rate of dissipation are chosen to describe the degradation. The results for a specific boundary value problem, using our model compares well with the experimental creep data for PMR-15 resin that is aged in air.Comment: 13 pages, 2 figures, submitted to Mechanics of Time-dependent Material