Classical Equations for Quantum Systems

The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e. such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of the noise consisting of the fluctuations that typical mechanisms of decoherence produce. We describe the derivation of phenomenological equations of motion explicitly for a particular class of models. Probabilities of the correlations in time that define equations of motion are explicitly considered. Fully non-linear cases are studied. Methods are exhibited for finding the form of the phenomenological equations of motion even when these are only distantly related to those of the fundamental action. The demonstration of the connection between quantum-mechanical causality and causalty in classical phenomenological equations of motion is generalized. The connections among decoherence, noise, dissipation, and the amount of coarse graining necessary to achieve classical predictability are investigated quantitatively.Comment: 100pages, 1 figur

Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows

When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical experiments indicate that the motion near a parabolic resonance exhibits new type of chaotic behavior which includes instabilities in some directions and long trapping times in others. Moreover, in a degenerate case, near a {\it flat parabolic resonance}, large scale instabilities appear. A model arising from an atmospherical study is shown to exhibit flat parabolic resonance. This supplies a simple mechanism for the transport of particles with {\it small} (i.e. atmospherically relevant) initial velocities from the vicinity of the equator to high latitudes. A modification of the model which allows the development of atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities are clearly observed

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Quasi-Homogeneous Thermodynamics and Black Holes

We propose a generalized thermodynamics in which quasi-homogeneity of the thermodynamic potentials plays a fundamental role. This thermodynamic formalism arises from a generalization of the approach presented in paper [1], and it is based on the requirement that quasi-homogeneity is a non-trivial symmetry for the Pfaffian form $\delta Q_{rev}$. It is shown that quasi-homogeneous thermodynamics fits the thermodynamic features of at least some self-gravitating systems. We analyze how quasi-homogeneous thermodynamics is suggested by black hole thermodynamics. Then, some existing results involving self-gravitating systems are also shortly discussed in the light of this thermodynamic framework. The consequences of the lack of extensivity are also recalled. We show that generalized Gibbs-Duhem equations arise as a consequence of quasi-homogeneity of the thermodynamic potentials. An heuristic link between this generalized thermodynamic formalism and the thermodynamic limit is also discussed.Comment: 39 pages, uses RevteX. Published version (minor changes w.r.t. the original one

Mode Switching Time Scales in the Classical Variable Stars

Near the edges of the instability strip the rate of stellar evolution is larger than the growth-rate of the pulsation amplitude, and the same holds whenever the star is engaged in pulsational mode switching. Stellar evolution therefore controls both the onset of pulsation at the edges of the instability strip and of mode switching inside it. Two types of switchings (bifurcations) occur. In a soft bifurcation the switching time scale is the inverse harmonic mean of the pulsational modal growth-rate and of the stellar evolution rate. In a hard bifurcation the switching times can be substantially longer than the thermal time scale which is typically of the order of a hundred periods for Cepheids and RR Lyrae. We discuss some of the observational consequences, in particular the paucity of low amplitude pulsators at the edges of the instability strip.Comment: 5 pages, 3 figures, ApJ (in press

Hydrostatic models for the rotation of extra-planar gas in disk galaxies

We show that fluid stationary models are able to reproduce the observed, negative vertical gradient of the rotation velocity of the extra-planar gas in spiral galaxies. We have constructed models based on the simple condition that the pressure of the medium does not depend on density alone (baroclinic instead of barotropic solutions: isodensity and isothermal surfaces do not coincide). As an illustration, we have successfully applied our method to reproduce the observed velocity gradient of the lagging gaseous halo of NGC 891. The fluid stationary models discussed here can describe a hot homogeneous medium as well as a "gas" made of discrete, cold HI clouds with an isotropic velocity dispersion distribution. Although the method presented here generates a density and velocity field consistent with observational constraints, the stability of these configurations remains an open question.Comment: 12 pages, 9 figures. Accepted for publication in Astronomy and Astrophysic

Communication Gaps Associated With Donor‐Derived Infections

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109830/1/ajt12978.pd

Disk Planet Interactions and Early Evolution in Young Planetary Systems

We study and review disk protoplanet interactions using local shearing box simulations. These suffer the disadvantage of having potential artefacts arising from periodic boundary conditions but the advantage, when compared to global simulations, of being able to capture much of the dynamics close to the protoplanet at high resolution for low computational cost. Cases with and without self sustained MHD turbulence are considered. The conditions for gap formation and the transition from type I migration are investigated and found to depend on whether the single parameter M_p R^3/(M_* H^3), with M_p, M_*, R and H being the protoplanet mass, the central mass, the orbital radius and the disk semi-thickness respectively exceeds a number of order unity. We also investigate the coorbital torques experienced by a moving protoplanet in an inviscid disk. This is done by demonstrating the equivalence of the problem for a moving protoplanet to one where the protoplanet is in a fixed orbit which the disk material flows through radially as a result of the action of an appropriate external torque. For sustainable coorbital torques to be realized a quasi steady state must be realized in which the planet migrates through the disk without accreting significant mass. In that case although there is sensitivity to computational parameters, in agreement with earlier work by Masset & Papaloizou (2003) based on global simulations, the coorbital torques are proportional to the migration speed and result in a positive feedback on the migration, enhancing it and potentially leading to a runaway. This could lead to a fast migration for protoplanets in the Saturn mass range in massive disks and may be relevant to the mass period correlation for extrasolar planets which gives a preponderance of sub Jovian masses at short orbital period.Comment: To appear in Celestial Mechanics and Dynamical Astronomy (with higher resolution figures

Enhanced Software for Scheduling Space-Shuttle Processing

The Ground Processing Scheduling System (GPSS) computer program is used to develop streamlined schedules for the inspection, repair, and refurbishment of space shuttles at Kennedy Space Center. A scheduling computer program is needed because space-shuttle processing is complex and it is frequently necessary to modify schedules to accommodate unanticipated events, unavailability of specialized personnel, unexpected delays, and the need to repair newly discovered defects. GPSS implements constraint-based scheduling algorithms and provides an interactive scheduling software environment. In response to inputs, GPSS can respond with schedules that are optimized in the sense that they contain minimal violations of constraints while supporting the most effective and efficient utilization of space-shuttle ground processing resources. The present version of GPSS is a product of re-engineering of a prototype version. While the prototype version proved to be valuable and versatile as a scheduling software tool during the first five years, it was characterized by design and algorithmic deficiencies that affected schedule revisions, query capability, task movement, report capability, and overall interface complexity. In addition, the lack of documentation gave rise to difficulties in maintenance and limited both enhanceability and portability. The goal of the GPSS re-engineering project was to upgrade the prototype into a flexible system that supports multiple- flow, multiple-site scheduling and that retains the strengths of the prototype while incorporating improvements in maintainability, enhanceability, and portability