Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28])

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

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

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

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

Self-consistent anisotropic oscillator with cranked angular and vortex velocities

The Kelvin circulation is the kinematical Hermitian observable that measures the true character of nuclear rotation. For the anisotropic oscillator, mean field solutions with fixed angular momentum and Kelvin circulation are derived in analytic form. The cranking Lagrange multipliers corresponding to the two constraints are the angular and vortex velocities. Self-consistent solutions are reported with a constraint to constant volume.Comment: 12 pages, LaTex/RevTex, Phys. Rev. C4

Communication Gaps Associated With Donor‐Derived Infections

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

Pro-Inflammatory CD11c+CD206+ Adipose Tissue Macrophages Are Associated With Insulin Resistance in Human Obesity

OBJECTIVE: Insulin resistance and other features of the metabolic syndrome have been causally linked to adipose tissue macrophages (ATMs) in mice with diet-induced obesity. We aimed to characterize macrophage phenotype and function in human subcutaneous and omental adipose tissue in relation to insulin resistance in obesity. RESEARCH DESIGN AND METHODS: Adipose tissue was obtained from lean and obese women undergoing bariatric surgery. Metabolic markers were measured in fasting serum and ATMs characterized by immunohistology, flow cytometry, and tissue culture studies. RESULTS ATMs comprised CD11c(+)CD206(+) cells in "crown" aggregates and solitary CD11c(-)CD206(+) cells at adipocyte junctions. In obese women, CD11c(+) ATM density was greater in subcutaneous than omental adipose tissue and correlated with markers of insulin resistance. CD11c(+) ATMs were distinguished by high expression of integrins and antigen presentation molecules; interleukin (IL)-1beta, -6, -8, and -10; tumor necrosis factor-alpha; and CC chemokine ligand-3, indicative of an activated, proinflammatory state. In addition, CD11c(+) ATMs were enriched for mitochondria and for RNA transcripts encoding mitochondrial, proteasomal, and lysosomal proteins, fatty acid metabolism enzymes, and T-cell chemoattractants, whereas CD11c(-) ATMs were enriched for transcripts involved in tissue maintenance and repair. Tissue culture medium conditioned by CD11c(+) ATMs, but not CD11c(-) ATMs or other stromovascular cells, impaired insulin-stimulated glucose uptake by human adipocytes. CONCLUSIONS: These findings identify proinflammatory CD11c(+) ATMs as markers of insulin resistance in human obesity. In addition, the machinery of CD11c(+) ATMs indicates they metabolize lipid and may initiate adaptive immune responses

Eclipsing binaries in open clusters. I. V615 Per and V618 Per in h Per

We derive absolute dimensions for two early-type main sequence detached eclipsing binaries in the young open cluster h Persei (NGC 869). V615 Persei has a spectral type of B7V and a period of 13.7d. V618 Persei is A2V and has a period of 6.4d. New ephemerides are calculated for both systems. The masses of the component stars have been derived using high-resolution spectroscopy and are 4.08+/-0.06 Msun and 3.18+/-0.05 Msun for V615 Per and 2.33+/-0.03 Msun and 1.56+/-0.02 Msun for V618 Per. The radii have been measured by fitting the available light curves using EBOP and are 2.29+/-0.14 Rsun and 1.90+/-0.09 Rsun for V615 Per and 1.64+/-0.07 Rsun and 1.32+/-0.07 Rsun for V618 Per. By comparing the observed spectra of V615 Per to synthetic spectra from model atmospheres we find that the effective temperatures of the two stars are 15000+/-500 K and 11000+/-500 K. The equatorial rotational velocities of the primary and secondary components of V615 Per are 28+/-5 km/s and 8+/-5 km/s, respectively. Both components of V618 Per rotate at 10+/-5 km/s. The equatorial rotational velocities for synchronous rotation are about 10 km/s for all four stars. The timescales for orbital circularisation for both systems, and the timescale for rotational synchronisation of V615 Per, are much greater than the age of h Per. Their negligible eccentricities and equatorial rotational velocities therefore support the hypothesis that they were formed by 'delayed breakup'. We have compared the radii of these stars to models by the Granada and the Padova groups for stars of the same masses but different compositions. We conclude that the metallicity of the stars is about Z=0.01. This appears to be the first estimate of the bulk metallicity of h Per. Recent photometric studies have assumed a solar metallicity so their results should be reviewed.Comment: Accepted for publication in MNRAS (15 pages, 9 figures

Statistical Mechanics and the Physics of the Many-Particle Model Systems

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green's functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasiparticle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spin-fermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasiaverages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.Comment: 77 pages, 1 figure, Refs.37