Interaction between disk and extended corona in a general relativistic framework

We study the polarization of relativistic fluids using the relativistic density operator at global and local equilibrium. In global equilibrium, a new technique to compute exact expectation values is introduced, which is used to obtain the exact polarization vector for fields of any spin. The same result has been extended to the case of massless fields. Furthermore, it is demonstrated that at local equilibrium not only the thermal vorticity but also the thermal shear contribute to the polarization vector. It is shown that assuming an isothermal local equilibrium, the new term can solve the polarization sign puzzle in heavy ion collisions.

Solute rejection and its redistribution during freezing and melting are basic topics introduced by the Dutch physical chemist H.W.B. Roozeboom more than a century ago [1, 2] to explain the influence of phase equilibria on the solidification behavior of alloys. Solute redistribution occurs at a moving solid–liquid interface when limited—or so-called local—thermodynamic equilibrium prevails, often aided by transport processes (diffusion and convective mixing) acting primarily within the melt phase ahead of the advancing interface. In this chapter several important settings are explored involving the rejection and redistribution of solutes under differing conditions of solidification. Specifically, during alloy freezing it will be shown that the condition of local thermodynamic equilibrium usually holds, whereas total—or so-called global—equilibrium seldom, if ever, occurs. Nevertheless, both local and global equilibria represent useful idealizations as thermodynamic limits, between which operate most solidification and single crystal growth processes encountered in practice. Local equilibria at solid–liquid interfaces are also exploited in several solidification-based ultrapurification methods, such as repeated unidirectional freezing and multipass zone melting, both of which processes will be explored in detail in this chapter.

Here we study the rapid X-ray variability (using XMM-Newton observations) of three neutron-star low-mass X-ray binaries (1RXS J180408.9-342058, EXO 1745-248, and IGR J18245-2452) during their recently proposed very hard spectral state (Parikh et al. 2017). All our systems exhibit a strong to very strong noise component in their power density spectra (rms amplitudes ranging from 34% to 102%) with very low characteristic frequencies (as low as 0.01 Hz). These properties are more extreme than what is commonly observed in the canonical hard state of neutron-star low-mass X-ray binaries observed at X-ray luminosities similar to those we observe from our sources. This suggests that indeed the very hard state is a distinct spectral-timing state from the hard state, although we argue that the variability behaviour of IGR J18245-2452 is very extreme and possibly this source was in a very unusual state. We also compare our results with the rapid X-ray variability of the accreting millisecond X-ray pulsars IGR J00291+5934 and Swift J0911.9-6452 (also using XMM-Newton data) for which previously similar variability phenomena were observed. Although their energy spectra (as observed using the Swift X-ray telescope) were not necessarily as hard (i.e., for Swift J0911.9-6452) as for our other three sources, we conclude that likely both sources were also in very similar state during their XMM-Newton observations. This suggest that different sources that are found in this new state might exhibit different spectral hardness and one has to study both the spectral as well as rapid variability to identify this unusual state.

The different electron distributions in the hard and soft spectral states of black hole binaries could be caused by kinetic processes and changing because of varying physical conditions in the corona. In the presence of a magnetic field in the corona, the electron distribution can appear thermal, even when acceleration mechanisms would produce non-thermal distributions. This is due to fast and efficient thermalization through synchrotron self-absorption. In this paper, we have analysed data from 6 yr of observations of Cygnus X-1 with the INTEGRAL observatory and produced 12 high-quality, stacked broad-band hard X-ray spectra representative of the whole range of spectral shapes observed in this source. We then fit these spectra with hybrid thermal/non-thermal Comptonization models and study the evolution of the physical parameters of the accretion flow across the spectral transition. In particular, we use the BELM model to constrain the magnetic field in the corona through its effects on the coronal emission. Indeed, the hot electrons of the X-ray corona produce soft (optical-UV) synchrotron radiation which is then Comptonized and may affect the temperature of the electrons (and thus the slope of the X-ray spectrum) through Compton cooling. We find that in the softer states, the emission is dominated by Comptonization of the disc photons and the magnetic field is at most of the order of 10 6 G. In the harder states, the data are consistent with a pure synchrotron self-Compton model, although a significant contribution of Comptonization of disc photons may not be excluded. If the non-thermal excess observed above a few hundred keV in the hard state is produced in the same region as the bulk of the thermal Comptonization, we obtain an upper limit on the coronal magnetic field of about 10 5 G. If, on the other hand, the non-thermal excess is produced in a different location (such as the jet or a different part of the corona), the constraints on the magnetic field in the hard state are somewhat relaxed and the upper limit rises to 10 7 G. We discuss these constraints in the context of current accretion flow models.

Chapter 3 - Fundamentals of Nonequilibrium Thermodynamics

We present a systematic study of the response properties of two-band (multi-gap) superconductors with spin-singlet (s-wave) pairing correlations, which are assumed to be caused by both intraband (\lambda_{ii}, i=1,2) and interband (\lambda_{12}) pairing interactions. In this first of three planned publications we concentrate on the properties of such superconducting systems in global and local thermodynamic equilibrium, the latter including weak perturbations in the stationary long-wavelength limit. The discussion of global thermodynamic equilibrium must include the solution (analytical in the Ginzburg-Landau and the low temperature limit) of the coupled self-consistency equations for the two energy gaps \Delta_i(T), i=1,2. These solutions allow to study non-universal behavior of the two relevant BCS-M\"uhlschlegel parameters, namely the specific heat discontinuity \Delta C/C_N and the zero temperature gaps \Delta_i(0)/\pi k_B T_c, i=1,2. The discussion of a local equilibrium situation includes the calculation of the supercurrent density as a property of the condensate, and the calculation of both the specific heat capacity and the spin susceptibility as properties of the gas of thermal excitations in the spirit of a microscopic two-fluid description. Non-monotonic behavior in the temperature dependences of the gaps and all these local response functions is predicted to occur particularly for very small values of the interband pair-coupling constant \lambda_{12}.

The emission of steady compact jets observed in the hard spectral state of X-ray binaries is likely to be powered by internal shocks caused by fluctuations of the outflow velocity. The dynamics of the internal shocks and the resulting spectral energy distribution (SED) of the jet is very sensitive to the shape of the Power Spectral Density (PSD) of the fluctuations of the jet Lorentz factor. I use Monte-Carlo simulations to investigate this dependence. It turns out that Lorentz factor fluctuations injected at the base of the jet with a flicker noise power spectrum (i.e. P(f) ∝ 1/f) naturally produce the canonical flat SED observed from radio to IR band in X-ray binary systems in the hard state. This model also predicts a strong, wavelength dependent, variability that resembles the observed one. In particular, strong sub-second variability is predicted in the infrared and optical bands.

GRS 1915+105 is a very peculiar black hole binary that exhibits accretion-related states that are not observed in any other stellar-mass black hole system. One of these states, however – referred to as the plateau state – may be related to the canonical hard state of black hole X-ray binaries. Both the plateau and hard state are associated with steady, relatively lower X-ray emission and flat/inverted radio emission, that is sometimes resolved into compact, self-absorbed jets. However, while generally black hole binaries quench their jets when the luminosity becomes too high, GRS 1915+105 seems to sustain them despite the fact that it accretes at near- or super-Eddington rates. In order to investigate the relationship between the plateau and the hard state, we fit two multiwavelength observations using a steady-state outflow-dominated model, developed for hard-state black hole binaries. The data sets consist of quasi-simultaneous observations in radio, near-infrared and X-ray bands. Interestingly, we find both significant differences between the two plateau states, as well as between the best-fitting model parameters and those representative of the hard state. We discuss our interpretation of these results, and the possible implications for GRS 1915+105's relationship to canonical black hole candidates.

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model which is divided into five subpopulations, namely susceptible subpopulations, latent subpopulations, infected subpopulations receiving treatment at home, and infected subpopulations receiving treatment at the hospital, and cured subpopulations. The analysis of qualitative behavior in the model includes determining the local and global equilibrium and stability points. The results of the analysis shows that the model has two equilibrium points, namely a disease-free equilibrium point and the endemic equilibrium point. The existence of endemic equilibrium point and the local and global stability of the two equilibrium points depend on the basic reproduction number denoted by . If , there is only disease-free equilibrium point. If , there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease-free equilibrium point is locally and globally asymptotically stable if . While, if , the endemic equilibrium point will be asymptotically stable locally and globally.

Local and global equilibrium states of composite thermodynamic systems are discussed from a phenomenological "Gibbsian" point of view with special emphasis on the principle of minimum entropy production, starting from a system of linear differential equations modelling the evolution of such systems from local to global equilibrium or steady states caused by diffusion.

Spin polarization induced by magnetic field and the relativistic Barnett effect

Pricing for Coordination in Open–Loop Differential Games

A local conditional variational principle of pressures and local conditional equilibrium states

This article provides a self-contained pedagogical introduction to the relativistic kinetic theory of a dilute gas propagating on a curved spacetime manifold (M,g) of arbitrary dimension. Special emphasis is made on geometric aspects of the theory in order to achieve a formulation which is manifestly covariant on the relativistic phase space. Whereas most previous work has focussed on the tangent bundle formulation, here we work on the cotangent bundle associated with (M,g) which is more naturally adapted to the Hamiltonian framework of the theory. In the first part of this work we discuss the relevant geometric structures of the cotangent bundle T*M, starting with the natural symplectic form on T*M, the one-particle Hamiltonian and the Liouville vector field, defined as the corresponding Hamiltonian vector field. Next, we discuss the Sasaki metric on T*M and its most important properties, including the role it plays for the physical interpretation of the one-particle distribution function. In the second part of this work we describe the general relativistic theory of a collisionless gas, starting with the derivation of the collisionless Boltzmann equation for a neutral simple gas. Subsequently, the description is generalized to a charged gas consisting of several species of particles and the general relativistic Vlasov-Maxwell equations are derived for this system. The last part of this work is devoted to a transparent derivation of the collision term, leading to the general relativistic Boltzmann equation on (M,g). The meaning of global and local equilibrium and the stringent restrictions for the existence of the former on a curved spacetime are discussed. We close this article with an application of our formalism to the expansion of a homogeneous and isotropic universe filled with a collisional simple gas and its behavior in the early and late epochs. [abbreviated version]

We report on the long-term monitoring of X-ray dips from the ultracompact low-mass X-ray binary (LMXB) XB 1916-053. Roughly one-month interval observations were carried out with the Rossi X-ray Timing Explorer (RXTE) during 1996, during which the source varied between dim, hard states and more luminous, soft states. The dip spectra and dip light curves were compared against both the broadband luminosity and the derived mass accretion rate (). The dips spectra could be fitted by an absorbed blackbody plus cutoff power-law nondip spectral model, with additional absorption ranging from 0 to > 100 × 1022 cm-2. The amount of additional blackbody absorption was found to vary with the source luminosity. Our results are consistent with an obscuration of the inner disk region by a partially ionized outer disk. The size of the corona, derived from the dip ingress times, was found to be ~109 cm. The corona size did not correlate with the coronal temperature, but seemed to increase when also increased. We discuss our findings in the context of an evaporated accretion disk corona model and an ADAF-type model.