Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudospectral Domain Decomposition Method. II. Limit-Cycle Behavior in accretion disks around Kerr black holes

For the first time ever, we derive equations governing the time-evolution of fully relativistic slim accretion disks in the Kerr metric, and numerically construct their detailed non-stationary models. We discuss applications of these general results to a possible limit-cycle behavior of thermally unstable disks. Our equations and numerical method are applicable in a wide class of possible viscosity prescriptions, but in this paper we use a diffusive form of the "standard alpha prescription" that assumes the viscous torque is proportional to the total pressure. In this particular case, we find that the parameters which dominate the limit-cycle properties are the mass-supply rate and the value of the alpha-viscosity parameter. Although the duration of the cycle (or the outburst) does not exhibit any clear dependence on the black hole spin, the maximal outburst luminosity (in the Eddington units) is positively correlated with the spin value. We suggest a simple method for a rough estimate of the black hole spin based on the maximal luminosity and the ratio of outburst to cycle durations. We also discuss a temperature-luminosity relation for the Kerr black hole accretion discs limit-cycle. Based on these results we discuss the limit-cycle behavior observed in microquasar GRS 1915+105. We also extend this study to several non-standard viscosity prescriptions, including a "delayed heating" prescription recently stimulated by the recent MHD simulations of accretion disks.Comment: 36 pages, 6 figures, 1 table. Accepted by ApJ

Default, Currency Crises and Sovereign Credit Ratings

Sovereign credit ratings play an important role in determining the terms and the extent to which countries have access to international capital markets. In principle, there is no reason why changes in sovereign credit ratings should be expected to systematically predict a currency crisis. In practice, however, in developing countries there is a strong link between currency crises and default. About 85 percent of all the defaults in the sample are linked with currency crises. The results presented here suggest that sovereign credit ratings systematically fail to anticipate currency crises--but do considerably better predicting defaults. Downgrades usually follow the currency crisis--possibly highlighting how currency instability increases default risk.

Stiffness pathologies in discrete granular systems: bifurcation, neutral equilibrium, and instability in the presence of kinematic constraints

The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently non-symmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally non-linear, and even small assemblies require the analysis of multiple stiffness branches, with each branch region being a pointed convex cone in displacement-space. These aspects of the particle-level stiffness relationship gives rise to three types of micro-scale failure: neutral equilibrium, bifurcation and path instability, and instability of equilibrium. These three pathologies are defined in the context of four types of displacement constraints, which can be readily analyzed with certain generalized inverses. That is, instability and non-uniqueness are investigated in the presence of kinematic constraints. Bifurcation paths can be either stable or unstable, as determined with the Hill-Bazant-Petryk criterion. Examples of simple granular systems of three, sixteen, and sixty four disks are analyzed. With each system, multiple contacts were assumed to be at the friction limit. Even with these small systems, micro-scale failure is expressed in many different forms, with some systems having hundreds of micro-scale failure modes. The examples suggest that micro-scale failure is pervasive within granular materials, with particle arrangements being in a nearly continual state of instability

A comparative survey of integrated learning systems

This paper presents the duction framework for unifying the three basic forms of inference - deduction, abduction, and induction - by specifying the possible relationships and influences among them in the context of integrated learning. Special assumptive forms of inference are defined that extend the use of these inference methods, and the properties of these forms are explored. A comparison to a related inference-based learning frame work is made. Finally several existing integrated learning programs are examined in the perspective of the duction framework

Partial Disorder and Metal-Insulator Transition in the Periodic Anderson Model on a Triangular Lattice

Ground state of the periodic Anderson model on a triangular lattice is systematically investigated by the mean-field approximation. We found that the model exhibits two different types of partially disordered states: one is at half filling and the other is at other commensurate fillings. In the latter case, the kinetic energy is lowered by forming an extensive network involving both magnetic and nonmagnetic sites, in sharp contrast to the former case in which the nonmagnetic sites are rather isolated. This spatially extended nature of nonmagnetic sites yields a metallic partially-disordered state by hole doping. We discuss the mechanism of the metal-insulator transition by the change of electronic structure.Comment: 4 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp

Complexity of the stable marriage and stable roommate problems in three dimensions

The stable marriage problem is a matching problem that pairs members of two sets. The objective is to achieve a matching that satisfies all participants based on their preferences. The stable roommate problem is a variant involving only one set, which is partitioned into pairs with a similar objective. There exist asymptotically optimal algorithms that solve both problems.In this paper, we investigate the complexity of three dimensional extensions of these problems. This is one of twelve research directions suggested by Knuth in his book on the stable marriage problem. We show that these problems are NP-complete, and hence it is unlikely that there exist efficient algorithms for their solutions.Applying the polynomial tranformation developed in this paper, we extend the NP-completeness result to include the problem of matching couples - who are both medical school graduates - to pairs of hospital resident positions. This problem is important in practice and is dealth with annually by NRMP, the centralized program that matches all medical school graduates in the United States to available resident positions