Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Kerr black hole

In our program of studying numerically the so-called Bondi-Hoyle accretion in the fully relativistic regime, we present here first results concerning the evolution of matter accreting supersonically onto a rotating (Kerr) black hole. These computations generalize previous results where the non-rotating (Schwarzschild) case was extensively considered. We parametrize our initial data by the asymptotic conditions for the fluid and explore the dependence of the solution on the angular momentum of the black hole. Towards quantifying the robustness of our numerical results, we use two different geometrical foliations of the black hole spacetime, the standard form of the Kerr metric in Boyer-Lindquist coordinates as well as its Kerr-Schild form, which is free of coordinate singularities at the black hole horizon. We demonstrate some important advantages of using such horizon adapted coordinate systems. Our numerical study indicates that regardless of the value of the black hole spin the final accretion pattern is always stable, leading to constant accretion rates of mass and momentum. The flow is characterized by a strong tail shock, which, unlike the Schwarzschild case, is increasingly wrapped around the central black hole as the hole angular momentum increases. The rotation induced asymmetry in the pressure field implies that besides the well known drag, the black hole will experience also a lift normal to the flow direction. This situation exhibits some analogies with the Magnus effect of classical fluid dynamics.Comment: 33 pages, 20 figures, submited to MNRA

Unveiling vertical state downscaling: identity and/or the economy?

State rescaling may take a variety of shapes although scant research has been carried out into the mechanisms and economic incentives that underpin rescaling processes. Recent literature in economics, economic sociology and political economy has identified at least two broad rescaling mechanisms, namely the development of regional identity - operating at the cultural level and proxing preference heterogeneity-, and the heterogeneity in levels of economic development, which influence the extent of regional redistribution. This paper empirically examines the mechanisms of vertical state rescaling by drawing upon empirical evidence from Catalonia and the Basque Country, to explore the evolution of sub-state identity and the rise of inter-territorial fiscal grievances - weakening intraregional economic solidarity. Findings corroborate the idea that the combination of widening sub-national identity raises the costs of managing heterogeneous spatial identities and strengthens support for vertical state downscaling. Similarly, ending regional fiscal solidarity it is found to increase the average income of Catalonia by 37% and even 17% in the Basque Country. However, the effect of regional identity exceeds that of regional redistribution in explaining state rescaling support in the magnitude of one to seven. These findings speak to the debate on the formation of Europe, in that they reveal limits to regional redistribution and highlight the importance of a common spatial identity

Monetary reform in times of Charles II (1679-1686): aspects concerning the issued dispositions

During the reign of Carlos II drastic monetary reform was carried out, which once and for all ended the tremendous monetary instability that took place in Castile throughout the whole Seventeenth century. Between 1680 and 1686, six monetary rules were adopted. The path chosen to attain the stability was not easy due to the state of the coinage. The reform tried to provide the Kingdom with a currency properly valued for which it was later decreed the devaluation and then the subsequent removal of the circulating copper coins. Simultaneously, along with the gathered metal, new purely copper made coins were ordered with adjusted value. Once the stability of the lesser value coinage was obtained, the reach of the reform was extended to the gold and silver pieces to equate them to the new monetary values

Log-log Convexity of Type-Token Growth in Zipf's Systems

It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system - the so-called Heaps' law. We show that a careful definition of Zipf's law leads to the violation of Heaps' law in random systems, and obtain alternative growth curves. These curves fulfill universal data collapses that only depend on the value of the Zipf's exponent. We observe that real books behave very much in the same way as random systems, despite the presence of burstiness in word occurrence. We advance an explanation for this unexpected correspondence

Biased Risk Perceptions of Longevity and Disability in Old Age

Rational learning theories postulate that information channels and cognitive biases such as individual optimism may influence an individuals assessment of the risk of undesired events, especially with regard to those that have a cumulative nature. This is the case with disability in old age, which may take place upon survival to an advanced age, and such factors have been regarded as responsible for certain individual behaviours (for example, the limited incidence of insurance purchase). This paper examines the determinants of individual perceptions with regard to disability in old age and longevity. The cumulative nature of such perceptions of risk is tested, and potential biases are identified, including optimism and a set of information determinants. Empirical evidence from a representative survey of Catalonia is presented to illustrate these effects. The findings from this research suggest a significant overestimation of disability in old age, yet this is not the case with longevity. Furthermore, individual perceptions with regard to disability in old age, unlike those with regard to longevity, exhibit on aggregate an optimistic bias and, are perceived as cumulative risks. Gender influences the perceived risk of disability in old age at a population level but not at the individual level, and the opposite holds true for age. Finally, self-reported health status is the main variable behind risk perceptions at both the individual and population level.longevity, disability in old age, risk perceptions, optimism, cumulative risks

Higgsino mass matrix ansatz for MSSM

An ansatz, Det. $M_{\tilde H}=0,$ for the Higgsino mass matrix in string orbifold trinification is suggested toward the minimal supersymmetric standard model(MSSM). Small instanton solutions effective around the GUT scale can fulfil this condition. An argument that the couplings contain a moduli field is given for a dynamical realization of this Higgsino mass matrix ansatz.Comment: 15 pages of LaTeX fil

The runaway instability of thick discs around black holes. I. The constant angular momentum case

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma-ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time-dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux-conservative system and solved using a suitable Godunov-type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self-gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc-to-hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical timescale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole ($2.5 \mathrm{M_\odot}$) and a large range of mass fluxes (\dot{m} \ga 10^{-3} \mathrm{M_{\odot}/s}). The implications of our results in the context of gamma-ray bursts are briefly discussed.Comment: 20 pages, 16 figures, to appear in MNRA