Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations. Consequently, we provide a complete characterization of the group and phase velocities for these two cases, together with some non-trivial remarks on the nature of wave dispersion in fractional models.Comment: 18 pages, 7 figure

Black Holes and Cosmological Constant in Bosonic String Theory: Some Remarks

(some corrections in the semiclassical study and one reference added).Comment: 17 pages; PHYZZX; IFUM 450/F

Magnetic fields in the overshoot zone: The great escape

In order that magnetic flux be confined within the solar interior for times comparable to the solar cycle period it has been suggested that the bulk of the solar toroidal field is stored in the convectively stable overshoot region situated beneath the convection zone proper. Such a magnetic field, though, is still buoyant and is therefore subject to Rayleigh-Taylor type instabilities. The model problem of an isolated region of magnetic field embedded in a convectively stable atmosphere is considered. The fully nonlinear evolution of the two dimensional interchange of modes is studied, thereby shedding some light on one of the processes responsible for the escape of flux from the solar interior

Quantum Models of Black Hole Evaporation

The discovery of black-hole evaporation represented in many respects a revolutionary event in scientific world; as such, in giving answers to open questions, it gave rise to new problems part of which are still not resolved. Here we want to make a brief review of such problems and examine some possible solutions. Invited Talk at the "Workshop on String Theory, Quantum Gravity and the Unification of the Fundamental Interactions" Rome, September 21-26Comment: 9 pages, ROM2F-92/6

A Conformal Affine Toda Model of 2D Black Holes: A Quantum Study of the Evaporation End-Point

In this paper we reformulate the dilaton-gravity theory of Callan \etal\ as a new effective conformal field theory which turns out to be a generalization of the so-called $SL_2$-conformal affine Toda (CAT) theory studied some times ago by Babelon and Bonora. We quantize this model, thus keeping in account the dilaton-gravity quantum effects. We then implement a Renormalization Group analysis to study the black hole thermodynamics and the final state of the Hawking evaporation.Comment: 15 pages, phyzzx, ROM-2F-92-5

On the convergence of Magnetorotational turbulence in stratified isothermal shearing boxes

We consider the problem of convergence in stratified isothermal shearing boxes with zero net magnetic flux. We present results with the highest resolution to-date--up to 200 grid-point per pressure scale height--that show no clear evidence of convergence. Rather, the Maxwell stresses continue to decrease with increasing resolution. We propose some possible scenarios to explain the lack of convergence based on multi-layer dynamo systems.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter

The alpha-effect in rotating convection: a comparison of numerical simulations

Numerical simulations are an important tool in furthering our understanding of turbulent dynamo action, a process that occurs in a vast range of astrophysical bodies. It is important in all computational work that comparisons are made between different codes and, if non-trivial differences arise, that these are explained. Kapyla et al (2010: MNRAS 402, 1458) describe an attempt to reproduce the results of Hughes & Proctor (2009: PRL 102, 044501) and, by employing a different methodology, they arrive at very different conclusions concerning the mean electromotive force and the generation of large-scale fields. Here we describe why the simulations of Kapyla et al (2010) are simply not suitable for a meaningful comparison, since they solve different equations, at different parameter values and with different boundary conditions. Furthermore we describe why the interpretation of Kapyla et al (2010) of the calculation of the alpha-effect is inappropriate and argue that the generation of large-scale magnetic fields by turbulent convection remains a problematic issue.Comment: Submitted to MNRAS. 5 pages, 3 figure

Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes

We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. We choose radiative boundary conditions at the vertical boundaries in which the heat flux is propor- tional to the fourth power of the temperature. We compare the results with the corresponding cases in which fixed temperature boundary conditions are applied. The most notable result is that the formation of a fully convective state in which the density is nearly constant as a function of height and the heat is transported to the upper and lower boundaries by overturning motions is robust and persists even in cases with radiative boundary conditions. Interestingly, in the convective regime, although the diffusive transport is negligible the mean stratification does not relax to an adiabatic state.Comment: 11 pages, 4 figures, accepted for publication in ApJ Letter

Magnetic Helicities and Dynamo Action in Magneto-rotationally Driven Turbulence

We examine the relationship between magnetic flux generation, taken as an indicator of large-scale dynamo action, and magnetic helicity, computed as an integral over the dynamo volume, in a simple dynamo. We consider dynamo action driven by Magneto-Rotational Turbulence (MRT) within the shearing-box approximation. We consider magnetically open boundary conditions that allow a flux of helicity in or out of the computational domain. We circumvent the problem of the lack of gauge invariance in open domains by choosing a particular gauge -- the winding gauge -- that provides a natural interpretation in terms of average winding number of pairwise field lines. We use this gauge precisely to define and measure the helicity and helicity flux for several realizations of dynamo action. We find in these cases, that the system as a whole does not break reflectional symmetry and the total helicity remains small even in cases when substantial magnetic flux is generated. We find no particular connection between the generation of magnetic flux and the helicity or the helicity flux through the boundaries. We suggest that this result may be due to the essentially nonlinear nature of the dynamo processes in MRT.Comment: 26 pages, 10 figures, ApJ accepte

Observables in the equivariant A-model

We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: the first one is conjectured to compute the correlators of the A-model with target the Marsden-Weinstein reduced space; in the second one we recover the topological Yang-Mills action coupled with A-model so that the A-model observables are closed under supersymmetry.Comment: 16 pages; minor correction