Scaling law for the heating of solar coronal loops

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations, used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum $E_k\simeq k^{-3/2}$ and heating rate levels compatible with the heating requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfven time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.Comment: 12 pages, 4 figures. Astrophysical Journal Letters (in press

Quasi-exact solvability beyond the SL(2) algebraization

We present evidence to suggest that the study of one dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual \sla(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the \sla(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic hamiltonian cannot be expressed as a polynomial in the generators of \sla(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on superintegrabilit

Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge

The properties of the Gribov region in SU(2) Euclidean Yang-Mills theories in the maximal Abelian gauge are investigated. This region turns out to be bounded in all off-diagonal directions, while it is unbounded along the diagonal one. The soft breaking of the BRST invariance due to the restriction of the domain of integration in the path integral to the Gribov region is scrutinized. Owing to the unboundedness in the diagonal direction, the invariance with respect to Abelian transformations is preserved, a property which is at the origin of the local U(1) Ward identity of the maximal Abelian gauge.Comment: 15 pages, one reference added, version accepted for publication in Phys. Rev.

An algorithm to obtain global solutions of the double confluent Heun equation

A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those Wronskians. The feasibility of the method is shown in an example, namely, the Schroedinger equation with a quasi-exactly-solvable potential

Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics

The nonlinear dynamics of a bundle of magnetic flux ropes driven by stationary fluid motions at their endpoints is studied, by performing numerical simulations of the magnetohydrodynamic (MHD) equations. The development of MHD turbulence is shown, where the system reaches a state that is characterized by the ratio between the Alfven time (the time for incompressible MHD waves to travel along the field lines) and the convective time scale of the driving motions. This ratio of time scales determines the energy spectra and the relaxation toward different regimes ranging from weak to strong turbulence. A connection is made with phenomenological theories for the energy spectra in MHD turbulence.Comment: Published in Physics of Plasma

Substructure in clusters containing wide-angle tailed radio galaxies. I. New redshifts

We present new redshifts and positions for 635 galaxies in nine rich clusters containing Wide-Angle Tailed (WAT) radio galaxies. Combined with existing data, we now have a sample of 18 WAT-containing clusters with more than 10 redshifts. This sample contains a substantial portion of the WAT clusters in the VLA 20 cm survey of Abell clusters, including 75% of WAT clusters in the complete survey (z0.09. It is a representative sample which should not contain biases other than selection by radio morphology. We graphically present the new data using histograms and sky maps. A semi-automated procedure is used to search for emission lines in the spectra in order to add and verify galaxy redshifts. We find that the average apparent fraction of emission line galaxies is about 9% in both the clusters and the field. We investigate the magnitude completeness of our redshift surveys with CCD data for a test case, Abell 690. This case indicates that our galaxy target lists are deeper than the detection limit of a typical MX exposure, and they are 82% complete down to R=19.0. The importance of the uniformity of the placement of fibers on targets is posited, and we evaluate this in our datasets. We find some cases of non-uniformities which may influence dynamical analyses. A second paper will use this database to look for correlations between the WAT radio morphology and the cluster's dynamical state.Comment: 15 pages, 5 figures, 7 tables. To appear in the Astronomical Journa

Misleading signatures of quantum chaos

The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution and the spectral rigidity given by $\Delta_3(L)$. It is shown that some standard unfolding procedures, like local unfolding and Gaussian broadening, lead to a spurious increase of the spectral rigidity that spoils the $\Delta_3(L)$ relationship with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.Comment: 4 pages, 5 figures, submitted to Physical Review

Moving black holes via singularity excision

We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations of single, non-moving black holes. The excision procedure also shares elements used in recent work to study the dynamics of a scalarfield in the background of a single, boosted black hole. The robustness of our excision method is tested with single black-hole evolutions using a coordinate system in which the coordinate location of the black hole, and thus the excision boundary, moves throughout the computational domain.Comment: 9 pages and 11 figure