Spatial and Spectral Multifractality of the Local Density of States at the Mobility Edge

We performed numerical calculations of the local density of states (LDOS) at disorder induced localization-delocalization transitions. The LDOS defines a spatial measure for fixed energy and a spectral measure for fixed position. At the mobility edge both measures are multifractal and their generalized dimensions $D(q)$ and $\tilde{D}(q)$ are found to be proportional: $D(q)=d\tilde{D}(q)$, where $d$ is the dimension of the system. This observation is consistent with the identification of the frequency-dependent length scale $L_\omega \propto \omega^{-1/d}$ as an effective system size. The calculations are performed for two- and three-dimensional dynamical network models with local time evolution operators. The energy dependence of the LDOS is obtained from the time evolution of the local wavefunction amplitude of a wave packet, providing a numerically efficient way to obtain information about the multifractal exponents of the system.Comment: updated 2 references, no further change

Modèles linéaires stochastiques théoriques pour la réponse des petits bassins

En rendant aléatoires les intrants du modèle déterministe en cascade de réservoirs linéaires de Nash-Dooge, on obtient des modèles linéaires stochastiques adaptés aux petits bassins, qui peuvent être formulés comme des systèmes dynamiques stochastiques linéaires simples représentés par des équations différentielles stochastiques (EDS). Les processus du système, la précipitation et les pertes dues à l'évapotranspiration (cette dernière étant considérée comme un intrant négatif), sont respectivement modélisés par un processus composé de Poisson et par un bruit blanc gaussien à moyenne nulle superposé à une moyenne déterministe. Pour la réponse superficielle et la réponse souterraine, on propose des modèles stochastiques en cascades de Nash-Dooge à n réservoirs linéaires égaux et à deux réservoirs en parallèle. Des travaux récents sur la genèse des débits ont conduit à mettre au point un modèle dynamique grossier, plus plausible conceptuellement, formé de régimes à réponse rapide et à réponse lente parallèles. Ce modèle est élaboré en attribuant au réservoir lent toutes les pertes d'évapotranspiration, les fluctuations de celle-ci étant modélisées par un bruit gaussien coloré à moyenne nulle et en rationalisant un modèle d'infiltration linéarisé fonction d'un écoulement à régime lent précédant une précipitation. En fait, cette contribution vise à donner une portée plus générale à la théorie déterministe de Nash-Dooge basée sur l'hydrogramme unitaire, afin de l'étendre à une théorie linéaire stochastique de réponse d'un bassin.By randomizing the inputs to the deterministic Nash-Dooge linear reservoir cascade, linear stochastic conceptual response models suitable for small catchments are formulated as simple linear stochastic dynamical systems within the formalism of stochastic differential equations (SDE’s). The system driving processes, rainfall and evapotranspiration losses, the latter regarded as a negative input, are modeled respectively as a compound Poisson process and a mean zero white Gaussian noise superposed on a deterministic mean. Elementary stochasticized Nash-Dooge cascades of n equal linear reservoirs and two reservoirs in parallel are given as potential models of surface and subsurface response. On consideration of recent discoveries concerning streamflow generation, a more conceptually plausible coarse-grained dynamical model of parallel quick and slow response regimes is developed by confining all evapotranspiration losses to the slow reservoir, modeling evapotranspiration fluctuations as mean zero colored Gaussian noise and rationalizing a linearized infiltration model dependent on slow regime outflow just prior to an event. In essence, the effort is directed towards generalizing the deterministic Nash-Dooge theory of the unit hydrograph to a linear stochastic theory of catchment response

On the Dynamics and Structure of Three-Dimensional Trans-Alfvenic Jets

Three-dimensional magnetohydrodynamical simulations of strongly magnetized ``light'' conical jets have been performed. An investigation of the transition from sub-Alfv\'enic to super-Alfv\'enic flow has been made for nearly poloidal and for helical magnetic fields. The jets are stable to asymmetric modes of jet distortion provided they are sub-Alfv\'enic over most of their interior but destabilize rapidly when they become on average super-Alfv\'enic. The jets are precessed at the origin and the resulting small amplitude azimuthal motion is communicated down the jet to the Alfv\'en point where it couples to a slowly moving and rapidly growing helical twist. Significant jet rotation can contribute to destabilization via increase in the velocity shear between the jet and the external medium. Destabilization is accompanied by significant mass entrainment and the jets slow down significantly as denser external material is entrained. Synchrotron intensity images satisfactorily reveal large scale helical structures but have trouble distinguishing a large amplitude elliptical jet distortion that appears as an apparent pinching in an intensity image. Smaller scale jet distortions are not clearly revealed in intensity images, largely as a result of the relatively small total pressure variations that accompany destabilization and growing distortions. Fractional polarization is high as a result of the strong ordered magnetic fields except where the intensity image suggests cancellation of polarization vectors by integration through twisted structures.Comment: 27 pages, 11 figures, AASTeX, to appear in Oct 20 issue of ApJ, postscript versions of Figures 5 and 6 are available at this URL http://crux.astr.ua.edu/~rosen/tralf/hr.htm

Fedosov supermanifolds: II. Normal coordinates

The study of recently introduced Fedosov supermanifolds is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.Comment: 12 pages, Late

B-Meson Distribution Amplitudes of Geometric Twist vs. Dynamical Twist

Two- and three-particle distribution amplitudes of heavy pseudoscalar mesons of well-defined geometric twist are introduced. They are obtained from appropriately parametrized vacuum-to-meson matrix elements by applying those twist projectors which determine the enclosed light-cone operators of definite geometric twist and, in addition, observing the heavy quark constraint. Comparing these distribution amplitudes with the conventional ones of dynamical twist we derive relations between them, partially being of Wandzura-Wilczek type; also sum rules of Burkhardt-Cottingham type are derived.The derivation is performed for the (double) Mellin moments and then re-summed to the non-local distribution amplitudes. Furthermore, a parametrization of vacuum-to-meson matrix elements for non-local operators off the light-cone in terms of distribution amplitudes accompanying independent kinematical structures is derived.Comment: 18 pages, Latex 2e, no figure

Dynamics and Structure of Three-Dimensional Trans-Alfvenic Jets. II. The Effect of Density and Winds

Two three-dimensional magnetohydrodynamical simulations of strongly magnetized conical jets, one with a poloidal and one with a helical magnetic field, have been performed. In the poloidal simulation a significant sheath (wind) of magnetized moving material developed and partially stabilized the jet to helical twisting. The fundamental pinch mode was not similarly affected and emission knots developed in the poloidal simulation. Thus, astrophysical jets surrounded by outflowing winds could develop knotty structures along a straight jet triggered by pinching. Where helical twisting dominated the dynamics, magnetic field orientation along the line-of-sight could be organized by the toroidal flow field accompanying helical twisting. On astrophysical jets such structure could lead to a reversal of the direction of Faraday rotation in adjacent zones along a jet. Theoretical analysis showed that the different dynamical behavior of the two simulations could be entirely understood as a result of dependence on the velocity shear between jet and wind which must exceed a surface Alfven speed before the jet becomes unstable to helical and higher order modes of jet distortion.Comment: 25 pages, 15 figures, in press Astrophysical Journal (September

A Newly Discovered Bordetella Species Carries a Transcriptionally Active CRISPR-Cas with a Small Cas9 Endonuclease

Background Clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated genes (cas) are widely distributed among bacteria. These systems provide adaptive immunity against mobile genetic elements specified by the spacer sequences stored within the CRISPR. Methods The CRISPR-Cas system has been identified using Basic Local Alignment Search Tool (BLAST) against other sequenced and annotated genomes and confirmed via CRISPRfinder program. Using Polymerase Chain Reactions (PCR) and Sanger DNA sequencing, we discovered CRISPRs in additional bacterial isolates of the same species of Bordetella. Transcriptional activity and processing of the CRISPR have been assessed via RT-PCR. Results Here we describe a novel Type II-C CRISPR and its associated genes—cas1, cas2, and cas9—in several isolates of a newly discovered Bordetella species. The CRISPR-cas locus, which is absent in all other Bordetella species, has a significantly lower GC-content than the genome-wide average, suggesting acquisition of this locus via horizontal gene transfer from a currently unknown source. The CRISPR array is transcribed and processed into mature CRISPR RNAs (crRNA), some of which have homology to prophages found in closely related species B. hinzii. Conclusions Expression of the CRISPR-Cas system and processing of crRNAs with perfect homology to prophages present in closely related species, but absent in that containing this CRISPR-Cas system, suggest it provides protection against phage predation. The 3,117-bp cas9 endonuclease gene from this novel CRISPR-Cas system is 990 bp smaller than that of Streptococcus pyogenes, the 4,017-bp allele currently used for genome editing, and which may make it a useful tool in various CRISPR-Cas technologies

A survey of parallel algorithms for fractal image compression

This paper presents a short survey of the key research work that has been undertaken in the application of parallel algorithms for Fractal image compression. The interest in fractal image compression techniques stems from their ability to achieve high compression ratios whilst maintaining a very high quality in the reconstructed image. The main drawback of this compression method is the very high computational cost that is associated with the encoding phase. Consequently, there has been significant interest in exploiting parallel computing architectures in order to speed up this phase, whilst still maintaining the advantageous features of the approach. This paper presents a brief introduction to fractal image compression, including the iterated function system theory upon which it is based, and then reviews the different techniques that have been, and can be, applied in order to parallelize the compression algorithm