CH 3 GHz Observations of the Galactic Center

A 3 $\times$ 3 map of the Galactic Center was made at 9\arcmin resolution and 10\arcmin spacing in the CH $^2\Pi_{1/2}$, J=1/2, F=1-1 transition at 3335 MHz. The CH emission shows a velocity extent that is nearly that of the CO(1-0) line, but the CH line profiles differ markedly from the CO. The 3335 MHz CH transition primarily traces low-density molecular gas and our observations indicate that the mass of this component within $\sim$ 30 pc of the Galactic Center is $\sim$ 9 $\times$ 10$^6$ M$_\odot$. The CO-H$_2$ conversion factor obtained for the low-density gas in the mapped region is greater than that thought to apply to the dense molecular gas at the Galactic Center. In addition to tracing the low-density molecular gas at the Galactic Center, the CH spectra show evidence of emission from molecular clouds along the line of sight both in the foreground and background. The scale height of these clouds ranges from 27 - 109 pc, consistent with previous work based on observations of molecular clouds in the inner Galaxy.Comment: 29 pages, 12 figure

CO Distribution and Kinematics Along the Bar in the Strongly Barred Spiral NGC 7479

We report on the 2.5 arcsec (400 pc) resolution CO (J = 1 -> 0) observations covering the whole length of the bar in the strongly barred late-type spiral galaxy NGC 7479. CO emission is detected only along a dust lane that traverses the whole length of the bar, including the nucleus. The emission is strongest in the nucleus. The distribution of emission is clumpy along the bar outside the nucleus, and consists of gas complexes that are unlikely to be gravitationally bound. The CO kinematics within the bar consist of two separate components. A kinematically distinct circumnuclear disk, < 500 pc in diameter, is undergoing predominantly circular motion with a maximum rotational velocity of 245 km/s at a radius of 1 arcsec (160 pc). The CO-emitting gas in the bar outside the circumnuclear disk has substantial noncircular motions which are consistent with a large radial velocity component, directed inwards. The CO emission has a large velocity gradient across the bar dust lane, ranging from 0.5 to 1.9 km/s/pc after correcting for inclination, and the projected velocity change across the dust lane is as high as 200 km/s. This sharp velocity gradient is consistent with a shock front at the location of the bar dust lane. A comparison of H-alpha and CO kinematics across the dust lane shows that although the H-alpha emission is often observed both upstream and downstream from the dust lane, the CO emission is observed only where the velocity gradient is large. We also compare the observations with hydrodynamic models and discuss star formation along the bar.Comment: 16 pages, including 10 figures. Accepted for publication in Ap

Magnetic hysteresis in Ising-like dipole-dipole model

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis and allowed us to have a deeper insight into the series of metastable states developed during this process.Comment: REVTEX, 10 pages including 4 figure

Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

A deep submillimetre survey of the Galactic Centre

We present first results from a submillimetre continuum survey of the Galactic Centre `Central Molecular Zone' (CMZ), made with SCUBA on the James Clerk Maxwell Telescope. SCUBA's scan-map mode has allowed us to make extremely wide-field maps of thermal dust emission with unprecedented speed and sensitivity. We also discuss some issues related to the elimination of artefacts in scan-map data. Our simultaneous 850/450 micron maps have a total size of approximately 2.8 x 0.5 degrees (400 x 75 pc) elongated along the galactic plane. They cover the Sgr A region-including Sgr A*, the circumnuclear disc, and the +20 km/s and +50 km/s clouds; the area around the Pistol; Sgr B2-the brightest feature on the map; and at their Galactic Western and Eastern edges the Sgr C and Sgr D regions. There are many striking features such as filaments and shell-like structures, as well as point sources such as Sgr A* itself. The total mass in the Central Molecular Zone is greater than that revealed in previous optically-thin molecular line maps by a factor of ~3, and new details are revealed on scales down to 0.33 pc across this 400 pc wide region.Comment: 12 pages, 3 figures, (figures now smaller, in paper body), accepted by ApJ

On the robustness of scale invariance in SOC models

A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The system is critical only at a special point Jc in the coupling parameter space. However, the critical region around this point, where approximate scale invariance holds, is very large, suggesting a mechanism for explaining the ubiquity of scale invariance in Nature.Comment: 6 pages, 4 figures; submitted to Physical Review E; http://link.aps.org/doi/10.1103/PhysRevE.59.496

Universal mean moment rate profiles of earthquake ruptures

Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on long spatio-temporal scales, we discuss results associated with a heterogeneous fault with long range stress-transfer interactions. To better understand earthquake dynamics we focus on faults with Gutenberg-Richter like earthquake statistics and develop two universal scaling functions as a stronger test of the theory against observations than mere scaling exponents that have large error bars. Universal shape profiles contain crucial information on the underlying dynamics in a variety of systems. As in magnetic systems, we find that our analysis for earthquakes provides a good overall agreement between theory and observations, but with a potential discrepancy in one particular universal scaling function for moment-rates. The results reveal interesting connections between the physics of vastly different systems with avalanche noise.Comment: 13 pages, 5 figure

Stable, metastable and unstable states in the mean-field RFIM at T=0

We compute the probability of finding metastable states at a given field in the mean-field random field Ising model at T=0. Remarkably, this probability is finite in the thermodynamic limit, even on the so-called ``unstable'' branch of the magnetization curve. This implies that the branch is reachable when the magnetization is controlled instead of the magnetic field, in contrast with the situation in the pure system.Comment: 10 pages, 3 figure

Statistics of Earthquakes in Simple Models of Heterogeneous Faults

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps