Multigrid Methods in Lattice Field Computations

The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of freedom in the problem. Current and potential benefits for lattice field computations are outlined. They include: $O(n)$ solution of Dirac equations; just $O(1)$ operations in updating the solution (upon any local change of data, including the gauge field); similar efficiency in gauge fixing and updating; $O(1)$ operations in updating the inverse matrix and in calculating the change in the logarithm of its determinant; $O(n)$ operations per producing each independent configuration in statistical simulations (eliminating CSD), and, more important, effectively just $O(1)$ operations per each independent measurement (eliminating the volume factor as well). These potential capabilities have been demonstrated on simple model problems. Extensions to real life are explored.Comment: 4

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping delta away from half-filling, finite-size density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = pi(1-delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities.Comment: 24 pages, 17 figures. Follow-up to cond-mat/0209444. (v2) Some revisions in text, improved presentation. Minor changes in title, abstract and reference

Alpine Turbulence and Blowing Snow

Blowing snow in mountainous terrain is a complex nonlinear phenomenon driven by turbulent eddies with length scales ranging from millimetres to kilometres. Turbulent motions across a wide spectrum of sizes are superimposed on each other, interacting through a non-stationary energy and momentum cascade. In cold regions, snow redistribution by these turbulent motions impacts hydrology, glaciology, avalanche safety, and civil engineering. Blowing snow models typically rely on relating time-averaged turbulence statistics, which may oversimplify the complexity of the flow, especially in complex mountainous terrain, to steady-state snow transport. The present research sought to improve the understanding of the dominant structures in ASL turbulence relevant to snow transport, as well as characterize the short timescale response of blowing snow to specific eddy structures. A fundamental experiment was designed utilizing high-speed videography of laser illuminated near-surface blowing snow saltation coupled with adjacent 3D sonic anemometer wind measurements at two heights. The experiments were conducted at Fortress Mountain Snow Laboratory in the Canadian Rockies of Alberta during nighttime blowing snow storms. Novel applications of particle tracking velocimetry and binarization algorithms to blowing snow recordings allowed extraction of time resolved snow particle velocities synchronized with instantaneous wind velocities, as well as time series of volumetric averages of blowing snow density in the first 30 mm above the surface. High-speed blowing snow video and measurements revealed the importance of the often- overlooked creep mode of transport to both transport initiation and flux. Blowing snow velocity and flux profiles were found to be temporally variable and dependent on instantaneous wind speed, with dominant modes of transport varying during turbulent gusts. Sweep and ejection wind events were coupled to blowing snow responses on sub-second timescales, with each quadrant event playing a unique role in transport initiation and sustaining snow fluxes. Finally, large low-frequency turbulent motions, hypothesized to follow a top-down characterization, were found to modulate the amplitude of near-surface turbulence, as well as directly contribute to blowing snow fluxes. The role of intermittent coherent turbulent structures challenges the ability of time-averaged turbulence statistics to represent the complexity of wind-snow coupling, especially in mountainous terrain. The strong relationship found between large-scale turbulence modulating eddies and near-surface turbulence, also challenges the efficacy of applying steady- state laboratory-derived flux relationships to model transport in the ASL. The results presented here, along with recent advances on coherent turbulent structures provide an optimistic semi- deterministic avenue for improving blowing snow models in complex mountainous terrain

Study of plasma turbulence by ultrafast sweeping reflectometry on the Tore Supra tokamak

Plasma turbulence limits the performance of fusion reactors. Measuring and character- izing the turbulence properties is therefore a crucial issue in order to understand such phenomena. The goal of this thesis is to study the properties of plasma turbulence from ultrafast sweeping reflectometry measurements performed on the Tore Supra Tokamak. Reflectometry is a radar technique that is used to measure the electron density and its fluctuations. In the first part, we compare Langmuir probe and reflectometer data and discuss the possibility to characterize turbulence properties from the reconstructed fluctuating density profiles. Then, we show that the radial variation of the time and spatial scales of the turbulence as well as its radial velocity can be estimated from a cross-correlation analysis applied to the raw reflectometer signals. The modifications of the turbulence properties observed during a parametric scan are interpreted in the light of TEM and ITG turbulence. Finally, we show that the additional heating leads to a significant increase of the radial velocity in the plasma close to the tokamak wall

Quantum Hair on Black Holes

A black hole may carry quantum numbers that are {\it not} associated with massless gauge fields, contrary to the spirit of the ``no-hair'' theorems. We describe in detail two different types of black hole hair that decay exponentially at long range. The first type is associated with discrete gauge charge and the screening is due to the Higgs mechanism. The second type is associated with color magnetic charge, and the screening is due to color confinement. In both cases, we perform semi-classical calculations of the effect of the hair on local observables outside the horizon, and on black hole thermodynamics. These effects are generated by virtual cosmic strings, or virtual electric flux tubes, that sweep around the event horizon. The effects of discrete gauge charge are non-perturbative in $\hbar$, but the effects of color magnetic charge become $\hbar$-independent in a suitable limit. We present an alternative treatment of discrete gauge charge using dual variables, and examine the possibility of black hole hair associated with discrete {\it global} symmetry. We draw the distinction between {\it primary} hair, which endows a black hole with new quantum numbers, and {\it secondary} hair, which does not, and we point out some varieties of secondary hair that occur in the standard model of particle physics.Comment: (100 pages