Fractal Spectrum of a Quasi_periodically Driven Spin System

We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from [email protected]

Comparing Methods for Interpolation to Improve Raster Digital Elevation Models

Digital elevation models (DEMs) are available as raster files at 100m, 30m, and 10m resolutions for the contiguous United States and are used in a variety of geographic analyses. Some projects may require a finer resolution. GIS software offers many options for interpolating data to higher resolutions. We compared ten interpolation methods using 10m sample data from the Ouachita Mountains in central Arkansas. We interpolated the 10m DEM to 5m, 2.5m, and 1m resolutions and compared the absolute mean difference (AMD) for each using surveyed control points. Overall, there was little difference in the accuracy between interpolation methods at the resolutions tested and minimal departure from the original 10m raster

Design for waste-management system

Study was made and system defined for water-recovery and solid-waste processing for low-rise apartment complexes. System can be modified to conform with unique requirements of community, including hydrology, geology, and climate. Reclamation is accomplished by treatment process that features reverse-osmosis membranes

Study of water recovery and solid waste processing for aerospace and domestic applications. Volume 2: Final report

The manner in which current and advanced technology can be applied to develop practical solutions to existing and emerging water supply and waste disposal problems is evaluated. An overview of water resource factors as they affect new community planning, and requirements imposed on residential waste treatment systems are presented. The results of equipment surveys contain information describing: commercially available devices and appliances designed to conserve water; devices and techniques for monitoring water quality and controlling back contamination; and advanced water and waste processing equipment. System concepts are developed and compared on the basis of current and projected costs. Economic evaluations are based on community populations of from 2,000 to 250,000. The most promising system concept is defined in sufficient depth to initiate detailed design

Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

It is shown that correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail

What determines the spreading of a wave packet?

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and eigenfunctions, resp., are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved the k-th moment increases as t^(k*beta) with beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound. Furthermore, we show that in d dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent D_2^psi - d and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure

Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

Quantum Return Probability for Substitution Potentials

We propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete Schrodinger operators. We compute it for some non-periodic substitution potentials with different degrees of randomness, and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves, i.e., more random the sequence smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM