Relic Gravitational Waves and Their Detection

The range of expected amplitudes and spectral slopes of relic (squeezed) gravitational waves, predicted by theory and partially supported by observations, is within the reach of sensitive gravity-wave detectors. In the most favorable case, the detection of relic gravitational waves can be achieved by the cross-correlation of outputs of the initial laser interferometers in LIGO, VIRGO, GEO600. In the more realistic case, the sensitivity of advanced ground-based and space-based laser interferometers will be needed. The specific statistical signature of relic gravitational waves, associated with the phenomenon of squeezing, is a potential reserve for further improvement of the signal to noise ratio.Comment: 25 pages, 9 figures included, revtex. Based on a talk given at "Gyros, Clocks, and Interferometers: Testing General Relativity in Space" (Germany, August 99

Detecting relic gravitational radiation from string cosmology with LIGO

A characteristic spectrum of relic gravitational radiation is produced by a period of ``stringy inflation" in the early universe. This spectrum is unusual, because the energy-density rises rapidly with frequency. We show that correlation experiments with the two gravitational wave detectors being built for the Laser Interferometric Gravitational Observatory (LIGO) could detect this relic radiation, for certain ranges of the parameters that characterize the underlying string cosmology model.Comment: 6 pages, 5 eps figures, Revte

Effects of Processing Residual Stresses on Fatigue Crack Growth Behavior of Structural Materials: Experimental Approaches and Microstructural Mechanisms

Fatigue crack growth mechanisms of long cracks through fields with low and high residual stresses were investigated for a common structural aluminum alloy, 6061-T61. Bulk processing residual stresses were introduced in the material by quenching during heat treatment. Compact tension (CT) specimens were fatigue crack growth (FCG) tested at varying stress ratios to capture the closure and Kmax effects. The changes in fatigue crack growth mechanisms at the microstructural scale are correlated to closure, stress ratio, and plasticity, which are all dependent on residual stress. A dual-parameter ΔK-Kmax approach, which includes corrections for crack closure and residual stresses, is used uniquely to connect fatigue crack growth mechanisms at the microstructural scale with changes in crack growth rates at various stress ratios for low- and high-residual-stress conditions. The methods and tools proposed in this study can be used to optimize existing materials and processes as well as to develop new materials and processes for FCG limited structural applications

Self-Organized Branching Processes: A Mean-Field Theory for Avalanches

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.Comment: 4 pages + 4 ps figure

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

We address the issue of finding an optimal detection method for a discontinuous or intermittent gravitational wave stochastic background. Such a signal might sound something like popcorn popping. We derive an appropriate version of the maximum likelihood detection statistic, and compare its performance to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. The maximum likelihood statistic performs better than the cross-correlation statistic when the background is sufficiently non-Gaussian. For both ground and space based detectors, this results in a gain factor, ranging roughly from 1 to 3, in the minimum gravitational-wave energy density necessary for detection, depending on the duty cycle of the background. Our analysis is exploratory, as we assume that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. Before this detection method can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.Comment: 25 pages, 12 figures, submitted to physical review D, added revisions in response to reviewers comment

Fine Structure of Avalanches in the Abelian Sandpile Model

We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the degree of complexity in the fine structure of avalanches, which is a direct consequence of the intricate superposition of the boundaries of successive waves, avalanches fall into two different categories. We propose scaling ans\"{a}tz for these avalanche types and verify them numerically. We find that while the first type of avalanches has a simple scaling behavior, the second (complex) type is characterized by an avalanche-size dependent scaling exponent. This provides a framework within which one can understand the failure of a consistent scaling behavior in this model.Comment: 10 page

The Sensitivity of Ligo to a Stochastic Background, and its Dependance on the Detector Orientations

We analyze the sensitivity of a network of interferometer gravitational-wave detectors to the gravitational-wave stochastic background, and derive the dependence of this sensitivity on the orientations of the detector arms. We build on and extend the recent work of Christensen, but our conclusion for the optimal choice of orientations of a pair of detectors differs from his. For a pair of detectors (such as LIGO) that subtends an angle at the center of the earth of \,\alt 70^\circ, we find that the optimal configuration is for each detector to have its arms make an angle of $45^\circ$ (modulo $90^\circ$) with the arc of the great circle that joins them. For detectors that are farther separated, each detector should instead have one arm aligned with this arc. We also describe in detail the optimal data-analysis algorithm for searching for the stochastic background with a detector network, which is implicit in earlier work of Michelson. The LIGO pair of detectors will be separated by $\sim 3000 \, {\rm km}$. The minimum detectable stochastic energy-density for these detectors with their currently planned orientations is $\sim 3\%$ greater than what it would be if the orientations were optimal.Comment: 56 pages, 10 figures, Caltech preprint GRP-347, submitted to Phys Rev D, uses revtex macro

Clay content drives carbon stocks in soils under a plantation of Eucalyptus saligna Labill. in southern Brazil

Soil carbon accumulation is largely dependent on net primary productivity. To our knowledge, there have been no studies investigating the dynamics of carbon accumulation in weathered subtropical soils, especially in managed eucalyptus plantations. We quantified the seasonal input of leaf litter, the leaf decomposition rate and soil carbon stocks in an commercial plantation of Eucalyptus saligna Labill. in southern Brazil. Our goal was to evaluate, through multiple linear regression, the influence that certain chemical characteristics of litter, as well as chemical and physical characteristics of soil, have on carbon accumulation in soil organic matter fractions. Variables related to the chemical composition of litter were not associated with the soil carbon stock in the particulate and mineral fractions. However, certain soil characteristics were significantly associated with the carbon stock in both fractions. The concentrations of nutrients associated with plant growth and productivity, such as phosphorus, sulfur, copper and zinc, were associated with variations in the labile carbon pool (particulate fraction). Clay content was strongly associated with the carbon stock in the mineral fraction. The carbon accumulation and stabilization in weathered subtropical Ultisol seems to be mainly associated with the intrinsic characteristics of the soil, particularly clay content, rather than with the quantity, chemical composition or decomposition rate of the litter