Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Canonical Bose gas simulations with stochastic gauges

A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Stochastic structure and individual-tree growth models

The majority of past and current individual-tree growth modelling methodologies have failed to characterise and incorporate structured stochastic components. Rather, they have relied on deterministic predictions or have added an unstructured random component to predictions. In particular, spatial stochastic structure has been neglected, despite being present in most applications of individual-tree growth models. Spatial stochastic structure (also called spatial dependence or spatial autocorrelation) eventuates when spatial influences such as competition and micro-site effects are not fully captured in models. Temporal stochastic structure (also called temporal dependence or temporal autocorrelation) eventuates when a sequence of measurements is taken on an individual-tree over time, and variables explaining temporal variation in these measurements are not included in the model. Nested stochastic structure eventuates when measurements are combined across sampling units and differences among the sampling units are not fully captured in the model. This review examines spatial, temporal, and nested stochastic structure and instances where each has been characterised in the forest biometry and statistical literature. Methodologies for incorporating stochastic structure in growth model estimation and prediction are described. Benefits from incorporation of stochastic structure include valid statistical inference, improved estimation efficiency, and more realistic and theoretically sound predictions. It is proposed in this review that individual-tree modelling methodologies need to characterise and include structured stochasticity. Possibilities for future research are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

Simulating quantum interference in a three-level system with perpendicular transition dipole moments

We consider a three-level V-type atomic system with the ground state coupled by a laser field to only one of the excited states, and with the two excited states coupled together by a dc field. Although the dipole moments of the two dipole-allowed transitions are assumed perpendicular, we demonstrate that this system emulates to a large degree a three-level system with parallel dipole moments-the latter being a system that exhibits quantum interference and displays a number of interesting features. As examples, we show that the system can produce extremely large values for the intensity-intensity correlation function, and that its resonance fluorescence spectrum can display ultranarrow lines. The dressed states for this system are identified, and the spectral features are interpreted in terms of transitions among these dressed states. We also show that this system is capable of exhibiting considerable squeezing.

The importance of forest area and configuration relative to local habitat factors for conserving forest mammals: A case study of koalas in Queensland, Australia

The loss and fragmentation of forest habitats by human land use are recognised as important factors influencing the decline of forest-dependent fauna. Mammal species that are dependent upon forest habitats are particularly sensitive to habitat loss and fragmentation because they have highly specific habitat requirements, and in many cases have limited ability to move through and utilise the land use matrix. We addressed this problem using a case study of the koala (Phascolarctos cinereus) surveyed in a fragmented rural-urban landscape in southeast Queensland, Australia. We applied a logistic modelling and hierarchical partitioning analysis to determine the importance of forest area and its configuration relative to site (local) and patch-level habitat variables. After taking into account spatial auto-correlation and the year of survey, we found koala occurrence increased with the area of all forest habitats, habitat patch size and the proportion of primary Eucalyptus tree species; and decreased with mean nearest neighbour distance between forest patches, the density of forest patches, and the density of sealed roads. The difference between the effect of habitat area and configuration was not as strong as theory predicts, with the configuration of remnant forest becoming increasingly important as the area of forest habitat declines. We conclude that the area of forest, its configuration across the landscape, as well as the land use matrix, are important determinants of koala occurrence, and that habitat configuration should not be overlooked in the conservation of forest-dependent mammals, such as the koala. We highlight the implications of these findings for koala conservation. (c) 2006 Elsevier Ltd. All rights reserved.

Linking riparian vegetation spatial structure in Australian tropical savannas to ecosystem health indicators: semi-variogram analysis of high spatial resolution satellite imagery

Government agencies responsible for riparian environments are assessing the combined utility of field survey and remote sensing for mapping and monitoring indicators of riparian zone health. The objective of this work was to determine if the structural attributes of savanna riparian zones in northern Australia can be detected from commercially available remotely sensed image data. Two QuickBird images and coincident field data covering sections of the Daly River and the South Alligator River - Barramundie Creek in the Northern Territory were used. Semi-variograms were calculated to determine the characteristic spatial scales of riparian zone features, both vegetative and landform. Interpretation of semi-variograms showed that structural dimensions of riparian environments could be detected and estimated from the QuickBird image data. The results also show that selecting the correct spatial resolution and spectral bands is essential to maximize the accuracy of mapping spatial characteristics of savanna riparian features. The distribution of foliage projective cover of riparian vegetation affected spectral reflectance variations in individual spectral bands differently. Pan-sharpened image data enabled small-scale information extraction (< 6 m) on riparian zone structural parameters. The semi-variogram analysis results provide the basis for an inversion approach using high spatial resolution satellite image data to map indicators of savanna riparian zone health.

Usefulness of B-type natriuretic peptide in hypertensive patients with exertional dyspnea and normal left ventricular ejection fraction and correlation with new echocardiographic indexes of systolic and diastolic function

B-type natriuretic peptide (BNP) levels increase in systolic heart failure (HF). However, the value of BNP in hypertensive patients with suspected diastolic HF (symptoms suggestive of HF but normal ejection fraction) and its relation to myocardial function in these patients is unclear. We prospectively studied 72 ambulatory hypertensive subjects (40 women, mean age 58 +/- 8 years) with exertional dyspnea and ejection fraction greater than or equal to50%. Diastolic function was evaluated with transmitral and pulmonary venous Doppler, mitral annular velocities (pulsed-wave tissue Doppler), and flow propagation velocity (color M-mode). Systolic function was assessed with strain and strain rate derived from color tissue Doppler imaging. BNP was related to myocardial function and the presence or absence of global diastolic dysfunction. By conventional Doppler criteria, 34 patients had normal left ventricular diastolic function and 38 had isolated diastolic dysfunction. BNP values were higher in patients with diastolic dysfunction (46 +/- 48 vs 20 +/- 20 pg/ml, p = 0.004) and were related independently to blood pressure, systolic strain rate, left atrial function (p < 0.01 for all), and age (p = 0.015). Patients with diastolic dysfunction and pseudonormal filling had higher BNP levels compared with impaired relaxation (89 +/- 47 vs 35 +/- 42 pg/ml, p = 0.001). However, 79% of patients with diastolic dysfunction had BNP levels within the normal range. We conclude that in ambulatory hypertensive patients with symptoms suggestive of mild HF and normal ejection fraction, BNP is related to atrial and ventricular systolic parameters, blood pressure, and age. Although elevated in the presence of diastolic dysfunction, the BNP level mostly is in the normal range and, therefore, has limited diagnostic value in stable patients with suspected diastolic HF. (C) 2003 by Excerpta Medica, Inc.

Response of B-type natriuretic pepticle to exercise in hypertensive patients with suspected diastolic heart failure: Correlation with cardiac function, hemodynamics, and workload

Background Diastolic heart failure (DHF) is characterized by dyspnea due to increased left ventricular (LV) filling pressures during stress. We sought the relationship of exercise-induced increases in B-type natriuretic peptide (BNP) to LV filling pressures and parameters of cardiovascular performance in suspected DHF. Methods Twenty-six treated hypertensive patients with suspected DHF (exertional dyspnea, LV ejection fraction >50%, and diastolic dysfunction) underwent maximal exercise echocardiography using the Bruce protocol. BNP, transmitral Doppler, and tissue Doppler for systolic (So) and early (Ea) and late (Aa) diastolic mitral annular velocities were obtained at rest and peak stress. LV filling pressures were estimated with E/Ea ratios. Results Resting BNP correlated with resting pulse pressure (r=0.45, P=0.02). Maximal exercise performance (4.6 +/- 2.5min) was limited by dyspnea. Blood pressure increased with exercise (from 143 +/- 19/88 +/- 8 to 191 +/- 22/90 +/- 10 mm Hg); 13 patients (50%) had a hypertensive response. Peak exercise BNP correlated with peak transmitral E velocity (r = 0.41, P <.05) and peak heart rate (r = -0.40, P <.05). BNP increased with exercise (from 48 57 to 74 97 pg/mL, P =.007), and the increment of BNP with exercise was associated with maximal workload and peak exercise So, Ea, and Aa (P <.01 for all). Filling pressures, approximated by lateral E/Ea ratio, increased with exercise (7.7 +/- 2.0 to 10.0 +/- 4.8, P <.01). BNP was higher in patients with possibly elevated filling pressures at peak exercise (E/Ea >10) compared to those with normal pressures (123 +/- 124 vs 45 +/- 71 pg/mL, P =.027). Conclusions Augmentation of BNP with exercise in hypertensive patients with suspected DHF is associated with better exercise capacity, LV systolic and diastolic function, and left atrial function. Peak exercise BNP levels may identify exercise-induced elevation of filling pressures in DHF.

Correlation of habitual physical activity levels with flow mediated dilation of the brachial artery in 5-10 year old children

Endothelial dysfunction is an early key event of atherogenesis. Both fitness level and exercise intervention have been shown to positively influence endothelial function. In a cross-sectional study of 47 children, the relationship between habitual physical activity and flow-mediated dilation (FMD) of the brachial artery was explored. Habitual physical activity levels (PALs) were assessed using a validated stable isotope technique, and FMD of the brachial artery was measured via high-resolution ultrasound. The results showed that habitual physical activity significantly correlated with FMD (r=0.39, P=0.007), and remained the most influential variable on dilation in multivariate analysis. Although both fitness level and exercise intervention have previously been shown to positively influence FMD, this is the first time that a relationship with normal PALs has been investigated, especially, at such a young age. These data support the concept that physical activity exerts its protective effect on cardiovascular health via the endothelium and add further emphasis to the importance of physical activity in childhood.