Rupture cascades in a discrete element model of a porous sedimentary rock

We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized spherical particles which are then connected by breakable beams. Loading at a constant strain rate the cohesive elements fail and the resulting stress transfer produces sudden bursts of correlated failures, directly analogous to the sources of acoustic emissions in real experiments. The source size, energy, and duration can all be quantified for an individual event, and the population analyzed for their scaling properties, including the distribution of waiting times between consecutive events. Despite the non-stationary loading, the results are all characterized by power law distributions over a broad range of scales in agreement with experiments. As failure is approached temporal correlation of events emerge accompanied by spatial clustering.Comment: 5 pages, 4 figure

Long-range, critical-point dynamics in oil field flow rate data

Earthquake triggering data exhibit long-range spatio-temporal correlations of the power-law form C(l) ∼ l−α and anomalously-slow temporal diffusion of the mean triggering distance of the form: 〈l〉 ∼ tH, with H < 0.5. We examine spatio-temporal correlations in subsurface effective stress state caused by fluid injection and extraction at well sites in a hydrocarbon reservoir using a multivariate statistical regression model, and observe long-range correlations in flow rate that cannot be caused by Darcy flow alone. Significantly-correlated well pairs align with the directions of incipient horizontal-displacement tensile and shear failure in the present-day stress field, while the contours of the first principal component of the regression matrix closely follow the macroscopic fault pattern in the main producing horizon. The correlation function for well pairs has a power-law form with α ≈ 0.5, and the mean correlation distance increases with H ≈ 0.33, implying a similar critical-point response to perturbations in effective stress as the earthquake data

Permeability evolution during progressive development of deformation bands in porous sandstones

[1] Triaxial deformation experiments were carried out on large (0.1 m) diameter cores of a porous sandstone in order to investigate the evolution of bulk sample permeability as a function of axial strain and effective confining pressure. The log permeability of each sample evolved via three stages: (1) a linear decrease prior to sample failure associated with poroelastic compaction, (2) a transient increase associated with dynamic stress drop, and (3) a systematic quasi-static decrease associated with progressive formation of new deformation bands with increasing inelastic axial strain. A quantitative model for permeability evolution with increasing inelastic axial strain is used to analyze the permeability data in the postfailure stage. The model explicitly accounts for the observed fault zone geometry, allowing the permeability of individual deformation bands to be estimated from measured bulk parameters. In a test of the model for Clashach sandstone, the parameters vary systematically with confining pressure and define a simple constitutive rule for bulk permeability of the sample as a function of inelastic axial strain and effective confining pressure. The parameters may thus be useful in predicting fault permeability and sealing potential as a function of burial depth and faul

Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appropriate "atomic" units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^2 a/a_u$ and $\gamma/N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the "Bohr" radius and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities can be removed with the help of uniform semiclassical approximations which are constructed over a wide energy range for different types of codimension one and two catastrophes. Using the uniform approximations and applying the high-resolution harmonic inversion method we calculate fully resolved semiclassical photoabsorption spectra, i.e., individual eigenenergies and transition matrix elements at laboratory magnetic field strengths, and compare them with the results of exact quantum calculations.Comment: 26 pages, 9 figures, submitted to J. Phys.

Long-Term X-ray Monitoring of 1E 1740.7-2942 and GRS 1758-258

We report on long-term observations of the Galactic-bulge black hole candidates 1E 1740.7-2942 and GRS 1758-258 with the Rossi X-Ray Timing Explorer. 1E 1740.7-2942 has been observed 77 times and GRS 1758-258 has been observed 82 times over the past 1000 days. The flux of each object has varied by no more than a factor of 2.5 during this period, and the indices of the energy spectra have varied by no more than 0.4. The power spectra are similar to other black-hole candidates: flat-topped noise, breaking to a power law. Each object has exhibited a brightening that lasted for several months, and we have a found a time lag between the photon power-law index and the count rate. In both sources, the spectrum is softest during the decline from the brightening. This behavior can be understood in the context of thin-disk and advection-dominated accretion flows coexisting over a wide range of radii, with the implication that both sources have low-mass companions and accrete via Roche-lobe overflow.Comment: Accepted for publication in The Astrophysical Journa

Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let