2,024 research outputs found
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
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.
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 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 and
, where is the particle number, the scattering length,
the "Bohr" radius and 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.
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
Damage growth in fibre bundle models with localized load sharing and environmentally-assisted ageing
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
A Poisson model for earthquake frequency uncertainties in seismic hazard analysis
Frequency-magnitude distributions, and their associated uncertainties, are of
key importance in statistical seismology. When fitting these distributions, the
assumption of Gaussian residuals is invalid since event numbers are both
discrete and of unequal variance. In general, the observed number in any given
magnitude range is described by a binomial distribution which, given a large
total number of events of all magnitudes, approximates to a Poisson
distribution for a sufficiently small probability associated with that range.
In this paper, we examine four earthquake catalogues: New Zealand (Institute of
Geological and Nuclear Sciences), Southern California (Southern California
Earthquake Center), the Preliminary Determination of Epicentres and the Harvard
Centroid Moment Tensor (both held by the United States Geological Survey).
Using independent Poisson distributions to model the observations, we
demonstrate a simple way of estimating the uncertainty on the total number of
events occurring in a fixed time period.Comment: 9 pages, 3 figures; accepted by GRL after minor addition
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