2,149 research outputs found
Re-examination of log-periodicity observed in the seismic precursors of the 1989 Loma Prieta earthquake
Based on several empirical evidence, a series of papers has advocated the
concept that seismicity prior to a large earthquake can be understood in terms
of the statistical physics of a critical phase transition. In this model, the
cumulative Benioff strain (BS) increases as a power-law time-to-failure before
the final event. This power law reflects a kind of scale invariance with
respect to the distance to the critical point. A few years ago, on the basis of
a fit of the cumulative BS released prior to the 1989 Loma Prieta earthquake,
Sornette and Sammis [1995] proposed that this scale invariance could be
partially broken into a discrete scale invariance (DSI). The observable
consequence of DSI takes the form of log-periodic oscillations decorating the
accelerating power law. They found that the quality of the fit and the
predicted time of the event are significantly improved by the introduction of
log-periodicity. Here, we present a battery of synthetic tests performed to
quantify the statistical significance of this claim. We find that log-periodic
oscillations with frequency and regularity similar to those of the Loma Prieta
case are very likely to be generated by the interplay of the low pass filtering
step due to the construction of cumulative functions together with the
approximate power law acceleration. Thus, the single Loma Prieta case alone
cannot support the initial claim and additional cases and further study are
needed to increase the signal-to-noise ratio if any. The present study will be
a useful methodological benchmark for future testing of additional events when
the methodology and data to construct reliable Benioff strain function become
available.Comment: LaTeX, JGR preprint with AGU++ v16.b and AGUTeX 5.0, use packages
graphicx and psfrag, 23 eps figures, 17 pages. In press J. Geophys. Re
Learning Relaxation for Multigrid
During the last decade, Neural Networks (NNs) have proved to be extremely
effective tools in many fields of engineering, including autonomous vehicles,
medical diagnosis and search engines, and even in art creation. Indeed, NNs
often decisively outperform traditional algorithms. One area that is only
recently attracting significant interest is using NNs for designing numerical
solvers, particularly for discretized partial differential equations. Several
recent papers have considered employing NNs for developing multigrid methods,
which are a leading computational tool for solving discretized partial
differential equations and other sparse-matrix problems. We extend these new
ideas, focusing on so-called relaxation operators (also called smoothers),
which are an important component of the multigrid algorithm that has not yet
received much attention in this context. We explore an approach for using NNs
to learn relaxation parameters for an ensemble of diffusion operators with
random coefficients, for Jacobi type smoothers and for 4Color GaussSeidel
smoothers. The latter yield exceptionally efficient and easy to parallelize
Successive Over Relaxation (SOR) smoothers. Moreover, this work demonstrates
that learning relaxation parameters on relatively small grids using a two-grid
method and Gelfand's formula as a loss function can be implemented easily.
These methods efficiently produce nearly-optimal parameters, thereby
significantly improving the convergence rate of multigrid algorithms on large
grids.Comment: This research was carried out under the supervision of Prof. Irad
Yavneh and Prof. Ron Kimmel. XeLate
The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2
Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution
Strict calculation of the light statistics at the output of a travelling wave optical amplifier
A new method for calculating the probability density function of the photon number propagating through a travelling wave optical amplifier with no restriction on its working regime (linear and nonlinear) is reported. The authors show that the widely used Gaussian approximation of the probability density function does not match the real statistics if the incident optical power is small.Peer ReviewedPostprint (published version
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