1,214 research outputs found

    Model-based fit procedure for power-law-like spectra

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    1/fα1/f^\alpha noises are ubiquitous and affect many measurements. These noises are both a nuisance and a peculiarity of several physical systems; in dielectrics, glasses and networked liquids it is very common to study this noise to gather useful information. Sometimes it happens that the noise has a power-law shape only in a certain frequency range, and contains other important features, that are however difficult to study because simple fits often fail. Here I propose a model-based fit procedure that performs well on spectra obtained in a molecular dynamics simulation.Comment: 12 postscript figures, submitted to J. Comp. Phy

    Collective Phenomena and Non-Finite State Computation in a Human Social System

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    We investigate the computational structure of a paradigmatic example of distributed social interaction: that of the open-source Wikipedia community. We examine the statistical properties of its cooperative behavior, and perform model selection to determine whether this aspect of the system can be described by a finite-state process, or whether reference to an effectively unbounded resource allows for a more parsimonious description. We find strong evidence, in a majority of the most-edited pages, in favor of a collective-state model, where the probability of a "revert" action declines as the square root of the number of non-revert actions seen since the last revert. We provide evidence that the emergence of this social counter is driven by collective interaction effects, rather than properties of individual users.Comment: 23 pages, 4 figures, 3 tables; to appear in PLoS ON

    Analytical Considerations of the Stretched Exponential/Power Law Exponential Relations Used for Time-Rate Decline Curve Analysis

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    Since their introduction to the petroleum literature in 2008/2009, the stretched exponential (SE) and the power-law exponential (PLE) relations have become the "conservative" standard for time-rate (decline curve) analysis of well performance data from low/ultra-low permeability reservoirs. The origins of the SE relation can be traced to Rudolf Kohlraush circa 1854; however, its use as an expression for time-rate production data analysis essentially began in 2009 with Valkó. The PLE time-rate relation, on the other hand, was derived empirically (and independently) from observations of well performance data by Jones in 1942 and by Ilk and Blasingame in 2008. To date, there is no "proof" of the SE/PLE from a theoretical basis; however, there are many references devoted to the characteristic functions which have been proposed or derived from the given form of these relations. In this work, we attempt to provide analytical and semi-analytical bases/relations for the SE/PLE functional form to deliver insight on its mathematical behavior and to offer an understanding of its performance as a production forecasting tool. Our first approach consists on approximating the SE/PLE relation by a truncated sum-of-exponentials providing that the SE/PLE model behave as a linear superposition of exponentially decaying functions. For completeness, we extend this work to approximate the hyperbolic and modified hyperbolic time-rate relations with this mentioned sum-of-exponentials function. Next, we develop numerical approximations of the SE/PLE relation in the Laplace domain using three approaches — using the Taylor series expansion, the Laguerre quadrature, and applying the methodology proposed by Blasingame which transform a piecewise power-law function into the Laplace domain. Our goal in this section is to use the Laplace transform and the convolution identity to resolve the SE/PLE decline model in the Laplace domain with the perspective that there may be some sort of diagnostic capability or another sort of mathematical identity, which in the process, may arise. The last part of this work is devoted to "reverse engineer" the flowing bottomhole pressure required to generate a specific SE/PLE case using numerical reservoir simulation. By means of the pseudosteady-state flow equation, the material balance equation, and a prescribed time-rate model (for our case, the SE/PLE, and the hyperbolic time-rate relations), we are able to get a mathematical expression for the flowing bottomhole pressure as a function of time. This mathematical model will be compared against well performance obtained from numerical reservoir simulation. This part of the "reverse engineering" approach provides a "proof of concept" of the validity of the SE/PLE time-rate relation and corroborates the derived functional form of the flowing bottomhole pressure

    High-resolution modal analysis

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    Usual modal analysis techniques are based on the Fourier transform. Due to the Delta T . Delta f limitation, they perform poorly when the modal overlap mu exceeds 30%. A technique based on a high-resolution analysis algorithm and an order-detection method is presented here, with the aim of filling the gap between the low- and the high-frequency domains (30%<mu<100%). A pseudo-impulse force is applied at points of interests of a structure and the response is measured at a given point. For each pair of measurements, the impulse response of the structure is retrieved by deconvolving the pseudo-impulse force and filtering the response with the result. Following conditioning treatments, the reconstructed impulse response is analysed in different frequency-bands. In each frequency-band, the number of modes is evaluated, the frequencies and damping factors are estimated, and the complex amplitudes are finally extracted. As examples of application, the separation of the twin modes of a square plate and the partial modal analyses of aluminium plates up to a modal overlap of 70% are presented. Results measured with this new method and those calculated with an improved Rayleigh method match closely

    A simultaneous sparse approximation method for multidimensional harmonic retrieval

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    International audienceIn this paper, a new method for the estimation of the parameters of multidimensional (R-D) harmonic and damped complex signals in noise is presented. The problem is formulated as R simultaneous sparse approximations of multiple 1-D signals. To get a method able to handle large size signals while maintaining a sufficient resolution, a multigrid dictionary refinement technique is associated to the simultaneous sparse approximation. The refinement procedure is proved to converge in the single R-D mode case. Then, for the general multiple modes case, the signal tensor model is decomposed in order to handle each mode separately in an iterative scheme. The proposed method does not require an association step since the estimated modes are automatically "paired". We also derive the Cramér-Rao lower bounds of the parameters of modal R-D signals. The expressions are given in compact form in the single tone case. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed method

    Matlab-Based Algorithm for Real Time Analysis of Multiexponential Transient Signals

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    Multiexponential transient signals are particularly important due to their occurrences in many natural phenomena and human applications. For instance, it is important in the study of nuclear magnetic resonance (NMR) in medical diagnosis (Cohn-Sfetcu et al., 1975)), relaxation kinetics of cooperative conformational changes in biopolymers (Provencher, 1976), solving system identification problems in control and communication engineering (Prost and Guotte, 1982), fluorescence decay of proteins (Karrakchou et al., 1992), fluorescence decay analysis (Lakowicz, 1999). Several research work have been reported on the analysis of multicomponent transient signals following the pioneer work of Prony in 1795 (Prony, 1975) and Gardner et al. in 1959 (Gardner, 1979). Detailed review of several techniques for multicomponent transient signals’ analysis was recently reported in (Jibia, 2010)

    Some relations between Lagrangian models and synthetic random velocity fields

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    We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time increments. This interpretation allows direct association of the drift and noise terms entering the model, with the geometry of the turbulent fluctuations. In particular, the well known non-uniqueness problem in the well-mixedness approach is solved in terms of the antisymmetric part of the velocity correlations; its relation with the presence of non-zero mean helicity and other geometrical properties of the flow is elucidated. The well-mixedness condition appears to be a special case of the relation between conditional velocity increments of the random field and the one-point Eulerian velocity distribution, allowing generalization of the approach to the transport of non-tracer quantities. Application to solid particle transport leads to a model satisfying, in the homogeneous isotropic turbulence case, all the conditions on the behaviour of the correlation times for the fluid velocity sampled by the particles. In particular, correlation times in the gravity and in the inertia dominated case, respectively, longer and shorter than in the passive tracer case; in the gravity dominated case, correlation times longer for velocity components along gravity, than for the perpendicular ones. The model produces, in channel flow geometry, particle deposition rates in agreement with experiments.Comment: 54 pages, 8 eps figures included; contains additional material on SO(3) and on turbulent channel flows. Few typos correcte

    Parameter estimation of compact binaries using the inspiral and ringdown waveforms

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    We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.Comment: matching cqg versio
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