A Time Domain Characterization of the Fine Local Regularity of Functions

Kolwankar, Kiran M.; Véhel, Jacques Lévy

doi:10.1007/s00041-002-0016-3

Cited by 41 publications

(43 citation statements)

References 5 publications

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“…The Hölder exponent is defined through consideration of the differentiability of a signal relative to polynomial approximations about a particular point [59,60]. These are given by a Taylor series expansion:…”

Section: Hölder Exponentsmentioning

confidence: 99%

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

2016

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Owing to their frequent occurrence in the natural environment, there has been significant interest in refining our understanding of flow over dunes and other bedforms. Recent work in this area has focused, in particular, on their shear layer characteristics and the manner by which flow structures are generated. However, field-based studies, are reliant on single-, or multi-point measurements, rather than delimiting flow structures from the velocity gradient tensor as is possible in numerical work. Here, we extract pointwise time series from a well-resolved large-eddy simulation as a means to connect these two approaches. The at-a-point analysis technique is termed the velocityintermittency quadrant method and relates the fluctuating, longitudinal velocity, u ′ 1 (t), to its fluctuating pointwise Hölder regularity, α ′ 1 (t).Despite the difference in boundary conditions, our results agree very well with previous experiments that show the importance, in the region above the dunes, of a quadrant 3 (uflow configuration. Our higher density of sampling beneath the shear layer and close to the bedforms relative to past experimental work reveals a negative correlation between u ′ 1 (t) and α

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Section: Hölder Exponentsmentioning

confidence: 99%

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

2016

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“…This approach was discussed by Kolwankar and Lévy Vehel (2002) and considered to be more accurate than wavelet based methods. For the comparison of the differential sensitivity of metrics to the presence of multifractality (Sect.…”

Section: Calculating Hölder Exponentsmentioning

confidence: 99%

Characterizing the structure of nonlinear systems using gradual wavelet reconstruction

Keylock

2010

Nonlin. Processes Geophys.

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Abstract. In this paper, classical surrogate data methods for testing hypotheses concerning nonlinearity in time-series data are extended using a wavelet-based scheme. This gives a method for systematically exploring the properties of a signal relative to some metric or set of metrics. A signal continuum is defined from a linear variant of the original signal (same histogram and approximately the same Fourier spectrum) to the exact replication of the original signal. Surrogate data are generated along this continuum with the wavelet transform fixing in place an increasing proportion of the properties of the original signal. Eventually, chaotic or nonlinear behaviour will be preserved in the surrogates. The technique permits various research questions to be answered and examples covered in the paper include identifying a threshold level at which signals or models for those signals may be considered similar on some metric, analysing the complexity of the Lorenz attractor, characterising the differential sensitivity of metrics to the presence of multifractality for a turbulence time-series, and determining the amplitude of variability of the Hölder exponents in a multifractional Brownian motion that is detectable by a calculation method. Thus, a wide class of analyses of relevance to geophysics can be undertaken within this framework.

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“…Instead, we need a notion of a "local value for H " that can vary over a signal. This measure of signal regularity is the Hölder/Lipshitz exponent α p (Mallat, 1999;Kolwankar and Lévy-Véhel, 2002).…”

Section: The Data and Testing Proceduresmentioning

confidence: 99%

Improved preservation of autocorrelative structure in surrogate data using an initial wavelet step

Keylock

2008

Nonlin. Processes Geophys.

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Abstract. Surrogate data generation algorithms are useful for hypothesis testing or for generating realisations of a process for data extension or modelling purposes. This paper tests a well known surrogate data generation method against a stochastic and also a hybrid wavelet-Fourier transform variant of the original algorithm. The data used for testing vary in their persistence and intermittency, and include synthetic and actual data. The hybrid wavelet-Fourier algorithm outperforms the others in its ability to match the autocorrelation function of the data, although the advantages decrease for high intermittencies and when attention is only directed towards the early part of the autocorrelation function. The improved performance is attributed to the wavelet step of the algorithm.

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A Time Domain Characterization of the Fine Local Regularity of Functions

Cited by 41 publications

References 5 publications

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

Characterizing the structure of nonlinear systems using gradual wavelet reconstruction

Improved preservation of autocorrelative structure in surrogate data using an initial wavelet step

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