Self-affinity of time series with finite domain power-law power spectrum

Yordanov, O.I.; Nickolaev, N. I.

doi:10.1103/physreve.49.r2517

Cited by 35 publications

(13 citation statements)

References 28 publications

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“…These results were obtained in terms of an arbitrary-roughness profile [17,18,26,27] and an arbitrary-roughness power spectrum for the random surface profile. Some cases these problems are analyzed for random surfaces with specific power spectrum: (i) corrugated fractal surface with band-limited power law spectrum [11,39,40]; (ii) isotropic fractal surface with band-limited power law spectrum (with sharp cutoffs band) [50]; (iii) corrugated and isotropic non-fractal surface with single correlation length dominated roughness [18,27]. These studies do not address the questions related to statistically isotropic band-limited fractal roughness without sharp cutoffs.…”

Section: Introductionmentioning

confidence: 98%

“…In order to capture the complexity arising from the irregular interfaces (i.e., rough, porous, and partially active interfaces) one often uses the concept of fractals [31,32]. The fractal irregularities are usually understood in particular in terms of self-similar [31][32][33] or in general as self-affine [7,[31][32][33][34][35][36][37][38][39][40][41] fractals. The response of a rough interface depends on the electrochemical regime.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Jha

Sangal

Kant

2008

Journal of Electroanalytical Chemistry

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Jha

Sangal

Kant

2008

Journal of Electroanalytical Chemistry

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“…These disorders have varying degrees of randomness and can be fractal or nonfractal in nature. The fractal irregularities are usually understood in terms of self-similar − or, in general, as self-affine − fractals.…”

Section: Introductionmentioning

confidence: 99%

Diffusion-Limited Reaction Rates on Self-Affine Fractals

Kant¹

1997

J. Phys. Chem. B

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The diffusion-limited reaction rate is determined on an approximately self-affine corrugated (random) surface fractal. We obtain the exact result for the low roughness and the asymptotic results (in three time regions) for the arbitrary and large roughness surfaces. These results show the anomalous time dependence for the mean flux and the mean excess flux for the large and small roughness surfaces, respectively. The intermediate time behavior of the reaction flux for the small roughness interface has the form 〈J〉 ∼ t -1/2 + const t -3/2+ H , but for the large roughness interfaces it has same form as predicted earlier, 〈J〉 ∼ t -1+ H /2, where H is Hurst's exponent. This nonuniversality and dependence of intermediate time behavior on the strength of fractality of the interface is not conceived by earlier works. We also show the localization of the active zones in the presence of roughness. Finally, these results unravel the connection between the total reaction flux and the crossover times to the roughness characteristics like fractal dimension, lower and upper fractal cutoff lengths, and the amplitude of the fluctuations (strength) of the fractal.

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“…The power spectrum of roughness, which is a morphological information parameter in the current expressions deduced in the previous section, can assume any form depending on the type of electrode randomness considered. An important class of morphological randomness found in electrodes is of band limited self-affine isotropic random fractals. − The power spectrum of such morphologies shows power-law behavior under limited length scales. The length scales, and L , are basically the lower and upper statistical cutoff lengths between which fractal behavior is observed. D H is fractal dimension which is a scale invariant property of roughness; τ is topothesy length and it is related to width of the interface.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Theory for Cyclic Staircase Voltammetry of Two Step Charge Transfer Mechanism at Rough Electrodes

Parveen

Kant

2016

J. Phys. Chem. C

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We have developed theory for cyclic (staircase) voltammetry (CSCV) of a two step reversible charge transfer (EE) mechanism for redox species with unequal diffusion coefficients at rough electrodes. The various surface microscopies provide details of random morphology of the electrode which is characterized through the power spectrum in our theory. For the finite fractal electrode model, anomalous enhancement and scan rate dependence of the CSCV or CV response is caused by fractal dimension (D H ), lower length scale of fractality ( ), and topothesy length ( τ). The peak current corresponding to both charge transfer steps is enhanced with an increase in roughness of the fractal electrode (through increase in D H or τ or decrease in ). The onset and offset of the anomalous regime is controlled by τ and , respectively. Results show that the electrode roughness has the potential to enhance the sensitivity of CSCV as an analytical technique. This is due to a decrease in the difference between the peak currents of two charge transfer steps and an increase in the ratio of the peak to the valley (minimum existing between the two peaks) current in the presence of roughness. Finally, we show that not accounting for roughness in data analysis may cause errors in estimation of composition, diffusion coefficient, improper assignment of electrode mechanism, and so forth.

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Self-affinity of time series with finite domain power-law power spectrum

Cited by 35 publications

References 28 publications

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Diffusion-Limited Reaction Rates on Self-Affine Fractals

Theory for Cyclic Staircase Voltammetry of Two Step Charge Transfer Mechanism at Rough Electrodes

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