Self-affine random surfaces

Yordanov, O.I.; Atanasov, Ivailo

doi:10.1140/epjb/e2002-00288-4

Cited by 28 publications

(25 citation statements)

References 3 publications

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“…Yordanov et al (2002) present a general expression for the ACF valid for the arbitrary topological dimension [31]. Since after the roughness measurement of the study sites, the geometric parameters are considered to be calculated on some arbitrary linear profiles, the ACF for a linear profile of the samples can be realised in the form of [32]:…”

Section: Power-law Inputs For the Iemmentioning

confidence: 99%

Better Estimated IEM Input Parameters Using Random Fractal Geometry Applied on Multi-Frequency SAR Data

et al. 2017

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Abstract:Microwave remote sensing can measure surface geometry. Via the processing of the Synthetic Aperture Radar (SAR) data, the earth surface geometric parameters can be provided for geoscientific studies, especially in geological mapping. For this purpose, it is necessary to model the surface roughness against microwave signal backscattering. Of the available models, the Integral Equation Model (IEM) for co-polarized data has been the most frequently used model. Therefore, by the processing of the SAR data using this model, the surface geometry can be studied. In the IEM, the surface roughness geometry is calculable via the height statistical parameter, the rms-height. However, this parameter is not capable enough to represent surface morphology, since it only measures the surface roughness in the vertical direction, while the roughness dispersion on the surface is not included. In this paper, using the random fractal geometry capability, via the implementation of the power-law roughness spectrum, the precision and correctness of the surface roughness estimation has been improved by up to 10%. Therefore, the random fractal geometry is implemented through the calculation of the input geometric parameters of the IEM using the power-law surface spectrum and the spectral slope. In this paper, the in situ roughness measurement data, as well as SAR images at frequencies of L, C, and X, have been used to implement and evaluate the proposed method. Surface roughness, according to the operational frequencies, exhibits a fractal or a diffractal behavior.

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Section: Power-law Inputs For the Iemmentioning

confidence: 99%

Better Estimated IEM Input Parameters Using Random Fractal Geometry Applied on Multi-Frequency SAR Data

et al. 2017

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“…There are four morphological parameters of fractality in this framework, namely D H , ', L and l. D H is the fractal dimension, a global property which describe scale invariance property of the roughness -an anomalous behavior in current and its time exponent is usually assumed to be function of this parameter; ' and L are lower and upper cutoff length scales of fractality, respectively; and l is the strength of fractal and related to topothesy of fractals [36,54,55], its units are cm 2D H À3 and l ! 0 implies no roughness.…”

Section: Isotropic Self-affine Fractal Surfacesmentioning

confidence: 99%

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Jha

Sangal

Kant

2008

Journal of Electroanalytical Chemistry

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“…An approximately self-affine fractal roughness has structure factor of form which is band-limited power law function [48,46]. Rough surfaces which exhibit statistical self-resemblance over all range of length scales can be described by the pure power-law power spectrum [47,48].…”

Section: Theoretical Model For Random Isotropic Fractal Roughnessmentioning

confidence: 99%

“…Rough surfaces which exhibit statistical self-resemblance over all range of length scales can be described by the pure power-law power spectrum [47,48]. However any real surface is characterized by power-law spectrum over a few decades in wave-numbers with a high and a low wave-number cutoff [48]. The band-limited power-law spectrum used in our calculation has a sharp cutoff at low wave-numbers and a sharp cutoff at high wave-numbers which is given by:…”

Section: Theoretical Model For Random Isotropic Fractal Roughnessmentioning

confidence: 99%

“…The interfacial irregularity in general is modeled with power spectrum of roughness. Four fractal morphological characteristics associated with the power spectrum of roughness are: fractal dimension ðD H Þ, lower ð'Þ and upper (L) cutoff length scales of fractality, and proportionality factor ðlÞ related to topothesy or strength of fractality [48]. Complexity in transport phenomena due to several morphological length scales and phenomenological length scales can be understood through a schematic diagram of a disordered working electrode as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Theory of partial diffusion-limited interfacial transfer/reaction on realistic fractals

Jha

Kant

2010

Journal of Electroanalytical Chemistry

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Self-affine random surfaces

Cited by 28 publications

References 3 publications

Better Estimated IEM Input Parameters Using Random Fractal Geometry Applied on Multi-Frequency SAR Data

Better Estimated IEM Input Parameters Using Random Fractal Geometry Applied on Multi-Frequency SAR Data

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Theory of partial diffusion-limited interfacial transfer/reaction on realistic fractals

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