Correlation Theory of Stationary and Related Random Functions

Yaglom, A. M.

doi:10.1007/978-1-4612-4620-6

Cited by 477 publications

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“…Further details can be found in [35,49]. In the purely scalar-valued case (l = 1), F( k) = E( k) and Q( k) = I.…”

Section: Discussionmentioning

confidence: 99%

“…One generic approach to simulating a Gaussian random field at a set of points is to recognize that the values of the random field at these points form a mean zero, jointly Gaussian collection of random variables [49]. The covariance matrix for these Gaussian random variables is obtained from evaluating the correlation function at the relative displacements between each pair of points.…”

Section: Direct Simulation Methodsmentioning

confidence: 99%

“…A homogeneous d-dimensional vector-valued random field u(x), x ∈ R d is called isotropic if the random field U T u(U x) has the same finite-dimensional distributions as those of the random field u( x) for any rotation matrix U ∈ SO(d) [10,35,49]. The spectral density tensor of an isotropic random field has the following general structure [35,49]:…”

Section: A2 Generalizations Of Randomization Methodsmentioning

confidence: 99%

“…The spectral density tensor of an isotropic random field has the following general structure [35,49]:…”

Section: A2 Generalizations Of Randomization Methodsmentioning

confidence: 99%

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Comparative analysis of multiscale Gaussian random field simulation algorithms

Kramer

Kurbanmuradov

Sabelfeld

2007

Journal of Computational Physics

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We analyze and compare the efficiency and accuracy of two simulation methods for homogeneous random fields with multiscale resolution. We consider in particular the Fourier-wavelet method and three variants of the Randomization method: (A) without any stratified sampling of wavenumber space, (B) with stratified sampling of wavenumbers with equal energy subdivision, (C) with stratified sampling with a logarithmically uniform subdivision. We focus primarily on fractal Gaussian random fields with Kolmogorov-type spectra. Previous work has shown that variants (A) and (B) of the Randomization method are only able to generate a self-similar structure function over three to four decades with reasonable computational effort. By contrast, variant (C), along with the Fourier-wavelet method, is able to reproduce accurate self-similar scaling of the structure function over a number of decades increasing linearly with computational effort (for our examples we will show that nine decades can be reproduced). We provide some conceptual and numerical comparison of the various cost contributions to each random field simulation method.We find that when evaluating ensemble averaged quantities like the correlation and structure functions, as well as some multi-point statistical characteristics, the Randomization method can provide good accuracy with less cost than the Fourierwavelet method. The cost of the Randomization method relative to the Fourierwavelet method, however, appears to increase with the complexity of the random field statistics which are to be calculated accurately. Moreover, the Fourier-wavelet method has better ergodic properties, and hence becomes more efficient for the computation of spatial (rather than ensemble) averages which may be important in simulating the solutions to partial differential equations with random field coefficients.

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“…Further details can be found in [35,49]. In the purely scalar-valued case (l = 1), F( k) = E( k) and Q( k) = I.…”

Section: Discussionmentioning

confidence: 99%

Section: Direct Simulation Methodsmentioning

confidence: 99%

Section: A2 Generalizations Of Randomization Methodsmentioning

confidence: 99%

“…The spectral density tensor of an isotropic random field has the following general structure [35,49]:…”

Section: A2 Generalizations Of Randomization Methodsmentioning

confidence: 99%

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Comparative analysis of multiscale Gaussian random field simulation algorithms

Kramer

Kurbanmuradov

Sabelfeld

2007

Journal of Computational Physics

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“…The main reasons for such-clearly inadequate from various viewpoints-analyses of spatiotemporal data should be attributed to the following facts: (i) the importance of spatiotemporal variability in the study of space-time phenomena was not fully appreciated until recently; and (ii) most 291 Spatiotemporal random fields } of the theoretical tools and mathematical techniques of data processing available have been designed to operate exclusively in time (time series methods; e.g., [16]) or exclusively in space (random fields, geostatistics; e.g., [22,32,331). Undoubtedly, the literature on the subject of applied space-time data analysis and processing is very limited and most aspects of importance in the analysis, modelling and estimation of spatiotemporal parameters have not been studied adequately.…”

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confidence: 99%

Probabilistic and Stochastic Methods in Analysis, with Applications

Byrnes¹

1992

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General Bottom‐Up Construction of Spherical Particles by Pulsed Laser Irradiation of Colloidal Nanoparticles: A Case Study on CuO

Wang

Kawaguchi

Pyatenko

et al. 2011

Chemistry A European J

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The development of a general method to fabricate spherical semiconductor and metal particles advances their promising electrical, optical, magnetic, plasmonic, thermoelectric, and optoelectric applications. Herein, by using CuO as an example, we systematically demonstrate a general bottom-up laser processing technique for the synthesis of submicrometer semiconductor and metal colloidal spheres, in which the unique selective pulsed heating assures the formation of spherical particles. Importantly, we can easily control the size and phase of resultant colloidal spheres by simply tuning the input laser fluence. The heating-melting-fusion mechanism is proposed to be responsible for the size evolution of the spherical particles. We have systematically investigated the influence of experimental parameters, including laser fluence, laser wavelength, laser irradiation time, dispersing liquid, and starting material concentration on the formation of colloidal spheres. We believe that this facile laser irradiation approach represents a major step not only for the fabrication of colloidal spheres but also in the practical application of laser processing for micro- and nanomaterial synthesis.

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Correlation Theory of Stationary and Related Random Functions

Cited by 477 publications

References 0 publications

Comparative analysis of multiscale Gaussian random field simulation algorithms

Comparative analysis of multiscale Gaussian random field simulation algorithms

Probabilistic and Stochastic Methods in Analysis, with Applications

General Bottom‐Up Construction of Spherical Particles by Pulsed Laser Irradiation of Colloidal Nanoparticles: A Case Study on CuO

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