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Random fields and stochastic Lagrangian models : analysis and applications in turbulence and porous media /
Probabilistic approach and stochastic simulation become more and more popular in all branches of science and technology, especially in problems where the data are randomly fluctuating, or they are highly irregular in deterministic sense. As a rule, in such problems it is very difficult and expensive...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
[2013]
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Sabelʹfelʹd, K. K. |q (Karl Karlovich) |1 https://id.oclc.org/worldcat/entity/E39PBJgX9kQ4F8wvFh87frCJDq | |
| 245 | 1 | 0 | |a Random fields and stochastic Lagrangian models : |b analysis and applications in turbulence and porous media / |c Karl K. Sabelfeld. |
| 260 | |a Berlin : |b De Gruyter, |c [2013] | ||
| 300 | |a 1 online resource (xv, 399 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Probabilistic approach and stochastic simulation become more and more popular in all branches of science and technology, especially in problems where the data are randomly fluctuating, or they are highly irregular in deterministic sense. As a rule, in such problems it is very difficult and expensive to carry out measurements to extract the desired data. As important examples the book mentions the turbulent flow simulation in atmosphere, and construction of flows through porous media. The temporal and spatial scales of the input parameters in this class of problems are varying enormously, and the behaviour is very complicated, so that there is no chance to describe it deterministically. | ||
| 505 | 0 | |a Preface; 1 Introduction; 1.1 Why random fields?; 1.2 Some examples; 1.3 Fundamental concepts; 1.3.1 Random functions in a broad sense; 1.3.2 Gaussian random vectors; 1.3.3 Gaussian random functions; 1.3.4 Random fields; 1.3.5 Stochastic measures and integrals; 1.3.6 Integral representation of random functions; 1.3.7 Random trajectories; 1.3.8 Stochastic differential, Ito integrals; 1.3.9 Brownian motion; 1.3.10 Multidimensional diffusion and Fokker-Planck equation; 1.3.11 Central limit theorem and convergence of a Poisson process to a Gaussian process. | |
| 505 | 8 | |a 2 Stochastic simulation of vector Gaussian random fields2.1 Introduction; 2.2 Discrete expansions related to the spectral representations of Gaussian random fields; 2.2.1 Spectral representations; 2.2.2 Series expansions; 2.2.3 Expansion with an even complex orthonormal system; 2.2.4 Expansion with a real orthonormal system; 2.2.5 Complex valued orthogonal expansions; 2.3 Wavelet expansions; 2.3.1 Fourier wavelet expansions; 2.3.2 Wavelet expansion; 2.3.3 Moving averages; 2.4 Randomized spectral models; 2.4.1 Randomized spectral models defined through stochastic integrals. | |
| 505 | 8 | |a 2.6.6 Fourier wavelet models of Gaussian random fields2.7 Comparison of Fourier wavelet and randomized spectral models; 2.7.1 Some technical details of RSM; 2.7.2 Some technical details of FWM; 2.7.3 Ensemble averaging; 2.7.4 Space averaging; 2.8 Conclusions; 2.9 Appendices; 2.9.1 Appendix A. Positive definiteness of the matrix B; 2.9.2 Appendix B. Proof of Proposition 2.1; 3 Stochastic Lagrangian models of turbulent flows: Relative dispersion of a pair of fluid particles; 3.1 Introduction; 3.2 Criticism of 2-particle models; 3.3 The quasi-1-dimensional Lagrangian model of relative dispersion. | |
| 505 | 8 | |a 3.3.1 Quasi-1-dimensional analog of formula (2.14a)3.3.2 Models with a finite-order consistency; 3.3.3 Explicit form of the model (3.26, 3.27); 3.3.4 Example; 3.4 A 3-dimensional model of relative dispersion; 3.5 Lagrangian models consistent with the Eulerian statistics; 3.5.1 Diffusion approximation; 3.5.2 Relation to the well-mixed condition; 3.5.3 A choice of the coefficients ai and bij; 3.6 Conclusions; 4 A new Lagrangian model of 2-particle relative turbulent dispersion; 4.1 Introduction; 4.2 An examination of Durbin's nonlinear model; 4.3 Mathematical formulation of a new model. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Random fields. | |
| 650 | 0 | |a Lagrangian functions. | |
| 650 | 0 | |a Lagrange spectrum. | |
| 650 | 4 | |a Lagrange spectrum. | |
| 650 | 4 | |a Lagrangian functions. | |
| 650 | 4 | |a Random fields. | |
| 650 | 6 | |a Champs aléatoires. | |
| 650 | 6 | |a Fonctions de Lagrange. | |
| 650 | 6 | |a Spectre de Lagrange. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a Lagrange spectrum |2 fast | |
| 650 | 7 | |a Lagrangian functions |2 fast | |
| 650 | 7 | |a Random fields |2 fast | |
| 758 | |i has work: |a Random fields and stochastic Lagrangian models (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFHt4dcmWPTJFbBjbGmy3P |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |z 9783110296648 |z 3110296640 |w (DLC) 2012039343 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1104258 |z Texto completo |
| 880 | 0 | |6 505-00/Armn |a Preface -- 1 Introduction -- 1.1 Why random fields-- 1.2 Some examples -- 1.3 Fundamental concepts -- 1.3.1 Random functions in a broad sense -- 1.3.2 Gaussian random vectors -- 1.3.3 Gaussian random functions -- 1.3.4 Random fields -- 1.3.5 Stochastic measures and integrals -- 1.3.6 Integral representation of random functions -- 1.3.7 Random trajectories -- 1.3.8 Stochastic differential, Ito integrals -- 1.3.9 Brownian motion -- 1.3.10 Multidimensional diffusion and Fokker-Planck equation -- 1.3.11 Central limit theorem and convergence of a Poisson process to a Gaussian process -- 2 Stochastic simulation of vector Gaussian random fields -- 2.1 Introduction -- 2.2 Discrete expansions related to the spectral representations of Gaussian random fields -- 2.2.1 Spectral representations -- 2.2.2 Series expansions -- 2.2.3 Expansion with an even complex orthonormal system -- 2.2.4 Expansion with a real orthonormal system -- 2.2.5 Complex valued orthogonal expansions -- 2.3 Wavelet expansions -- 2.3.1 Fourier wavelet expansions -- 2.3.2 Wavelet expansion -- 2.3.3 Moving averages -- 2.4 Randomized spectral models -- 2.4.1 Randomized spectral models defined through stochastic integrals -- 2.4.2 Stratified RSM for homogeneous random fields -- 2.5 Fourier wavelet models -- 2.5.1 Meyer wavelet functions -- 2.5.2 Evaluation of the coefficients and ℱmՓ and ℱmΨ -- 2.5.3 Cut-off parameters -- 2.5.4 Choice of parameters -- 2.6 Fourier wavelet models of homogeneous random fields based on randomization of plane wave decomposition -- 2.6.1 Plane wave decomposition of homogeneous random fields -- 2.6.2 Decomposition with fixed nodes -- 2.6.3 Decomposition with randomly distributed nodes -- 2.6.4 Some examples -- 2.6.5 Flow in a porous media in the first order approximation. | |
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