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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 |
Tabla de Contenidos:
- 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 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.
- 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.
- 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.