Diffusion in random fields. Applications to transport in groundwater (Q1738342)

There are 7 chapters and 6 appendices. Chapter 3 is devoted to numerical simulations of diffusion processes and GRW (global random walk) algorithms. Chapter 4 presents the mathematical model of diffusion in random fields in relation to applications to stochastic modeling in subsurface hydrology. Chapter 5 presents MC simulations of memory effects and ergodicity issues. Chapter 6 presents a mathematical frame of PDF approaches and numerical solutions of PDF evolution equations obtained with the GRW algorithm. Chapter 7 concludes the book by discussing the relation between model and measurement scales and it also introduces a new approach which accounts for measurement scale through spatio-temporal averages of GRW solutions. Some technical details are deferred to Appendices A--F: \begin{itemize} \item[A] Numerical simulation of diffusion processes \item[B] GRW solutions of Fokker-Planck equations \item[C] Numerical generation of random fields \item[D] Correlation structure of the Itô process. \item[E] Derivation of PDF equations by \(\delta\)-function method \item[F] Upscaled dispersion coefficients \end{itemize}