Diffusion in Random Fields
Diffusion in Random Fields

Author: Nicolae Suciu

Publisher: Springer

Published: 2019-05-31

Total Pages: 276

ISBN-13: 303015081X

DOWNLOAD EBOOK

This book presents, in an accessible and self-consistent way, the theory of diffusion in random velocity fields, together with robust numerical simulation approaches. The focus is on transport processes in natural porous media, with applications to contaminant transport in groundwater. Starting from basic information on stochastic processes, more challenging issues are subsequently addressed, such as the correlation structure of the diffusion process in random fields, the relation between memory effects and ergodic properties, derivation and parameterizations of evolution equations for probability densities, and the relation between measurements and spatio-temporal upscaling. Written for readers with a background in applied mathematics, engineering, physics or geophysics, the book offers an essential basis for further research in the stochastic modeling of groundwater systems.

Spectral Models of Random Fields in Monte Carlo Methods
Spectral Models of Random Fields in Monte Carlo Methods

Author: Serge M. Prigarin

Publisher: VSP

Published: 2001

Total Pages: 220

ISBN-13: 9789067643436

DOWNLOAD EBOOK

Spectral models were developed in the 1970s and have appeared to be very promising for various applications. Nowadays, spectral models are extensively used for stochastic simulation in atmosphere and ocean optics, turbulence theory, analysis of pollution transport for porous media, astrophysics, and other fields of science. The spectral models presented in this monograph represent a new class of numerical methods aimed at simulation of random processes and fields. The book is divided into four chapters, which deal with scalar spectral models and some of their applications, vector-valued spectral models, convergence of spectral models, and problems of optimisation and convergence for functional Monte Carlo methods. Furthermore, the monograph includes four appendices, in which auxiliary information is presented and additional problems are discussed. The book will be of value and interest to experts in Monte Carlo methods, as well as to those interested in the theory and applications of stochastic simulation.

Random Fields and Stochastic Lagrangian Models
Random Fields and Stochastic Lagrangian Models

Author: Karl K. Sabelfeld

Publisher: Walter de Gruyter

Published: 2012-12-06

Total Pages: 416

ISBN-13: 3110296810

DOWNLOAD EBOOK

The book presents advanced stochastic models and simulation methods for random flows and transport of particles by turbulent velocity fields and flows in porous media. Two main classes of models are constructed: (1) turbulent flows are modeled as synthetic random fields which have certain statistics and features mimicing those of turbulent fluid in the regime of interest, and (2) the models are constructed in the form of stochastic differential equations for stochastic Lagrangian trajectories of particles carried by turbulent flows. The book is written for mathematicians, physicists, and engineers studying processes associated with probabilistic interpretation, researchers in applied and computational mathematics, in environmental and engineering sciences dealing with turbulent transport and flows in porous media, as well as nucleation, coagulation, and chemical reaction analysis under fluctuation conditions. It can be of interest for students and post-graduates studying numerical methods for solving stochastic boundary value problems of mathematical physics and dispersion of particles by turbulent flows and flows in porous media.

Spatiotemporal Random Fields
Spatiotemporal Random Fields

Author: George Christakos

Publisher: Elsevier

Published: 2017-07-26

Total Pages: 698

ISBN-13: 0128030321

DOWNLOAD EBOOK

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. - Contains applications in the form of examples and case studies, providing readers with first-hand experiences - Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas - Includes significant updates from the previous edition, including a focus on new theoretical and applied results

Random Fields for Spatial Data Modeling
Random Fields for Spatial Data Modeling

Author: Dionissios T. Hristopulos

Publisher: Springer Nature

Published: 2020-02-17

Total Pages: 884

ISBN-13: 9402419187

DOWNLOAD EBOOK

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Random Fields
Random Fields

Author: Erik Vanmarcke

Publisher: World Scientific

Published: 2010

Total Pages: 363

ISBN-13: 9812563539

DOWNLOAD EBOOK

Random variation is a fact of life that provides substance to a wide range of problems in the sciences, engineering, and economics. There is a growing need in diverse disciplines to model complex patterns of variation and interdependence using random fields, as both deterministic treatment and conventional statistics are often insufficient. An ideal random field model will capture key features of complex random phenomena in terms of a minimum number of physically meaningful and experimentally accessible parameters. This volume, a revised and expanded edition of an acclaimed book first published by the M I T Press, offers a synthesis of methods to describe and analyze and, where appropriate, predict and control random fields. There is much new material, covering both theory and applications, notably on a class of probability distributions derived from quantum mechanics, relevant to stochastic modeling in fields such as cosmology, biology and system reliability, and on discrete-unit or agent-based random processes.Random Fields is self-contained and unified in presentation. The first edition was found, in a review in EOS (American Geophysical Union) to be ?both technically interesting and a pleasure to read ? the presentation is clear and the book should be useful to almost anyone who uses random processes to solve problems in engineering or science ? and (there is) continued emphasis on describing the mathematics in physical terms.?

Dynamical Processes in Condensed Molecular Systems
Dynamical Processes in Condensed Molecular Systems

Author: Joseph Klafter

Publisher: World Scientific

Published: 1989

Total Pages: 338

ISBN-13: 9789971508814

DOWNLOAD EBOOK

This review volume provides an up-to-date review of experimental methods and theoretical approaches in the study of dynamical processes in condensed molecular systems. The experimental contributions include hole burning in glasses and in proteins, optical dephasing in glasses, photo-conductivity in polymers, energy transfer among molecules in confining spaces and electron transfer in polar solvents. The theoretical part summarizes recent advances on hole burning, hierarchical aspects of relaxation and transport in disordered systems.