Random Fields And Stochastic Lagrangian Models

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Random Fields And Stochastic Lagrangian Models

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Author : Karl K. Sabelfeld
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-06

Random Fields And Stochastic Lagrangian Models written by Karl K. Sabelfeld and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Seminar On Stochastic Analysis Random Fields And Applications Vii

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Author : Robert C. Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-05

Seminar On Stochastic Analysis Random Fields And Applications Vii written by Robert C. Dalang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-05 with Mathematics categories.

This volume contains refereed research or review articles presented at the 7th Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona , Switzerland, in May 2011. The seminar focused mainly on: - stochastic (partial) differential equations, especially with jump processes, construction of solutions and approximations - Malliavin calculus and Stein methods, and other techniques in stochastic analysis, especially chaos representations and convergence, and applications to models of interacting particle systems - stochastic methods in financial models, especially models for power markets or for risk analysis, empirical estimation and approximation, stochastic control and optimal pricing. The book will be a valuable resource for researchers in stochastic analysis and for professionals interested in stochastic methods in finance.​

Modeling Approaches And Computational Methods For Particle Laden Turbulent Flows

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Author : Shankar Subramaniam
language : en
Publisher: Academic Press
Release Date : 2022-10-20

Modeling Approaches And Computational Methods For Particle Laden Turbulent Flows written by Shankar Subramaniam and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-20 with Technology & Engineering categories.

Modelling Approaches and Computational Methods for Particle-laden Turbulent Flows introduces the principal phenomena observed in applications where turbulence in particle-laden flow is encountered while also analyzing the main methods for analyzing numerically. The book takes a practical approach, providing advice on how to select and apply the correct model or tool by drawing on the latest research. Sections provide scales of particle-laden turbulence and the principal analytical frameworks and computational approaches used to simulate particles in turbulent flow. Each chapter opens with a section on fundamental concepts and theory before describing the applications of the modelling approach or numerical method. Featuring explanations of key concepts, definitions, and fundamental physics and equations, as well as recent research advances and detailed simulation methods, this book is the ideal starting point for students new to this subject, as well as an essential reference for experienced researchers. - Provides a comprehensive introduction to the phenomena of particle laden turbulent flow - Explains a wide range of numerical methods, including Eulerian-Eulerian, Eulerian-Lagrange, and volume-filtered computation - Describes a wide range of innovative applications of these models

Stochastic Methods For Boundary Value Problems

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Author : Karl K. Sabelfeld
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-09-26

Stochastic Methods For Boundary Value Problems written by Karl K. Sabelfeld and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.

This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics. Contents: Introduction Random walk algorithms for solving integral equations Random walk-on-boundary algorithms for the Laplace equation Walk-on-boundary algorithms for the heat equation Spatial problems of elasticity Variants of the random walk on boundary for solving stationary potential problems Splitting and survival probabilities in random walk methods and applications A random WOS-based KMC method for electron–hole recombinations Monte Carlo methods for computing macromolecules properties and solving related problems Bibliography

Spherical And Plane Integral Operators For Pdes

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Author : Karl K. Sabelfeld
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-29

Spherical And Plane Integral Operators For Pdes written by Karl K. Sabelfeld and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Mathematics categories.

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Diffusion In Random Fields

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Author : Nicolae Suciu
language : en
Publisher: Springer
Release Date : 2019-05-31

Diffusion In Random Fields written by Nicolae Suciu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Mathematics categories.

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.

Transport Barriers And Coherent Structures In Flow Data

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Author : George Haller
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-16

Transport Barriers And Coherent Structures In Flow Data written by George Haller and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-16 with Science categories.

Transport barriers are observed inhibitors of the spread of substances in flows. The collection of such barriers offers a powerful geometric template that frames the main pathways, or lack thereof, in any transport process. This book surveys effective and mathematically grounded methods for defining, locating and leveraging transport barriers in numerical simulations, laboratory experiments, technological processes and nature. It provides a unified treatment of material developed over the past two decades, focusing on the methods that have a solid foundation and broad applicability to data sets beyond simple model flows. The intended audience ranges from advanced undergraduates to researchers in the areas of turbulence, geophysical flows, aerodynamics, chemical engineering, environmental engineering, flow visualization, computational mathematics and dynamical systems. Detailed open-source implementations of the numerical methods are provided in an accompanying collection of Jupyter notebooks linked from the electronic version of the book.

Spatiotemporal Random Fields

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Author : George Christakos
language : en
Publisher: Elsevier
Release Date : 2017-07-26

Spatiotemporal Random Fields written by George Christakos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Science categories.

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

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Author : Dionissios T. Hristopulos
language : en
Publisher: Springer Nature
Release Date : 2020-02-17

Random Fields For Spatial Data Modeling written by Dionissios T. Hristopulos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-17 with Science categories.

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 And Spin Glasses

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Author : Cirano De Dominicis
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-26

Random Fields And Spin Glasses written by Cirano De Dominicis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-26 with Science categories.

Disordered magnetic systems enjoy non-trivial properties which are different and richer than those observed in their pure, non-disordered counterparts. These properties dramatically affect the thermodynamic behaviour and require specific theoretical treatment. This book deals with the theory of magnetic systems in the presence of frozen disorder, in particular paradigmatic and well-known spin models such as the Random Field Ising Model and the Ising Spin Glass. This is a unified presentation using a field theory language which covers mean field theory, dynamics and perturbation expansion within the same theoretical framework. Particular emphasis is given to the connections between different approaches such as statics vs. dynamics, microscopic vs. phenomenological models. The book introduces some useful and little-known techniques in statistical mechanics and field theory. This book will be of great interest to graduate students and researchers in statistical physics and basic field theory.