About this product

Product Identifiers

PublisherBirkhäuser Boston

ISBN-10146126622X

ISBN-139781461266228

eBay Product ID (ePID)14038369461

Product Key Features

Number of PagesIX, 270 Pages

LanguageEnglish

Publication NameStochastic Modeling of Microstructures

SubjectProbability & Statistics / General, Computer Simulation, Construction / Heating, Ventilation & Air Conditioning

Publication Year2012

TypeTextbook

Subject AreaMathematics, Computers, Technology & Engineering

AuthorKazimierz Sobczyk, David J. Kirkner

SeriesModeling and Simulation in Science, Engineering and Technology Ser.

FormatTrade Paperback

Dimensions

Item Weight15.5 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

Reviews"It is the objective of this book to provide the basic principles and results of the theory of random fields (both continuous and discrete) with special emphasis on methods that are important for the modeling of real random material microstructures.... The book may be viewed as a comprehensive introduction to the field of stochastic modeling of material microstructures and will be useful for researchers and professionals in material modeling, engineering and in applied mathematics in general." --Applications of Mathematics

Dewey Edition21

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal519.2/3

Table Of Content1. Probability and Random Variables: A Short Résumé.- 1.1 Basic Concepts.- 1.2 Some Probability Distributions.- 1.3 Convergence of Sequences of Random Variables.- 1.4 Stochastic Processes.- 2. Continuous Random Fields.- 2.1 Basic Concepts.- 2.2 Homogeneous Random Fields.- 2.3 Isotropic Random Fields.- 2.4 Locally Homogeneous and Isotropic Random Fields.- 2.5 Space-Time Random Fields.- 2.6 Vector-Valued Random Fields.- 2.7 Tensor-Valued Random Fields.- 2.8 Markov Random Fields.- 2.9 Fields Governed by Stochastic Equations.- 3. Random Point Fields.- 3.1 Basic Properties.- 3.2 Poisson Random Fields.- 3.3 Boolean Random Fields.- 3.4 Markov and Gibbs Fields.- 3.5 Random Configurations of Objects.- 3.6 Random Set Patterns.- 4. Statistical Inference.- 4.1 Introductory Remarks.- 4.2 Estimation of Mean and Covariance.- 4.3 Estimation of Spectral Density.- 4.4 Prediction Problems: Kriging.- 4.5 Spatial Sampling Design.- 4.6 Inference for Point Fields.- 4.7 Stereology.- 4.8 Simulation and Remarks.- 5. Material Media Microstructure: Modeling Issues.- 5.1 Basic Characteristics of Microstructure.- 5.2 Averaging Procedures.- 5.3 Homogenization and Smoothing.- 5.4 Random Porous Media.- 5.5 Spatial Randomness in Solid Materials.- 6. Physical Phenomena in Random Microstructures: Selected Applications.- 6.1 Introductory Remarks.- 6.2 Wave Propagation.- 6.3 Pollution Transport in Groundwater.- 6.4 Deformation of Random Elastic Materials.- 6.5 Random Microstructure and Fracture.- 6.6 Other Problems and Remarks.- References.- Author Index.

SynopsisA major challenge in applied mathematics and mechanics of materials is to describe various types of material microstructures. The details of the microstructure of most natural and engineered materials are usually obscure; uncertainty and randomness are the inherent features. This complexity due to material heterogeneity has not been adequately described by current classical models and theories. Stochastic Modeling of Microstructures presents a concise and unified presentation of the basic principles and tools for the modeling of real materials, natural and man-made, that possess complex, random heterogeneity. The book uses the language and methods of random field theory combined with the basic constructs of stochastic geometry and geometrical/spatial statistics in order to give the reader the knowledge necessary to model various types of material microstructures. In addition, the book provides a link between the theoretical constructs and physical microstructures via statistical inference from empirical data and the analysis of selected applied problems. Topics and Features: * The first comprehensive introduction to the new field of stochastic modeling of material microstructures * Basic tools required from the diverse subjects of random field theory, stochastic geometry, and spatial statistics are provided * Background concepts from probability theory and stochastic processes are provided * Applications from various fields are discussed, including stochastic wave propagation and the mechanics of porous media flow * The clear and integrated exposition guides the reader from the basics through problems of contemporary research interest * A familiarity with basic probability theory and the most common techniques of applied mathemathics is the only assumed prerequisite. All other concepts required for the stochastic modeling of material microstructures are provided. This book is ideal for a general scientific and engineering audience needing an in-depth guide to current ideas, methods, and models for the stochastic modeling of microstructures. It is an essential reference for practitioners, researchers, and professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics., A major challenge in applied mathematics and mechanics of materials isto describe various types of material microstructures. The details ofthe microstructure of most natural and engineered materials areusually obscure; uncertainty and randomness are the inherent features.This complexity due to material heterogeneity has not been A majorchallenge in applied mathematics and mechanics of materials is todescribe various types of material microstructures. The details of themicrostructure of most natural and engineered materials are usuallyobscure; uncertainty and randomness are the inherent features. Thiscomplexity due to material heterogeneity has not been adequatelydescribed by current classical models and theories. StochasticModeling of Microstructures presents a concise and unifiedpresentation of the basic principles and tools for the modeling ofreal materials, natural and man-made, that possess complex, randomheterogeneity. The book uses the language and methods of random fieldtheory combined with the basic constructs of stochastic geometry andgeometrical/spatial statistics in order to give the reader theknowledge necessary to model various types of materialmicrostructures. The application of the theoretical constructsreviewed in the first three chapters to the analysis of empirical datavia the tools of statistical inference is also discussed. The finalchapters address practical aspects of specific modeling problems.Features- ú First comprehensive introduction to the comparatively newfield of stochastic modeling of material microstructures úPresentation of basic tools required from the diverse subjects ofrandom field theory, stochastic geometry and spatial statistics úProvides background concepts from probability theory and stochasticprocesses are provided ú Applications from various fields arediscussed, including stochastic wave propagation and the mechanics of, This book presents the language of random field theory and the principles of stochastic geometry in order to give the systematic and concise knowledge necessary for modeling real random heterogeneous media. This book is ideal for a general scientific audience needing an in-depth guide to current ideas, methods and models for the stochastic modeling of microstructures. It is an essential reference for practitioners, researchers and professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.

LC Classification NumberQA273.A1-274.9