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Stochastic modeling of microstructures/ (Record no. 164783)

MARC details
000 -LEADER
fixed length control field	01486cam a22003254a 4500
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number	0817642331
040 ## - CATALOGING SOURCE
Transcribing agency	CUS
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number	519.23
Item number	SOB/S
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name	Sobczyk, Kazimierz.
245 10 - TITLE STATEMENT
Title	Stochastic modeling of microstructures/
Statement of responsibility, etc.	Kazimierz Sobczyk, David J. Kirkner.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc.	Boston :
Name of publisher, distributor, etc.	Birkhäuser,
Date of publication, distribution, etc.	c2001.
300 ## - PHYSICAL DESCRIPTION
Extent	viii, 270 p. :
Other physical details	ill. ;
Dimensions	25 cm.
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note	1. Probability and Random Variables: A Short Resume 5<br/>1.1 Basic Concepts .................. ... ........................... .......... ....5<br/>1.2 Some Probability Distributions ............. .......1......................... 11<br/>1.3 Convergence of Sequences of Random Variables ................................ 14<br/>1.4 Stochastic Processes .............................................................................17<br/>1.4.1 Basic Concepts ....................................... 17<br/>1.4.2 Mean and Covariance Function .............................................21<br/>1.4.3 Gaussian Processes .................................................................23<br/>1.4.4 Stationary Processes ..............................................................25<br/>1.4.5 Markov Processes ...................................................................29<br/>2. Continuous Random Fields 33<br/>2.1 Basic Concepts ......................... ..........................................................33<br/>2.2 Homogeneous Random Fields ..............................................................37<br/>2.3 Isotropic Random Fields ......................................................................41<br/>2.3.1 Definition and Spectral Analysis ............................................41<br/>2.3.2 Special Cases .........................................................................45<br/>2.3.3 Variance of Isotropic Fields .............................................. 49<br/>2.4 Locally Homogeneous and Isotropic Random Fields................ ..........51<br/>2.4.1 Locally Homogeneous Fields and the Structure Function .....51<br/>2.4.2 Locally Isotropic Fields ..........................................................53<br/>2.5 Space-Time Random Fields ..................................................................56<br/>2.6 Vector-Valued Random Fields ..............................................................59<br/><br/><br/><br/>2.6.1 Basic Concepts ............................ .................................. 59<br/>2.6.2 Isotropic Vector Random Fields ........................................ 60<br/>2.7 Tensor-Valued Random Fields ............................................................. 65<br/>2.8 Markov Random Fields ........................................................................ 71<br/>2.8.1 Basic Concepts................................................ .. ..... 71<br/>2.8.2 Brownian Fields .....................................................................73<br/>2.9 Fields Governed by Stochastic Equations . ........................... 74<br/>3. Random Point Fields 79<br/>3.1 Basic Properties........................... .................................. 79<br/>3.2 Poisson Random Fields ....................................................................... 85<br/>3.2.1 Homogeneous Poisson Random Field .................................. 85<br/>3.2.2 Inhomogeneous Poisson Field ...................................... 88<br/>3.2.3 Doubly Stochastic Poisson Field ....................................... . 90<br/>3.2.4 Poisson Cluster Field ........................................................... 92<br/>3.2.5 Poisson Hard-Core Field................................................... 93<br/>3.3 Boolean Random Fields ............................................................... 94<br/>3.4 Markov and Gibbs Fields ..................................................................... 98<br/>3.4.1 Markov Fields ........................................................................ 98<br/>3.4.2 Gibbs Fields ......................................................................... 102<br/>3.5 Random Configurations of Objects ........................ ................. 104<br/>3.5.1 Packing Problems ................................................................ 104<br/>3.5.2 General Probability Distributions ........................................10<br/>3.6 Random Set Patterns ........................................................................... 115<br/>3.6.1 Random Sets .........................................................................115<br/>3.6.2 Random Lines in a Plane ......................................................118<br/>3.6.3 Random Tessellations ...........................................................119<br/>4. Statistical Inference 123<br/>4.1 Introductory Remarks......................................................................... 123<br/>4.2 Estimation of Mean and Covariance .................................................. 124<br/>4.3 Estimation of Spectral Density........................................................... 127<br/><br/><br/><br/>4.4 Prediction Problems: Kriging ............................................................. 130<br/>4.5 Spatial Sampling Design.................................................................. 134<br/>4.6 Inference for Point Fields ................................................................... 137<br/>4.7 Stereology ....................................... 139<br/>4.8 Simulation and Remarks ..................................................................... 146<br/>5. Material Media Microstructure: Modeling Issues 149<br/>5.1 Basic Characteristics of Microstructure . .................................. 149<br/>5.1.1 Introductory Remarks ........................................................... 149<br/>5.1.2 Correlation Structure .......... ................................. 150<br/>5.1.3 Scales of Spatial Variation.................................................... 156<br/>5.1.4 Self-Similarity and Fractals .................................................. 160<br/>5.2 Averaging Procedures ........................................................................ 164<br/>5.2.1 Representative Elementary Volume (REV) .......................... 164<br/>5.2.2 Volume Averaging ................................................................ 166<br/>5.2.3 Probabilistic Averaging ....................................................... 168<br/>5.3 Homogenization and Smoothing ........................................................ 172<br/>5.3.1 Homogenization: Effective Parameters ................................ 172<br/>5.3.2 Equations for the Mean Field ............................................... 176<br/>5.3.3 Perturbation Smoothing ........................................................ 180<br/>5.4 Random Porous Media........................................................................ 182<br/>5.4.1 Basic Properties .................................................................... 182<br/>5.4.2 Darcy's Law and Its Justification ........................................ 184<br/>5.4.3 Stochastic Models of Porous Media ..................................... 188<br/>5.4.4 Other Problems and Remarks ............................................... 193<br/>5.5 Spatial Randomness in Solid Materials .............................................. 194<br/>5.5.1 Modeling Approaches .......................................................... 194<br/>5.5.2 Random Elastic Solid Media ................................................ 196<br/>6. Physical Phenomena in Random Microstructures:<br/>Selected Applications 203<br/>6.1 Introductory Remarks ........................................ .... ....203<br/>6.2 Wave Propagation .......................................205<br/><br/><br/><br/>6.2.1 Sound-Wave Effective Parameters...................................... 205<br/>6.2.2 Scattering by Randomly Distributed Inclusions .................. 209<br/>6.3 Pollution Transport in Groundwater.......... .............................. 218<br/>6.3.1 Stochastic Flow and Transport Models................................ 218<br/>6.3.2 Non-Local Mean Concentration Field .................................221<br/>6.4 Deformation of Random Elastic Materials . ................. 227<br/>6.5 Random Microstructure and Fracture . . ............................... 234<br/>6.5.1 General Remarks ................. ....234<br/>6.5.2 Crack Growth in Random Microstructure ...........................235<br/>6.6 Other Problems and Remarks.............. ............. 243<br/>References 247
650 #0 - SUBJECT
Keyword	Random fields.
650 #0 - SUBJECT
Keyword	Materials
General subdivision	Mathematical models.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name	Kirkner, David J.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type	General Books

Holdings
Withdrawn status	Lost status	Damaged status	Not for loan	Home library	Current library	Shelving location	Date acquired	Full call number	Accession number	Date last seen	Koha item type
				Central Library, Sikkim University	Central Library, Sikkim University	General Book Section	29/08/2016	519.23 SOB/S	P19696	29/08/2016	General Books