Stochastic modeling of microstructures/ (Record no. 164783)
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000 -LEADER | |
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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 |
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 |
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Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 29/08/2016 | 519.23 SOB/S | P19696 | 29/08/2016 | General Books |