Titlebook: Stochastic Modeling of Microstructures; Kazimierz Sobczyk,David J. Kirkner Textbook 2001 Birkhäuser Boston 2001 Microstructural Modeling.P

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书目名称Stochastic Modeling of Microstructures被引频次学科排名




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,Probability and Random Variables: A Short Résumé,h an appropriate measure of the possibility of the occurrence of various “uncertain” outcomes of experiments. The notions that should be rigorously defined in constructing such a general model of random phenomena are . i.e., a collection of all possible outcomes of an experiment; . and .. The mathem

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Continuous Random Fields,meter may be quite distinct in each particular situation. One of the best known examples of this type is Brownian motion; each coordinate of the Brownian particle is a random variable that changes in time. As we have seen in Chapter 1, such phenomena are modeled and studied using the theory of stoch

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Random Point Fields,d smoothly in space. For example, in statistical turbulence theory the velocity and pressure are commonly modeled by continuous random fields. Continuous fields can also constitute an adequate language for describing composite materials whose constituents differ slightly from one another and the pro

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Material Media Microstructure: Modeling Issues,nuum, which underlies the classical theories of material behavior (e.g., elasticity theory, electrodynamics), is often too idealized and does not reflect the complexity and heterogeneity inherent in real materials. Examples of such media include various types of composite materials, porous and crack

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Continuous Random Fields,ian particle is a random variable that changes in time. As we have seen in Chapter 1, such phenomena are modeled and studied using the theory of stochastic processes where families of random variables depending on a one-dimensional parameter (interpreted commonly as time) are considered.

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Random Point Fields,ous fields can also constitute an adequate language for describing composite materials whose constituents differ slightly from one another and the properties of the material as a whole change smoothly.

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Statistical Inference,ds and object patterns is necessary. As indicated in section 3.2.1, the first task is recognizing the basic features of a pattern and selection of a suitable model to represent the data. Then follows the problem of parameter estimation for the chosen random field using the available data.