Foundations of the Probabilistic Mechanics of Discrete Media (Foundations & philosophy of science & technology series)

This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of such variables. Hence the probabilistic mechanics of discrete media are based on the mathematical theory of probability and the axiomatics of measure theory. Content: FOUNDATIONS & PHILOSOPHY OF SCIENCE & TECHNOLOGY SERIES , Page ii Front Matter , Page iii Copyright , Page iv Preface , Pages v-vi 1 - Mathematical Preliminaries , Pages 1-45 2 - Markov Processes and Markov Random Fields , Pages 46-58 3 - General Formulation of Probabilistic Mechanics , Pages 59-81 4 - Probabilistic Mechanics of Solids , Pages 82-120 5 - Probabilistic Mechanics of Fluids , Pages 121-155 Bibliography , Pages 156-161 Subject Index , Pages 163-166 By D.r. Axelrad. Includes Index. Bibliography: P. 156-161.