Similarity and Modeling in Science and Engineering

Contents:

Introduction • Methodology of Modeling

Identification, Modeling and Simulation • Identification and Simulation • Cybernetics and Modeling • Physical Similarity and Modeling • Overview of the Information Theory of Modeling • Historical Development of Modeling • Classification and Properties of Models • Creation, Development and Transformation of a Model • Various Categorizations of Models • Sorting Models According to Degree of Abstraction • Model Simplification and Credibility • Tasks and Algorithmization of Solutions

Dimensional Analysis

Quantities, Dimensional Matrix and Similarity Criteria • Quantities and Units • Fundamental Theorems of Dimensional Analysis • Dimensional Matrix • Similarity Criteria • Determination of Number and Form of Similarity Criteria • Pi theorem • Matrix Solution of Similarity Criteria • Sets of Similarity Criteria • Examples • Conversion of Units and Quantities • Conversion of Units • Conversion of Quantities • Examples • Determination of Functional Relations • Functional Relation and Criterion Equation • Common Procedure • Improved Procedures • Examples • Applications • Thermomechanics of Solid Bodies • Thermomechanics of Fluids • Electricity and Magnetism • Mechanical Engineering ?

Methods of Similarity Analysis

Physical Phenomenological Model Analysis • Phenomenological Expression of Forces and Energies • Physical Significance of Similarity Criteria • Examples • Mathematical Model Analysis • Procedure Utilizing Scale Similarity Indicators • Procedure Utilizing Reference Quantities • Procedure Utilizing Integral Analogues • Example • Applications • Thermomechanics of Solid Bodies • Thermomechanics of Fluids • Electricity and Magnetism • Physical Chemistry • Rheology and Tribology • Technology • Ecology and Medicine

Mathematical Models

Characterization of Mathematical Models • Asymptotic Mathematical Models • Equations of Mathematical Physics • Conditions of Unambiguity • Mathematical Model Transformations • Methods of Tasks Solution • Phenomenological Mathematical Models • Phenomenological Model Formation and Evaluation • Applications • Electrical Engineering • Physical Technology • Mechanical Engineering ?

Physical Models

Characterization of Physical Models • Physical Modeling Procedure • Similarity Theorems • Similarity Criteria Transformations • Scales Determination in Physical Modeling • Example • Applications • Mechanics of Solid Bodies • Thermomechanics of Fluids • Mechanical Engineering ?

Physical Analogues

Characterization of Physical Analogues • Various Physical Analogies • Electrical Analogues of Physical Circuits and Systems • Analogues of Static Circuits and Systems • Analogues of Dynamic Circuits • Electrical Analogues of Physical Fields • Analogues of Steady Fields • Analogues of Unsteady Fields • Analogues of Basic Boundary Conditions • Analogues of Coupled Fields • Analogues of Wave-Diffusion Fields • Direct Modeling Method for Gradient Fields • Applications • Mechanics of Solid Bodies • Mechanics of Fluids • Thermomechanics ?

Deterministic Computer Models

Characterization of Deterministic Models • Numerical Deterministic Models • Matrix Operational Model • Models Based on the Finite Difference Method Principle • Models Based on the Finite Element Method Principle • Models Based on the Finite Volume Method Principle • Models Based on the Boundary Element Method Principle • Hybrid Deterministic Models and Systems • Applications • Mechanics of Solid Bodies • Thermomechanics • Physical Technology • Mechanical Engineering • Industrial medicine

Stochastic Computer Models

Characterization of Stochastic Models • Outline of General Theory • Mathematical Stochastic Model • Transition Probabilities of Internal Nodes • Transition Probabilities of Boundary Nodes • Numerical and Hybrid Stochastic Models • Models Based on the Probability Method Principle • Models Based on the Exodus Method Principle • Models Based on the Monte Carlo Method Principle • Stochastic Computers and Models • Stochastic Coding and Operations • Properties of Stochastic Computers and Models • Applications • Thermomechanics

Cybernetic Models

Black-box-type Models • Simultaneous Models • Structure and Properties • Neuron-web-type Models • Neural Networks • Neuron Models and Their Properties • Applications

Appendix

Physical Quantities and Constants • Mechanical and Acoustic Quantities • Thermal and Optical Quantities • Electrical and Magnetic Quantities • Subscripts • References • Index

About the Author:

Josef Kunes holds an M.Sc and Ph.D. in study of nuclear technique from Technical University, Plazen. He is also a post-graduate in study of experimental methods in mechanics from Technical University Dresden. He was awarded Grade I Scientific Qualification by the Presidium of the Czech. Ac. Sci. He also earned the Doctor of Technical Sciences degrees for the branch of Thermomechanics. Kunes has been a professor at Technical University, Prague.