Dimensional Analysis, Similarity, Analogy, and the Simulation Theory
Dimensional Analysis, Similarity, Analogy, and the Simulation Theory

Author:

Publisher:

Published: 1978

Total Pages:

ISBN-13:

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Dimensional analysis, similarity, analogy, and cybernetics are shown to be four consecutive steps in application of the simulation theory. This paper introduces the classes of phenomena which follow the same formal mathematical equations as models of the natural laws and the interior sphere of restraints groups of phenomena in which one can introduce simplfied nondimensional mathematical equations. The simulation by similarity in a specific field of physics, by analogy in two or more different fields of physics, and by cybernetics in nature in two or more fields of mathematics, physics, biology, economics, politics, sociology, etc., appears as a unique theory which permits one to transport the results of experiments from the models, convenably selected to meet the conditions of researches, constructions, and measurements in the laboratories to the originals which are the primary objectives of the researches. Some interesting conclusions which cannot be avoided in the use of simplified nondimensional mathematical equations as models of natural laws are presented. Interesting limitations on the use of simulation theory based on assumed simplifications are recognized. This paper shows as necessary, in scientific research, that one write mathematical models of general laws which will be applied to nature in its entirety. The paper proposes the extent of the second law of thermodynamics as the generalized law of entropy to model life and its activities. This paper shows that the physical studies and philosophical interpretations of phenomena and natural laws cannot be separated in scientific work; they are interconnected and one cannot be put above the others.

Similitude and Modelling
Similitude and Modelling

Author: E. Szücs

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 336

ISBN-13: 0080983782

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Similitude and Modeling describes the theoretical aspects and application of similitude method using mathematical apparatus. This book is organized into two parts encompassing 13 chapters, and begins with an introduction to a simple technological problem in similitude modeling. The first part deals with the concept, physical fundamentals, dimensional analysis, and approximate and partial modeling of similitude. This part explores also the preparation and evaluation of similitude experiments, as well as the general types of similitude invariants. The second part highlights the application areas of similitude modeling, including heat conduction and diffusion, fluid dynamics, elastic deformation, and chemical reactions. This book will prove useful to plant and design engineers.

Similarity and Modeling in Science and Engineering
Similarity and Modeling in Science and Engineering

Author: Josef Kuneš

Publisher: Springer Science & Business Media

Published: 2012-04-07

Total Pages: 451

ISBN-13: 1907343776

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The present text sets itself in relief to other titles on the subject in that it addresses the means and methodologies versus a narrow specific-task oriented approach. Concepts and their developments which evolved to meet the changing needs of applications are addressed. This approach provides the reader with a general tool-box to apply to their specific needs. Two important tools are presented: dimensional analysis and the similarity analysis methods. The fundamental point of view, enabling one to sort all models, is that of information flux between a model and an original expressed by the similarity and abstraction Each chapter includes original examples and applications. In this respect, the models can be divided into several groups. The following models are dealt with separately by chapter; mathematical and physical models, physical analogues, deterministic, stochastic, and cybernetic computer models. The mathematical models are divided into asymptotic and phenomenological models. The phenomenological models, which can also be called experimental, are usually the result of an experiment on an complex object or process. The variable dimensionless quantities contain information about the real state of boundary conditions, parameter (non-linearity) changes, and other factors. With satisfactory measurement accuracy and experimental strategy, such models are highly credible and can be used, for example in control systems.

Similarity Methods in Engineering Dynamics
Similarity Methods in Engineering Dynamics

Author: W.E. Baker

Publisher: Elsevier Publishing Company

Published: 1991-06-03

Total Pages: 404

ISBN-13:

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Here is the second revised and updated edition of probably the most practical sourcebook on similarity methods and modeling techniques available. Written by leading authorities who incorporate many of the latest advances in the field, this new work maps out techniques for modeling as well as instrumentation and data analysis for an extremely wide array of problems in engineering dynamics. This practical reference uses experimental test data on various engineering problems demonstrating exactly how and why these similarity methods work. The problems involve spread of oil slicks, explosive cratering, car crashes, space vehicle heat exchange, explosive forming, and more. The spectrum of topics covered and number of examples are far greater than in other texts. Of particular importance are the dissimilar material modeling techniques which bring new versatility and freedom to the modeler in structural dynamics. The book also contains a clear, in-depth discussion of the theory underlying modeling and includes alternate methods for developing model laws. The work will undoubtedly prove invaluable to every professional involved in testing or design of dynamic experiments.