Dimensional Analysis Beyond the Pi Theorem

Nonfiction, Science & Nature, Science, Physics, Thermodynamics, Mathematics, Applied, Technology
Cover of the book Dimensional Analysis Beyond the Pi Theorem by Bahman Zohuri, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Bahman Zohuri ISBN: 9783319457260
Publisher: Springer International Publishing Publication: November 2, 2016
Imprint: Springer Language: English
Author: Bahman Zohuri
ISBN: 9783319457260
Publisher: Springer International Publishing
Publication: November 2, 2016
Imprint: Springer
Language: English

Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem.  There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable.

A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time.  However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers.

In recent years there has been a surge of interest in self-similar solutions of the First and Second kind.  Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials.

Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation.  It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar.  Variables can be specifically chosen for the calculations.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem.  There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable.

A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time.  However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers.

In recent years there has been a surge of interest in self-similar solutions of the First and Second kind.  Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials.

Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation.  It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar.  Variables can be specifically chosen for the calculations.

More books from Springer International Publishing

Cover of the book Grammatical Inference by Bahman Zohuri
Cover of the book The Euro and the Crisis by Bahman Zohuri
Cover of the book Amnesia and the Nation by Bahman Zohuri
Cover of the book Engagement and Disengagement at Work by Bahman Zohuri
Cover of the book The Climate Change Crisis by Bahman Zohuri
Cover of the book Practical Applications of the Philosophy of Science by Bahman Zohuri
Cover of the book Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century by Bahman Zohuri
Cover of the book Numerical Mathematics and Advanced Applications ENUMATH 2017 by Bahman Zohuri
Cover of the book Plant, Soil and Microbes by Bahman Zohuri
Cover of the book Data Management Technologies and Applications by Bahman Zohuri
Cover of the book Origins and Originality in Family Therapy and Systemic Practice by Bahman Zohuri
Cover of the book Wireless Algorithms, Systems, and Applications by Bahman Zohuri
Cover of the book Henry James's Feminist Afterlives by Bahman Zohuri
Cover of the book The Case Against Bureaucratic Discretion by Bahman Zohuri
Cover of the book The Neuropharmacology of Nicotine Dependence by Bahman Zohuri
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy