PDF Ebook Scaling (Cambridge Texts in Applied Mathematics), by Grigory Isaakovich Barenblatt
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Scaling (Cambridge Texts in Applied Mathematics), by Grigory Isaakovich Barenblatt
PDF Ebook Scaling (Cambridge Texts in Applied Mathematics), by Grigory Isaakovich Barenblatt
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Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial to know the details of these laws, so that mathematical models can be properly formulated and analysed, and the phenomena in question can be more deeply understood. In this 2003 book, the author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural attributes of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.
- Sales Rank: #603341 in eBooks
- Published on: 2003-11-13
- Released on: 2003-11-13
- Format: Kindle eBook
Review
"This book describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are given a modern treatment here." Mechanical Engineering
"The book is accessible to a general mathematically literate audience: the complex physical phenomena are presented clearly and economically. Readers will be rewarded with a wealth of examples, with guiding general principles and with profound insights." American Mathematical Society Reviews
About the Author
G. I. Barenblatt is Emeritus G. I. Taylor Professor of Fluid Mechanics at the University of Cambridge, Emeritus Professor at the University of California, Berkeley, and Principal Scientist in the Institute of Oceanology of the Russian Academy of Sciences, Moscow.
Most helpful customer reviews
6 of 6 people found the following review helpful.
Excellent resource on scaling, pedagogically written, deep and insightful
By Secluded Path
I got this book on the hope to learn more on scaling and dimensional analysis techniques. I already owned Pankhurst's and Huntley's books on dimensional analysis as well as Lin and Segel's "Mathematics applied to deterministic problems in the Natural Sciences" but wanted to get more insight into the group theoretical aspects. At first I hesitated due to the slightly high price for such a thin book as this but at last I decided to buy it. I did not regret it. This is a great resource on the topic of scaling, showing both the theory and deep group-theoretical connections, everything explained very pedagogically and in accessible manner. I also encountered for the first time the useful concept of intermediate asymptotics. Beware potential readers though, this is not a novel and requires serious effort from your side to grasp this material.
9 of 11 people found the following review helpful.
Scaling up
By Alexander B.
Dimensional analysis is a must for physicists and applied mathematicians, and is usually taught to undergraduates very concisely. This short book will take it to the next level, both of mathematical rigor and of physical insight. The book is built around some well-chosen and carefully worked out examples, each a gem on its own. A pleasure to read.
0 of 0 people found the following review helpful.
think hard
By pete
deep
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