Scaling (Cambridge Texts in Applied Mathematics) [Paperback]

Grigory Isaakovich Barenblatt (Author)

Book Description

ISBN-10: 0521533945 | ISBN-13: 978-0521533942 | Publication Date: December 8, 2003

Starting from dimensional analysis and physical similarity, G. Barenblatt describes the art of discovering scaling laws. He demonstrates the concepts of intermediate asymptotics and the renormalization group as natural consequences of self-similarity and shows how and when these tools can tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used independently by biologists, chemists, astronomers, engineers and geoscientists.

Editorial Reviews

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

Book Description

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 consequences 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.

Product Details

• Paperback: 188 pages
• Publisher: Cambridge University Press (December 8, 2003)
• Language: English
• ISBN-10: 0521533945
• ISBN-13: 978-0521533942
• Product Dimensions: 9 x 6.1 x 0.4 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #648,353 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

9 of 11 people found the following review helpful:

5.0 out of 5 stars Scaling up, March 5, 2005

By 

Alexander B. (USA) - See all my reviews

This review is from: Scaling (Cambridge Texts in Applied Mathematics) (Paperback)

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.

4 of 4 people found the following review helpful:

5.0 out of 5 stars Excellent resource on scaling, pedagogically written, deep and insightful, September 5, 2010

By 

cincosauces - See all my reviews

This review is from: Scaling (Cambridge Texts in Applied Mathematics) (Paperback)

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.

5 of 16 people found the following review helpful:

3.0 out of 5 stars failure to Hurst and Feigenbaum, April 20, 2007

By 

R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews
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This review is from: Scaling (Cambridge Texts in Applied Mathematics) (Hardcover)

Scalding stream coming out of my head?
If it wasn't that this fellow is an ancient Russian scholar
who knew all the great ones personally ( Kolmogorov, von Karman,
etc.) I would have rated his book worse for what he left out
that is "need to know":
1) Hurst exponents ( H.E. Hurst 1951, 1955 Long term storage of reserviors)
2) Manfred Robert SchroederFractals, Chaos, Power Laws: Minutes from an Infinite Paradise
3) M. Feigenbaum ( scalings in terms of renormalizations)
4) Ludwig von Bertalanffy ( Allometric scallings)General System Theory: Foundations, Development, Applications
Talking about scaling and leaving out these fellows is pretty much unforgivable?
The contrary is his coverage of respiration, atomic bomb fireballs
and various fluid dynamic flows.
Barenblatt is just very old:
he hasn't kept up with stuff outside of
fluid dynamics very well?
It appears he got to the west after the cold war.
He's the real deal.
He reminds me of Mandelbrot in his picture.
He doesn't know everything,
but what he does know,
he is damned good at.