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About this book
About this book
Describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. The concepts of intermediate asymptotics and the renormalisation group as natural attributes of self-similarity are demonstrated. The author shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot.
Foreword; Introduction; 1. Dimensional analysis and physical similarity; 2. Self-similarity and intermediate asymptotics; 3. Scaling laws and self-similar solutions which cannot be obtained by dimensional analysis; 4. Complete and incomplete similarity; 5. Scaling and transformation groups and the renormalisation group; 6. Self-similar solutions and traveling waves; 7. Scaling laws and fractals; 8. Scaling laws for turbulent wall-bounded shear flows at very large Reynolds numbers; References; Index.
200 pages, 46 figs
'! deserves to be placed on the book shelf of every working applied mathematician.' ZAMP 'This book will become a classic ! Barenblatt's delightful book though, is more than [a] just an introduction to scaling: it can also be read as a philosophy of mathematical modelling. The writing is witty, insightful, and sometimes moving. Every time you read the book, you return refreshed and inspired ! One can only conclude that any mathematical scientist could be inspired to fundamental advances in their own domain after studying this marvellous book.' The Journal of Fluid Mechanics 'Professor Barenblatt has produced an admirable introduction to this subject, which combines lucid mathematical treatments with perceptive discussions of the principles ! Undergraduate and graduate students will benefit from courses based on this book, but the specialist will also find paradoxes and controversies quietly resolved by the careful use of the scaling methods discussed by Barenblatt. Needless to say, coming from this author, the book is clearly and elegantly written, well presented and well illustrated.' Contemporary Physics '! written in a concise and clear fashion ! Readers will be rewarded with a wealth of examples, with guiding general principles and with profound insights.' Mathematical Reviews ' ! a superb introduction !' Zentralblatt MATH