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.

‘… deserves to be placed on the book shelf of every working applied mathematician.’

Source: 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.'

Source: 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.'

Source: 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.'

Source: Mathematical Reviews

' … a superb introduction …'

Source: Zentralblatt MATH