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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.

Scaling laws (Statistical physics)

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Scaling laws (Statistical physics) --- Scaling laws (Statistical physics).

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Ising model --- Scaling laws (Statistical physics)

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Whether processes in the natural world are dependent or independent of the scale at which they operate is one of the major issues in hydrologic science. In this volume, leading hydrologists present their views on the role of scale effects in hydrologic phenomena occurring in a range of field settings, from the land surface to deep fractured rock. Self-contained and thought-provoking chapters cover both theoretical and applied hydrology. They provide critical insights into important topics such as general circulation models, floods, river networks, vadose-zone processes, groundwater transport, and fluid flow through fractured media. This book is intended as an accessible introduction for graduate students and researchers to some of the most significant questions and challenges that will face hydrologic science in the twenty-first century.

Hydrology --- Scaling laws (Statistical physics) --- Statistical methods.

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Scaling laws (Statistical physics) --- Complexity (Philosophy) --- Mathematical physics