Scaling Self similarity and Intermediate Asymptotics

Author: Grigory Isaakovich Barenblatt
Publisher: Cambridge University Press
ISBN: 9780521435222
Format: PDF, Docs
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Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.

Scaling

Author: Grigory Isaakovich Barenblatt
Publisher: Cambridge University Press
ISBN: 1107393957
Format: PDF, ePub, Docs
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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.

Computational Engineering

Author: Jürgen Geiser
Publisher: Springer-Verlag
ISBN: 3658187085
Format: PDF
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Das Buch bietet ein ausgewogenes Verhältnis zwischen Theorie und praktischen Anwendungen des berechnenden Ingenieurswesens. Es illustriert sowohl die mathematischen Modelle im Computational Engineering, wie auch die zugehörigen Simulationsmethoden für die verschiedenen Ingenieursanwendungen und benennt geeignete Softwarepakete. Die umfangreichen Beispiele aus der berechnenden Ingenieurswissenschaft, welche Wärme- und Massentransport, Plasmasimulation und hydrodynamische Transportprobleme einschließen, geben dem Leser einen Überblick zu den aktuellen Themen und deren praktische Umsetzung in spätere Simulationsprogramme. Übungsaufgaben und prüfungsrelevante Fragen schließen die einzelnen Kapitel ab.

Industrial Practice

Author: Florian Kongoli
Publisher: Wiley
ISBN:
Format: PDF, ePub, Mobi
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These proceedings on industrial practice from the Sohn International Symposium contain papers on metals and materials processing; iron making; nonferrous high temperature processing; steel; and aqueous and electrochemical processing. From the 2006 TMS Fall Extraction & Processing: Sohn International Symposium, held August 27 - 31, 2006, in San Diego, California.

Practical Applied Mathematics

Author: Sam Howison
Publisher: Cambridge University Press
ISBN: 9780521842747
Format: PDF, ePub, Mobi
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This book illustrates how the reader's knowledge of applied mathematics can be used to describe the world around them.