Scaling

by Barenblatt, G. I.

Type Book

Rate 0.0 /5

Details

Files

Reviews

Download

Title Statements

Full title :Scaling / Grigory Isaakovich Barenblatt.

Summary

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.

Edition Statements

Publication Date:2003.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2003.

The Physical Object

Description:1 online resource (xiv, 171 pages) : : illustrations

Edition Identifiers

ISBN:9780511814921, 0511814925
oclc:ocn817913196
LC Classification:QC174.85.S34
Dewey Decimal:530.15/95

Cover -- Title -- Copyright -- Dedication -- Contents -- Foreword -- Preface -- Introduction -- Chapter 1 Dimensional analysis and physical similarity -- 1.1 Dimensions -- 1.1.1 Measurement of physical quantities, units of measurement. Systems of units -- 1.1.2 Classes of systems of units -- 1.1.3 Dimension of a physical quantity -- 1.1.4 The dimension function is always a power-law monomial -- 1.1.5 Quantities with independent dimensions -- 1.2 Dimensional analysis -- 1.2.1 Governing parameters -- 1.2.2 Transformation to dimensionless parameters. Generalized homogeneity. .-theorem -- 1.2.3 Problems -- 1.3 Physical similarity -- 1.3.1 Physically similar phenomena -- 1.3.2 The rule for scaling the results for a physically similar model up to the prototype -- 1.3.3 Choosing the governing parameters of the model -- 1.3.4 Problems -- Chapter 2 Self-similarity and intermediate asymptotics -- 2.1 Gently sloping groundwater flow. A mathematical model -- 2.2 Very intense concentrated flooding: the self-similar solution -- 2.3 The intermediate asymptotics -- 2.4 Problem: very intense groundwater pulse flow -- the self-similar intermediate-asymptotic solution -- Chapter 3 Scaling laws and s…

Subjects

Lois d'échelle (Physique statistique) Scaling laws (Statistical physics) Schaalproblemen Schaalvergroting Selbstähnlichkeit Skalierungsgesetz Wetmatigheden Wiskundige modellen