ばいちょ(売価調査)、価格比較とネットでのお買い物を楽に

内容説明
Scaling laws reveal the fundamental property of phenomena， namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis， physical similarity theory， and general theory of scaling phenomena， using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields， including theoretical biology， fracture mechanics， atmospheric and oceanic phenomena， and flame propagation， are presented for which the ideas of scaling， intermediate asymptotics， self-similarity， and renormalisation were of decisive value in modelling.
Book Description
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.