Preface Foreword 0 Introduction 0.1 Dimensional analysis and physical similarity 0.2 Assumptions underlying dimensional analysis 0.3 Self-similar phenomena 0.4 Self-similar solutions as intermediate asymptotice.Tthe solutions of the first and second kind.Renormalization group 0.5 Self-similar and travelling waves 1 Dimensions,dimensional analysis and similarity 1.1 Dimensions 1.2 Dimensional Analysis 1.3 Similarity 2 The construction of intermediate-asymptotic solutions using dimensional analysis.Self-similar solutions 2.1 Heat propagation from a concentrated instantaneous source 2.2 Phenomena at the initial stage of a nuclear explosion 2.3 Self-similarity.Intermediate asymptotics 3 Self-similarities of the second kind:first examples 3.1 Flow of an ideal fluid past a wedge 3.2 Filtration in an elasto-plastic porous medium:the modified instantaneous heat source problem 4 Self-similarities of the second kind:further examples 4.1 Modified very intense explosion problem 4.2 The von Weizsacker-Zeldovich problem:an impulsive loading 5 Classifcation of similarity rules and self-similarity solutions.Arecipe for the application of similarity analysis 5.1 Complete and incomplete similarity 6 Scaling and transformation groups.Renormalization group 6.1 Dimensional analysis and transformation groups 6.2 The renormalisation group and incomplete similarity 7 Self-similar solutions and travelling waves 8 Invariant solutions:asymptotic conservation laws,spectrum of eigenvalues,and stability 9 Scaling in the deformation and fracture of solids 10 Scaling in turulence 11 Sacling in geophysical fluid dynamics 12 Scaling:miscellaneous special problems Afterword References Index
