Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure 1st Edition by Carlo Cattani, Jarema Jaroslavich Rushchitski ISBN 9812707840 978-9812707840

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Product details: 

ISBN 10: 9812707840

ISBN 13:  978-9812707840

Author:  Carlo Cattani, Jarema Jaroslavich Rushchitski 

This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three.All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems that are proposed in this book. By combining these new scientific concepts into a unitary model and enlightening readers on this pioneering field of research, readers will hopefully be inspired to explore the more advanced aspects of this promising scientific direction. The application of wavelet analysis to nanomaterials and waves in nanocomposites can be very appealing to both specialists working on theoretical developments in wavelets as well as specialists applying these methods and experiments in the mechanics of materials.

Table of contents: 

1 Preface
2 Introduction
3 Wavelet Analysis
4 Wavelet and Wavelet Analysis Preliminary Notion Lsuperscript
5 The space Lsuperscript
6 The spacesLsuperscript(p[greater than or equal]1)
7 The Hardy spaces Lsuperscript(p[greater than or equal]1)
8 The sketch scheme of wavelet analysis
9 Rademacher, Walsh and Haar Functions
10 System of Rademacher functions
11 System of Walsh functions
12 System of Haar functions
13 Integral Fourier Transform Heisenberg Uncertainty Principle
14 Window Transform Resolution
15 Examples of window functions
16 Properties of the window Fourier transform
17 Discretization and discrete window Fourier transform
18 Bases Orthogonal Bases Biorthogonal Bases
19 Frames Conditional and Unconditional Bases
20 Wojtaszczyk’s definition of unconditional basis
21 Meyer’s definition of unconditional basis
22 Donoho’s definition of unconditional basis
23 Definition of conditional basis
24 Multiresolution Analysis
25 Decomposition of the Space Lsuperscript
26 Discrete Wavelet Transform Analysis and Synthesis
27 Analysis transition from the fine scale to the coarse scale
28 Synthesis transition from the coarse scale to the fine scale
29 Wavelet Families
30 Haar wavelet
31 Stromberg wavelet
32 Gabor wavelet
33 Daubechies-Jaffard-Journe wavelet
34 Gabor-Malvar wavelet
35 Daubechies wavelet
36 Grossmann-Morlet wavelet
37 Mexican hat wavelet
38 Coifman wavelet – coiflet
39 Malvar-Meyer-Coifman wavelet
40 Shannon wavelet or sinc-wavelet
41 Cohen-Daubechies-Feauveau wavelet
42 Geronimo-Hardin-Massopust wavelet
43 Battle-Lemarie wavelet
44 Integral Wavelet Transform
45 Definition of the wavelet transform
46 Fourier transform of the wavelet
47 The property of resolution
48 Complex-value wavelets and their properties
49 The main properties of wavelet transform
50 Discretization of the wavelet transform
51 Orthogonal wavelets
52 Dyadic wavelets and dyadic wavelet transform
53 Equation of the function signal energy balance
54 Materials with Micro- or Nanostructure
55 Macro-, Meso-, Micro-, and Nanomechanics
56 Main Physical Properties of Materials
57 Thermodynamical Theory of Material Continua
58 Composite Materials
59 Classical Model of Macroscopic Effective Moduli
60 Other Microstructural Models
61 Bolotin model of energy continualization
62 Achenbach-Hermann model of effective stiffness
63 Models of effective stiffness of high orders
64 Asymptotic models of high orders
65 Drumheller-Bedford lattice microstructural models
66 Mindlin microstructural theory
67 Eringen microstructural model Eringen-Maugin model
68 Pobedrya microstructural theory
69 Structural Model of Elastic Mixtures
70 Viscoelastic mixtures
71 Piezoelastic mixtures
72 Computer Modelling Data on Micro- and Nanocomposites
73 Waves in Materials
74 Waves Around the World
75 Analysis of Waves in Linearly Deformed Elastic Materials
76 Volume and shear elastic waves in the classical approach
77 Plane elastic harmonic waves in the classical approach
78 Cylindrical elastic waves in the classical approach
79 Volume and shear elastic waves in the nonclassical approach
80 Plane elastic harmonic waves in the nonclassical approach
81 Analysis of Waves in Nonlinearly Deformed Elastic Materials
82 Basic notions of the nonlinear theory of elasticity Strains
83 Forces and stresses
84 Balance equations
85 Nonlinear elastic isotropic materials Elastic Potentials
86 Nonlinear Wave Equations
87 Nonlinear wave equations for plane waves Methods of solving
88 Method of successive approximations
89 Method of slowly varying amplitudes
90 Nonlinear wave equations for cylindrical waves
91 Comparison of Murnaghan and Signorini Approaches
92 Comparison of some results for plane waves
93 Comparison of cylindrical and plane wave in the Murnaghan model
94 Simple and Solitary Waves in Materials
95 Simple Riemann Waves
96 Simple waves in nonlinear acoustics
97 Simple waves in fluids
98 Simple waves in the general theory of waves
99 Simple waves in mechanics of electromagnetic continua
100 Solitary Elastic Waves in Composite Materials
101 Simple solitary waves in materials
102 Chebyshev-Hermite functions
103 Whittaker functions
104 Mathieu functions
105 Interaction of simple waves Self-generation
106 The solitary wave analysis
107 New Hierarchy of Elastic Waves in Materials
108 Classical harmonic waves periodic nondispersive
109 Classical arbitrary elastic waves D’Alembert waves
110 Classical harmonic elastic waves periodic dispersive
111 Nonperiodic elastic solitary waves with the phase velocity depending on the phase
112 Simple elastic waves with the phase velocity depending on the amplitude
113 Solitary Waves and Elastic Wavelets
114 Elastic Wavelets
115 The Link between the Trough Length and the Characteristic Length
116 Initial Profiles as Chebyshev-Hermite and Whittaker Functions
117 Some Features of the Elastic Wavelets
118 Solitary Waves in Mechanical Experiments
119 Ability of Wavelets in Detecting the Profile Features

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Carlo Cattani,Jarema Jaroslavich Rushchitski,Wavelet and Wave,Materials with Micro