Preface xi
Chapter 1 Uncertainties 1
1.1. Introduction 1
1.2. The reliability based design approach 2
1.2.1. The MC method 2
1.2.2. The perturbation method 3
1.2.3. The polynomial chaos method 7
1.3. The design of experiments method 9
1.3.1. Principle 9
1.3.2. The Taguchi method 10
1.4. The set approach 14
1.4.1. The method of intervals 15
1.4.2. Fuzzy logic based method 18
1.5. Principal component analysis 20
1.5.1. Description of the process 21
1.5.2. Mathematical roots 22
1.5.3. Interpretation of results 22
1.6. Conclusions 23
Chapter 2 Reliability-based Design Optimization 25
2.1. Introduction 25
2.2. Deterministic design optimization 26
2.3. Reliability analysis 27
2.3.1. Optimal conditions 30
2.4. Reliability-based design optimization 31
2.4.1. The objective function 31
2.4.2. Total cost consideration 32
2.4.3. The design variables 33
2.4.4. Response of a system by RBDO 33
2.4.5. Limit states 33
2.4.6. Solution techniques 33
2.5. Application: optimization of materials of an electronic circuit board 34
2.5.1. Optimization problem 36
2.5.2. Optimization and uncertainties 39
2.5.3. Results analysis 43
2.6. Conclusions 44
Chapter 3 The Waveâ"Particle Nature of Light 47
3.1. Introduction 48
3.2. The optical wave theory of light according to Huyghens and Fresnel 49
3.2.1. The three postulates of wave optics 49
3.2.2. Luminous power and energy 51
3.2.3. The monochromatic wave 51
3.3. The electromagnetic wave according to Maxwellâs theory 52
3.3.1. The Maxwell equations 52
3.3.2. The wave equation according to the Coulombâs gauge 56
3.3.3. The wave equation according to the Lorenzâs gauge 57
3.4. The quantum theory of light 57
3.4.1. The annihilation and creation operators of the harmonic oscillator 57
3.4.2. The quantization of the electromagnetic field and the potential vector 61
3.4.3. Field modes in the second quantization 66
Chapter 4 The Polarization States of Light 71
4.1. Introduction 71
4.2. The polarization of light by the matrix method 73
4.2.1. The Jones representation of polarization 76
4.2.2. The Stokes and Muller representation of polarization 81
4.3. Other methods to represent polarization 86
4.3.1. The Poincar© description of polarization 86
4.3.2. The quantum description of polarization 88
4.4. Conclusions 93
Chapter 5 Interaction of Light and Matter 95
5.1. Introduction 95
5.2. Classical models 97
5.2.1. The Drude model 103
5.2.2. The Sellmeir and Lorentz models 105
5.3. Quantum models for light and matter 111
5.3.1. The quantum description of matter 111
5.3.2. Jaynesâ"Cummings model 118
5.4. Semiclassical models 123
5.4.1. Taucâ"Lorentz model 127
5.4.2. Codyâ"Lorentz model 130
5.5. Conclusions 130
Chapter 6 Experimentation and Theoretical Models 133
6.1. Introduction 134
6.2. The laser source of polarized light 135
6.2.1. Principle of operation of a laser 136
6.2.2. The specificities of light from a laser 141
6.3. Laser-induced fluorescence 143
6.3.1. Principle of the method 143
6.3.2. Description of the experimental setup 145
6.4. The DR method 145
6.4.1. Principle of the method 146
6.4.2. Description of the experimental setup 148
6.5. Theoretical model for the analysis of the experimental results 149
6.5.1. Radiative relaxation 152
6.5.2. Non-radiative relaxation 153
6.5.3. The theoretical model of induced fluorescence 160
6.5.4. The theoretical model of the thermal energy transfer 163
6.6. Conclusions 170
Chapter 7 Defects in a Heterogeneous Medium 173
7.1. Introduction 173
7.2. Experimental setup 175
7.2.1. Pump laser 176
7.2.2. Probe laser 176
7.2.3. Detection system 177
7.2.4. Sample preparation setup 180
7.3. Application to a model system 182
7.3.1. Inert noble gas matrix 182
7.3.2. Molecular system trapped in an inert matrix 184
7.3.3. Experimental results for the induced fluorescence 188
7.3.4. Experimental results for the double resonance 198
7.4. Analysis by means of theoretical models 203
7.4.1. Determination of experimental time constants 203
7.4.2. Theoretical model for the induced fluorescence 209
7.4.3. Theoretical model for the DR 214
7.5. Conclusions 216
Chapter 8 Defects at the Interfaces 219
8.1. Measurement techniques by ellipsometry 219
8.1.1. The extinction measurement technique 222
8.1.2. The measurement by rotating optical component technique 223
8.1.3. The PM measurement technique 224
8.2. Analysis of results by inverse method 225
8.2.1. The simplex method 232
8.2.2. The LM method 234
8.2.3. The quasi-Newton BFGS method 237
8.3. Characterization of encapsulating material interfaces of mechatronic assemblies 237
8.3.1. Coating materials studied and experimental protocol 239
8.3.2. Study of bulk coatings 241
8.3.3. Study of defects at the interfaces 244
8.3.4. Results analysis 251
8.4. Conclusions 253
Chapter 9 Application to Nanomaterials 255
9.1. Introduction 255
9.2. Mechanical properties of SWCNT structures by MEF 256
9.2.1. Young's modulus of SWCNT structures 258
9.2.2. Shear modulus of SWCNT structures 259
9.2.3. Conclusion on the modeling results 260
9.3. Characterization of the elastic properties of SWCNT thin films 260
9.3.1. Preparation of SWCNT structures 261
9.3.2. Nanoindentation 262
9.3.3. Experimental results 263
9.4. Bilinear model of thin film SWCNT structure 265
9.4.1. SWCNT thin film structure 266
9.4.2. Numerical models of thin film SWCNT structures 268
9.4.3. Numerical results 269
9.5. Conclusions 274
Bibliography 275
Index 293
