Index
351
Nonlinear least-squares parameter estimation
(NLSE), 144
Normal modes of biaxial anisotropic media, 82
Nuclear magnetic resonance (NMR), 279
Numerical model for titanium, 192
O
A one-dimensional random surface, 160
Optimization via nonlinear least-squares, 3
P
Paramagnetic effects in CNT, 318
Paramagnetic spin dynamics, 319
Paramagnetic spin dynamics and the spin
Hamiltonian, 279
Pauli spin-matrices, 297
Piezoresistive effects in CNT’s, 312
‘POD’ curves, 191
Polak-Ribiere, 14
Probabilistic collation method (PCM), 168
Probabilistic collocation method (PCM), 157
Probability densities and numerical procedures,
158
Probability of detection (POD), 186
Problem No. 1: fastener with multisite damage
in a slab, 46
Problem No. 2: layer-stripping using
multifrequencies, 46
Problem No. 3: fastener with multisite damage
in bottom plate of a double-plate
system, 51
Problem No. 4: another layer-stripping
example using multifrequencies, 53
Proper orthogonal decomposition, 159
Q
QR-decomposition, 30
Quadratic density, 158
Quantum-mechanical model for conductivity,
313
R
Racetrack coil over Ti64, 132
Results for 4D-level 8, 225
S
Sample impedance calculations for lesions,
247
Scale (S) estimator, 45
Schrodinger wave equation, 319
A second example using VIC-3D(R), 64
A simple inverse problem for conductivity, 329
Second-order random functions, 159
Second set-theoretic result, 92
Sensitivity bound of solution, 145, 148
Sensitivity parameters for system response,
148
Set-theoretic estimation, 28
‘Single domain particle’, 324
Single-wall carbon nanotube (SWCN), 318
Slater-Koster tight-binding framework, 314
Sparse grid algorithm and hierarchal basis
system, 212, 213
Sparse grid starting point for inversion, 235
Spatial imaging using embedded CNT sensors,
332
Spin Hamiltonian, 319
Spin-Hamiltonian for Zeeman and exchange
interactions, 299
Statistical analysis of the feasible set, 31, 90
Steepest descent, 13
Stochastic Euler space, 193
Stochastic inverse problems, 143
Structure of CNT’s, 312
A surface-breaking checkerboard at 50 MHz,
38
A surface-breaking slot at 50kHz, 33
Summary of inversion algorithm, 142, 155
Superparamagnetic iron oxide, 324
Superparamagnetism in CNT’s, 312
T
Tangent coil over flawed workpiece, 135
TASMANIAN sparse grids module, 223
A test problem, 131
Thermally-activated transport model, 329
Tight-binding molecular dynamics (TBMD),
314
Transverse Ply with microcrack, 99, 106
‘Two-cell’ hypothesis, 27, 53, 54
Two-dimensional spline interpolation, 181
2D ellipsoidal confidence region, 156
U
Uniform density, 158
V
Voxel-based inversion via set-theoretic
estimation, 21
Z
Zero-cutoff threshold, 102
351
Nonlinear least-squares parameter estimation
(NLSE), 144
Normal modes of biaxial anisotropic media, 82
Nuclear magnetic resonance (NMR), 279
Numerical model for titanium, 192
O
A one-dimensional random surface, 160
Optimization via nonlinear least-squares, 3
P
Paramagnetic effects in CNT, 318
Paramagnetic spin dynamics, 319
Paramagnetic spin dynamics and the spin
Hamiltonian, 279
Pauli spin-matrices, 297
Piezoresistive effects in CNT’s, 312
‘POD’ curves, 191
Polak-Ribiere, 14
Probabilistic collation method (PCM), 168
Probabilistic collocation method (PCM), 157
Probability densities and numerical procedures,
158
Probability of detection (POD), 186
Problem No. 1: fastener with multisite damage
in a slab, 46
Problem No. 2: layer-stripping using
multifrequencies, 46
Problem No. 3: fastener with multisite damage
in bottom plate of a double-plate
system, 51
Problem No. 4: another layer-stripping
example using multifrequencies, 53
Proper orthogonal decomposition, 159
Q
QR-decomposition, 30
Quadratic density, 158
Quantum-mechanical model for conductivity,
313
R
Racetrack coil over Ti64, 132
Results for 4D-level 8, 225
S
Sample impedance calculations for lesions,
247
Scale (S) estimator, 45
Schrodinger wave equation, 319
A second example using VIC-3D(R), 64
A simple inverse problem for conductivity, 329
Second-order random functions, 159
Second set-theoretic result, 92
Sensitivity bound of solution, 145, 148
Sensitivity parameters for system response,
148
Set-theoretic estimation, 28
‘Single domain particle’, 324
Single-wall carbon nanotube (SWCN), 318
Slater-Koster tight-binding framework, 314
Sparse grid algorithm and hierarchal basis
system, 212, 213
Sparse grid starting point for inversion, 235
Spatial imaging using embedded CNT sensors,
332
Spin Hamiltonian, 319
Spin-Hamiltonian for Zeeman and exchange
interactions, 299
Statistical analysis of the feasible set, 31, 90
Steepest descent, 13
Stochastic Euler space, 193
Stochastic inverse problems, 143
Structure of CNT’s, 312
A surface-breaking checkerboard at 50 MHz,
38
A surface-breaking slot at 50kHz, 33
Summary of inversion algorithm, 142, 155
Superparamagnetic iron oxide, 324
Superparamagnetism in CNT’s, 312
T
Tangent coil over flawed workpiece, 135
TASMANIAN sparse grids module, 223
A test problem, 131
Thermally-activated transport model, 329
Tight-binding molecular dynamics (TBMD),
314
Transverse Ply with microcrack, 99, 106
‘Two-cell’ hypothesis, 27, 53, 54
Two-dimensional spline interpolation, 181
2D ellipsoidal confidence region, 156
U
Uniform density, 158
V
Voxel-based inversion via set-theoretic
estimation, 21
Z
Zero-cutoff threshold, 102
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