High Performance Computations in NMR

List of Figures......Page 10
List of Tables......Page 13
Introduction......Page 16
Computer Mechanics......Page 19
Data Types......Page 22
The Object......Page 23
Syntax......Page 24
Motivations......Page 28
Stacks......Page 29
An Array Object and Stacks......Page 30
Expression Template Implementation......Page 34
Optimizing For Hardware......Page 42
Basic Computer Architecture......Page 45
A Faster Matrix Multiplication......Page 52
Classical Mechanics......Page 57
Bloch Equation Magnetic Fields......Page 58
Quantum Mechanics......Page 74
Rotations......Page 75
Rotational Frames......Page 79
The Hamiltonians......Page 82
Quantum......Page 88
Classical......Page 89
Eigenvalue Problem......Page 91
ODE solvers......Page 93
The Direct Method......Page 97
Periodicity and Propagator Reduction......Page 98
Eigenspace......Page 104
Periodicity and Eigen--Space methods......Page 110
Powder Average Integration......Page 115
Conclusions and Comments......Page 118
Introduction......Page 120
Theoretical Evolutions (TE)......Page 121
Existing NMR Tool Kits......Page 123
BlochLib Design......Page 124
Existing Numerical Tool Kits......Page 125
Experimental and Theoretical Evolutions for NMR simulations......Page 126
BlochLib Layout......Page 127
Drawbacks......Page 136
Various Implementations......Page 138
Solid......Page 139
Classical Program: Magnetic Field Calculators......Page 144
Classical Programs: Bloch Simulations......Page 146
Conclusions......Page 155
Introduction......Page 156
Rotor Synchronization......Page 157
Average Hamiltonian......Page 158
Recoupling RSS......Page 160
C7......Page 165
Removable of Higher Order Terms......Page 166
The Sub--Units......Page 170
The Measure......Page 171
Algorithmic Flow......Page 173
Sequence Measures......Page 176
Transfer Efficiencies......Page 200
Conclusions......Page 211
Future Expansions......Page 216
Evolutionary Algorithms (EA)......Page 217
Neural Networks......Page 224
Final Remarks......Page 226
Bibliography......Page 228
C++ Template code used to generate prime number at compilation......Page 240
C++ Template meta-program to unroll a fixed length vector at compilation time......Page 241
C++ code for performing a matrix multiplication with L2 cache blocking and partial loop unrolling.......Page 243
An MPI master/slave implimentation framework......Page 245
C++ class for a 1 hidden layer Fully  connected back--propagation Neural Network......Page 247
Mathematica Package to generate Wigner Rotation matrices and Spin operators.......Page 254
Rational Reduction C++ Class......Page 259
Optimized static Hamiltonian FID propogation......Page 267
-COMPUTE C++ Class......Page 268
Solid configuration files......Page 278
Magnetic Field Calculator input file......Page 281
Example Classical Simulation of the Bulk Susceptibility......Page 282
Example Classical Simulation of the Modulated Demagnetizing Field......Page 289