The Automated Design of Materials Far From Equilibrium (eBook)

Supervisor's Foreword 10
Preface 14
Acknowledgments 16
Contents 18
1 Introduction 21
References 24
2 Artificial Evolution 26
2.1 Introduction 26
2.2 Deriving the CMA-ES Heuristically 29
2.2.1 Invariance Properties 33
2.2.2 The Benefit of Parameterization 36
2.3 Deriving Evolutionary Algorithms from Evolutionary Game Theory 37
2.3.1 The Replicator Equation 37
2.3.2 Parameterizing the Replicator Equation 39
2.3.3 Evolution Equations for the Exponential Family 40
2.3.4 Evolution for a Gaussian Distribution 40
2.3.5 Solving the Replicator Equation withExponential Families 41
2.3.6 Global Convergence for Replicator Equations 43
2.3.7 Change in Entropy 44
2.4 Computation Time and Evolution 45
References 46
3 Optimization 48
3.1 Introduction 48
3.1.1 Optimizing Materials at the Micro-scale 48
3.1.2 Shape in Granular Mechanics 49
3.1.3 Optimizing Granular Materials via Shape 51
3.2 Experiment and Simulation Methodology 52
3.2.1 Experimental Procedure 52
3.2.2 Simulation Procedure 53
3.2.3 Calibrating the Simulation Parameters 53
3.3 Developing a Representation for Shape 55
3.3.1 The Basic Blueprint Rules 55
3.3.2 Benchmarking the CMA-ES Using Blueprint Rules 56
3.3.3 The Generalized Blueprint Rules 58
3.4 Optimization Results 59
3.4.1 The Stiffest and the Softest Packing Shapes 60
3.4.2 Discovering Strain-Stiffeners 62
3.5 Summary 63
References 65
4 Inverse Problems 67
4.1 Introduction 67
4.1.1 Defining Inverse Problems 67
4.1.2 Design Rules as a Solution 68
4.2 Experiment and Simulation Methodology 70
4.2.1 Experimental Procedure 70
4.2.2 Simulation Procedure 71
4.3 Solving the Inverse Problem 73
4.3.1 Finding the Extreme Packing Shapes 73
4.3.2 Analysis of the Results 74
4.3.3 Creating and Using Design Rules 76
4.4 Summary 78
References 79
5 Transitions of Designs 80
5.1 Introduction 80
5.1.1 Stability of Designs 80
5.1.2 Designing a Granular Fluid to Freeze 81
5.2 Simulation Methodology 82
5.3 Examining Transitions Between Designs 82
5.3.1 Finding the First Shapes to Freeze 82
5.3.2 Families of Fastest Cooling Shapes 84
5.3.3 The Transition from Linear to Compact Geometries 85
5.4 Summary 87
References 89
6 Online Design 90
6.1 Introduction 90
6.2 Algorithmic Framework 91
6.3 A Particle on a Substrate 92
6.3.1 Problem Definition 92
6.3.2 Simulation Methodology 93
6.3.3 Controlling the Particle with a Linear Field 93
6.3.4 Controlling the Particle with a Complicated Potential 95
6.4 Folding a Toy Protein 96
6.4.1 Problem Definition 96
6.4.2 Simulation Methodology 97
6.4.3 Folding an Octahedron 98
6.5 Summary 99
References 102
7 Conclusions 103