Scientific Modeling and Simulations (eBook)

Contents 5
Scientific Modeling and Simulations 7
A retrospective on the journal of computer-aided materials design (JCAD), 1993--2007 9
Extrapolative procedures in modelling and simulations: the role of instabilities 11
Abstract 11
1 Introduction 11
1.1 Superconductivity 12
1.2 Low-temperature heat capacity 13
1.3 Crystals modelled as stacking of atomic spheres 14
2 Elastic shear instability and melting 15
3 Shear constants in alloys 16
4 Melting of superheated solids 18
5 Theoretical strength of solids 21
6 Another model---the linear chain 22
7 Four types of extrapolative procedures 23
8 Conclusions 24
Acknowledgements 24
References 24
Characteristic quantities and dimensional analysis 27
Abstract 27
1 Introduction 27
2 Four examples of characteristic quantities 28
2.1 Waves at sea 28
2.2 Temperature profile in the ground 29
2.3 Terminal velocity 29
2.4 Engineering science versus school physics 30
3 Waves revisited 31
4 Characteristic quantities 31
5 Buckingham's . theorem 33
6 Scaling 35
7 Systematics in the neglect of certain effects 35
7.1 Gravity waves in deep water 35
7.2 Small hole in a large sheet under stress 36
8 The Lennard-Jones model 37
9 The Lindemann melting criterion 39
10 Saturating conductivities -- a still unsolved problem 40
11 Conclusions 42
Appendix 1 42
1.1 Thermal conduction in a semi-infinite medium 42
1.2 Falling sphere with air resistance 43
Appendix 2 43
2.1 Spider silk 43
2.2 Rayleigh instability and Bénard cells 44
References 44
Accuracy of models 46
Abstract 46
1 Introduction 46
2 Robustness 47
2.1 The oil peak problem 47
2.2 The entropy of TiC 48
2.3 Discussion 50
3 Fitting of data---two different objectives 51
3.1 The CALPHAD method 51
3.2 Separation of contributions to the heat capacity 52
3.3 Discussion 53
4 Fitting in log-log plots 55
4.1 Introduction 55
4.2 Thermal conduction in insulators 55
5 Second-order effects 56
5.1 Introduction 56
5.2 Weakly inhomogeneous materials 56
6 Mislead by simple textbook results 57
6.1 The vibrational heat capacity 57
6.2 The electronic heat capacity 58
7 Conclusions 59
Appendix 1 60
Moment frequencies and thermodynamic functions 60
Appendix 2 60
Sum of power laws in a log-log plot 60
Appendix 3 61
Power law versus exponential behavior 61
References 61
Multiscale simulations of complex systems: computation meets reality 63
Abstract 63
1 Introduction 63
2 Two representative examples 64
3 Problems and prospects 67
Acknowledgements 68
References 68
Chemomechanics of complex materials: challenges and opportunities in predictive kinetic timescales 70
Abstract 70
1 Introduction 71
2 Putting rare events and rough energy landscapes in context of real materials 71
2.1 Rare events and rough energy landscapes 71
2.2 Diving in to rough energy landscapes of alloys, glasses, and biomolecules 73
3 Forced unbinding of biomolecular complexes 76
3.1 Does stiffness matter? Why ks perturbs the accessible molecular rupture forces 76
3.2 Enough is enough: practical requirements of rare event sampling in MD 78
4 Potential advances for chemomechanical analysis of other complex materials 79
5 Summary and outlook 81
References 82
Tight-binding Hamiltonian from first-principles calculations 84
1 Introduction 84
2 Quasi-atomic minimal-basis-sets orbitals 86
3 Tight-binding matrix elements in terms of QUAMBOs 89
4 Large-scale electronic calculations using the QUAMBO scheme 92
5 Concluding remarks 96
Acknowledgements 97
References 98
Atomistic simulation studies of complex carbon and silicon systems using environment-dependent tight-binding potentials 99
1 Introduction 99
2 Environment-dependent tight-binding potential model 100
2.1 General formalism of tight-binding potential model 100
2.2 EDTB potential model formalism 101
3 EDTB potential for carbon and its applicationa 103
3.1 EDTB potential for carbon 103
3.2 TBMD simulation of vacancy diffusion and reconstruction in grapheme 105
3.3 TBMD simulation of junction formation in carbon nanotubes 108
4 EDTB potential for silicon and its applications 110
4.1 EDTB potential for silicon 110
4.2 TBMD simulation studies of addimer diffusion on Si(100) surface 111
4.2.1 Diffusion between trough and the top of dimer row 115
4.2.2 Diffusion along the trough between the dimmer rows 117
4.3 TBMD study of dislocation core structure in Si 119
5 Future perspective 121
Acknowledgment 121
References 122
First-principles modeling of lattice defects: advancing our insight into the structure-properties relationship of ice 124
Abstract 124
1 Introduction 124
2 Molecular point defects 129
3 Bjerrum defect/molecular point defect interactions 135
4 Summary 140
Acknowledgements 141
References 141
Direct comparison between experiments and computations at the atomic length scale: a case study of graphene 143
Abstract 143
1 Introduction 143
2 Overview of multi-scale simulations in ductile metals 144
3 Mechanical experiments at small length scales 145
4 Mechanical experiments on monolayer graphene 147
5 Analysis of experiments 151
6 Suggestions for further simulations 153
7 Conclusions 154
Acknowledgements 155
References 155
Shocked materials at the intersection of experiment and simulation 158
Abstract 158
1 Introduction 159
2 Approaches to in situ studies of atomic processes under dynamic compression 160
2.1 X-ray techniques---Diffraction and scattering 161
2.1.1 Laser-based systems for x-ray diffraction 161
2.1.2 Accelerator-based light source for x-ray scattering 162
2.1.3 Computation-simulation 162
3 Materials response to shock loading 163
3.1 Inelastic response to shock loading (1D to 3D transition) 163
3.2 Phase transformations 169
3.2.1 Phase transition pathways 169
3.2.2 Phase transition under uniaxial shock compression along [001]BCC direction 170
3.2.3 Calculated observables for the a--e phase transition 170
3.2.4 In situ, Real-time diffraction measurements during the shock 172
3.2.5 The transformation mechanism 173
4 Future work 175
4.1 Dynamic melt: simulation and experiment 175
4.2 Damage: in situ void nucleation and growth 177
5 Conclusion 180
Acknowledgements 182
References 182
Calculations of free energy barriers for local mechanisms of hydrogen diffusion in alanates 186
Abstract 186
1 Introduction 186
2 Model and computations 188
2.1 The simulation set up and its validation 190
2.2 Collective variables for the local H-vacancy diffusion 191
2.3 Collective variables for the non-local H-vacancy diffusion 194
3 Methods 194
3.1 Temperature accelerated molecular dynamics 195
3.2 Radial basis representation of the free energy 196
4 Results 197
4.1 Local hydrogen diffusion 197
4.2 Non-local hydrogen diffusion 199
4.2.1 The TAMD trajectory 199
4.2.2 Radial basis reconstruction of the free energy 200
4.2.3 Calculation of the activation barrier 203
5 Conclusions 204
Acknowledgements 204
References 204
Concurrent design of hierarchical materials and structures 206
Abstract 206
1 Introduction 206
2 What is materials design? 214
2.1 Hierarchy of scales in concurrent design of materials and products 215
2.2 Goals of materials design 218
3 Some aspects of systems approaches for materials design 220
3.1 Role of thermodynamics 220
3.2 Challenges for top-down, inductive design 220
3.3 Uncertainty in materials design 221
3.4 Microstructure-mediated design 224
4 Applications of materials design 225
4.1 High strength and toughness steels 226
4.2 Integrating advances in 3D characterization and modeling tools 228
5 Educational imperatives for materials design 230
6 Future prospects 232
Closure 234
Acknowledgements 234
References 235
Enthalpy landscapes and the glass transition 240
Abstract 240
1 Introduction 241
2 The glass transition 242
3 The enthalpy landscape approach 246
3.1 Potential energy landscapes 247
3.2 Enthalpy landscapes 250
3.3 Nonequilibrium statistical mechanics 252
4 Simulation techniques 253
4.1 Locating inherent structures and transition points 254
4.2 Inherent structure density of states 259
4.3 Master equation dynamics 260
5 Nature of the glassy state 263
5.1 Continuously broken ergodicity and the residual entropy of glass 263
5.2 Supercooled liquid fragility 267
5.3 The Kauzmann paradox and the ideal glass transition 269
5.4 Fictive temperature and the glassy state 274
6 Conclusions 278
Acknowledgements 278
References 278
Advanced modulation formats for fiber optic communication systems 281
Abstract 281
1 Introduction and background 281
2 Modulation techniques 282
2.1 The electro-optic effect 282
2.2 Phase modulators 283
2.3 Amplitude modulators 283
2.3.1 Mach-Zehnder modulation with an ideal branching ratio 284
2.3.2 Mach-Zehnder modulation with a non-ideal branching ratio 286
2.3.3 Calculation of extinction ratio 287
2.3.4 Chirp induced by Mach-Zehnder modulation 288
3 Modulation formats 290
3.1 Nonreturn-to-zero (NRZ) 290
3.2 Return-to-zero (RZ) 291
3.2.1 RZ with 50% duty cycle 292
3.2.2 RZ with 33% duty cycle 294
3.2.3 Carrier-suppressed RZ (CSRZ) with 67% duty cycle 296
3.2.4 Chirped RZ (CRZ) 298
3.3 Duobinary 299
3.4 Modified duobinary 300
3.5 Differential phase-shift keyed (DPSK) 301
3.6 Return-to-zero DPSK (RZ-DPSK) 304
4 Impact on system performance 304
4.1 Amplified spontaneous emission (ASE) noise 306
4.2 Fiber nonlinearities 307
4.3 Linear cross-talk 308
4.4 Chromatic dispersion 308
4.5 Polarization mode dispersion (PMD) 308
5 Conclusions 308
Acknowledgements 309
References 309
Computational challenges in the search for and production of hydrocarbons 311
Abstract 311
1 Introduction 311
2 Part I. The big picture---geophysical imaging and inversion 312
2.1 Seismic imaging for exploration and production 312
2.2 Towards inversion for reservoir properties 316
2.3 Evolution to 4-D (time lapse) seismic and reservoir simulations 317
2.4 Inversion of seismic and electromagnetic wavefields 319
3 Part II. Formation evaluation---pore scale fundamentals of oil recovery 321
3.1 Borehole measurements 321
3.2 Drilling and geosteering 321
3.3 Porescale physics 322
3.3.1 Introduction 322
3.3.2 What do we want to achieve? 323
3.3.3 Porescale simulations 325
4 Part III. Simulation for new enabling technologies in the oil and gas industry 329
4.1 Introduction 329
4.2 Illuminating the oilfield with new sensor systems 329
4.3 Computational materials 330
4.3.1 High temperature polymer composites 331
5 Summary 332
Acknowledgements 334
References 334
Microscopic mechanics of biomolecules in living cells 336
Abstract 336
1 Cell mechanics and adhesion 340
2 Modelling molecules inside cells 344
3 Mechanical loading of single molecules 347
4 Nanomechanics of living polymers 350
5 Perspectives: physics, mechanics, and the multiscale modelling of biomolecules 352
References 356
Enveloped viruses understood via multiscale simulation: computer-aided vaccine design 360
Abstract 360
1 Introduction 361
2 Order parameters for connected structures 364
3 Order parameter fields for disconnected subsystems 366
4 Multiscale integration for enveloped virus modeling 367
5 Multiscale computations and the NanoX platform 371
6 Applications and conclusions 373
Acknowledgements 376
References 376
Computational modeling of brain tumors: discrete, continuum or hybrid? 378
Abstract 378
1 Introduction 379
2 In silico brain tumor modeling: objectives & challenges
3 Computational modeling approaches 381
3.1 Discrete modeling 381
3.2 Continuum modeling 383
4 Conclusions and perspectives 385
Acknowledgements 387
References 387
Editorial Policy 391
General Remarks 392
Lecture Notes in Computational Science and Engineering 393
Monographs in Computational Science and Engineering 395
Texts in Computational Science and Engineering 396

"Enveloped viruses understood via multiscale simulation: computer-aided vaccine design (p. 363-364)

Z. Shreif · P. Adhangale · S. Cheluvaraja · R. Perera · R. Kuhn · P. Ortoleva

Abstract Enveloped viruses are viewed as an opportunity to understand howhighly organized and functional biosystems can emerge from a collection ofmillions of chaotically moving atoms. They are an intermediate level of complexity between macromolecules and bacteria. They are a natural system for testing theories of self-assembly and structural transitions, and for demonstrating the derivation of principles of microbiology from laws of molecular physics. As some constitute threats to human health, a computer-aided vaccine and drug design strategy that would follow from a quantitative model would be an important contribution. However, current molecular dynamics simulation approaches are not practical for modeling such systems.

Our multiscale approach simultaneously accounts for the outer protein net and inner protein/genomic core, and their less structured membranous material and host fluid. It follows from a rigorous multiscale deductive analysis of laws of molecular physics. Two types of order parameters are introduced: (1) those for structures wherein constituent molecules retain long-lived connectivity (they specify the nanoscale structure as a deformation from a reference configuration) and (2) those for which there is no connectivity but organization is maintained on the average (they are field variables such as mass density or measures of preferred orientation). Rigorous multiscale techniques are used to derive equations for the order parameters dynamics. The equations account for thermal-average forces, diffusion coefficients, and effects of random forces. Statistical properties of the atomic-scale fluctuations and the order parameters are co-evolved. By combining rigorous multiscale techniques and modern supercomputing, systems of extreme complexity can be modeled.

Keywords Enveloped viruses · Structural transitions · All-atom multiscale analysis · Multiscale computation · Liouville equation · Langevin equations

1 Introduction

Deriving principles of microbial behavior from laws of molecular physics remains a grand challenge. While one expects many steps in the derivation can be accomplished based on the classical mechanics of an N-atom system, it is far from clear howto proceed in detail due to the extreme complexity of these supra-million atom systems.

Most notably, molecular dynamics (MD) codes are not practical for simulating even a simple bionanosystem of about 2 million atoms (e.g. a nonenveloped virus) over biologically relevant time periods (i.e. milliseconds or longer). For example, the efficientMDcode NAMD, run on a 1024-processor supercomputer [1], would take about 3000 years to simulate a simple virus over a millisecond; the largest NAMD simulation published to date is for a ribosome system of approximately 2.64 million atoms over few nanoseconds only [2].

We hypothesize that a first step in the endeavor to achieve a quantitative, predictive virology is to establish a rigorous intermediate scale description. Due to their important role in human health, complex structure, and inherent multiscale nature, enveloped viruses provide an ideal system for guiding and testing this approach. Experimental evidence suggests that an enveloped virus manifests three types of organization:"