Computational Multiscale Modeling of Fluids and Solids (eBook)

Career to Date: 2003-present Senior scientist in the Department of Numerical Simulation at the fraunhofer Ernst-Mach Institute (EMI) Managing project leader of the project "MMM-Tools", (Multiscale Materials Modeling) in cooperation of 9 different Fraunhofer-Institutes in Germany (www.mmm-tools.de) Advisor of Diploma and PhD students in Physics and Mathematics 2002-2003 Senior Computational Geneticist in the Department of Genetic Epidemiology at Lion Bioscience AG, Heidelberg, Germany 2001-2002 Manager at SAP Headquarters, Walldorf, Germany 2001 PhD in Physics 1998-2001 PhD Student of Prof. Kurt Kremer at the Max-Planck-Institute for Polymer Research, Mainz, Germany Assistant teacher at the Univ. of Mainz, Germany 1998 Graduation in Physics with Honors at the University of Ulm, Germany 1997-1998 Diploma Student in the Department of Theoretical Physics at the University of Ulm, Germany 1995-1996 Graduate Exchange Student at the University of Massachusetts at Amherst, MA, U.S.A. 1993-1995 Assistant Teacher at the University of Ulm, Germany 1993 German "Vordiplom" in physics with honors 1991 Studies in physics

Preface 6
Contents 12
Part I Fundamentals 17
1 Introduction 18
1.1 Physics on Different Length- and Timescales 19
1.2 What are Fluids and Solids? 24
1.3 The Objective of Experimental and Theoretical Physics 27
1.4 Computer Simulations – A Review 28
1.5 Suggested Reading 40
2 Multiscale Computational Materials Science 42
2.1 Some Terminology 45
2.2 What is Computational Material Science on Multiscales? 46
2.3 What is a Model? 50
2.4 Hierarchical Modeling Concepts above the Atomic Scale 59
2.5 Unification and Reductionism in Physical Theories 70
2.6 Computer Science, Algorithms, Computability and Turing Machines 92
Problems 121
3 Mathematical and Physical Prerequisites 123
3.1 Introduction 123
3.2 Sets and Set Operations 127
3.3 Topological Spaces 141
3.4 Metric Spaces and Metric Connection 173
3.5 Riemannian Manifolds 176
3.6 The Problem of Inertia and Motion: Coordinate Systems in Physics 179
3.7 Relativistic Field Equations 185
3.8 Suggested Reading 189
Problems 189
4 Fundamentals of Numerical Simulation 192
4.1 Basics of Ordinary and Partial Differential Equations in Physics 192
4.2 Numerical Solution of Differential Equations 202
4.3 Elements of Software Design 218
Problems 230
Part II Computational Methods on Multiscales 231
Summary of Part I 232
5 Computational Methods on Electronic/ Atomistic Scale 235
5.1 Introduction 235
5.2 Ab-initio Methods 236
5.3 Physical Foundations of Quantum Theory 240
5.4 Density Functional Theory 247
5.5 Car-Parinello Molecular Dynamics 249
5.6 Solving Schr¨ odinger’s Equation for Many-Particle Systems: Quantum Mechanics of Identical Particles 253
5.7 What Holds a Solid Together? 266
5.8 Semi-empirical Methods 269
5.9 Bridging Scales: Quantum Mechanics (QM) – Molecular Mechanics ( MM) 275
5.10 Concluding Remarks 276
6 Computational Methods on Atomistic/ Microscopic Scale 278
6.1 Introduction 278
6.2 Fundamentals of Statistical Physics and Thermodynamics 284
6.3 Classical Interatomic and Intermolecular Potentials 293
6.4 Classical Molecular Dynamics Simulations 303
6.5 Liquids, Soft Matter and Polymers 322
6.6 Monte Carlo Method 332
Problems 336
7 Computational Methods on Mesoscopic/ Macroscopic Scale 337
7.1 Example: Meso- and Macroscale Shock-Wave Experiments with Ceramics 340
7.2 Statistical Methods: Voronoi Tesselations and Power Diagrams for Modeling Microstructures of Ceramics 342
7.3 Dissipative Particle Dynamics 348
7.4 Ginzburg-Landau/Cahn-Hiliard Field Theoretic Mesoscale Simulation Method 350
7.5 Bridging Scales: Soft Particle Discrete Elements for Shock Wave Applications 352
7.6 Bridging Scales: Energetic Links between MD and FEM 362
7.7 Physical Theories for Macroscopic Phenomena: The Continuum Approach 365
7.8 Continuum Theory 368
7.9 Theory of Elasticity 371
7.10 Bridging Scale Application: Crack Propagation in a Brittle Specimen 383
8 Perspectives in Multiscale Materials Modeling 385
A Further Reading 388
General Physics 388
Programming Techniques 388
Journals and Conferences on Multiscale Materials Modeling and Simulation 389
B Mathematical Definitions 390
C Sample Code for the Main Routine of a MD Simulation 392
D A Sample Makefile 394
E Tables of Physical Constants 396
E.1 International System of Units (SI or mksA System) 396
E.2 Conversion Factors of Energy 397
List of Algorithms 398
List of Boxes 399
Solutions 400
Problems of Chapter 2 400
Problems of Chapter 3 403
Problems of Chapter 4 404
References 406
Index 428