Computational Multiscale Modeling of Fluids and Solids - Theory and Applications

Preface

Contents

Part I Fundamentals

1 Introduction

1.1 Physics on Different Length- and Timescales

1.2 What are Fluids and Solids?

1.3 The Objective of Experimental and Theoretical Physics

1.4 Computer Simulations – A Review

1.5 Suggested Reading

2 Multiscale Computational Materials Science

2.1 Some Terminology

2.2 What is Computational Material Science on Multiscales?

2.3 What is a Model?

2.4 Hierarchical Modeling Concepts above the Atomic Scale

2.5 Unification and Reductionism in Physical Theories

2.6 Computer Science, Algorithms, Computability and Turing Machines

Problems

3 Mathematical and Physical Prerequisites

3.1 Introduction

3.2 Sets and Set Operations

3.3 Topological Spaces

3.4 Metric Spaces and Metric Connection

3.5 Riemannian Manifolds

3.6 The Problem of Inertia and Motion: Coordinate Systems in Physics

3.7 Relativistic Field Equations

3.8 Suggested Reading

Problems

4 Fundamentals of Numerical Simulation

4.1 Basics of Ordinary and Partial Differential Equations in Physics

4.2 Numerical Solution of Differential Equations

4.3 Elements of Software Design

Problems

Part II Computational Methods on Multiscales

Summary of Part I

5 Computational Methods on Electronic/ Atomistic Scale

5.1 Introduction

5.2 Ab-initio Methods

5.3 Physical Foundations of Quantum Theory

5.4 Density Functional Theory

5.5 Car-Parinello Molecular Dynamics

5.6 Solving Schr¨ odinger’s Equation for Many-Particle Systems: Quantum Mechanics of Identical Particles

5.7 What Holds a Solid Together?

5.8 Semi-empirical Methods

5.9 Bridging Scales: Quantum Mechanics (QM) – Molecular Mechanics ( MM)

5.10 Concluding Remarks

6 Computational Methods on Atomistic/ Microscopic Scale

6.1 Introduction

6.2 Fundamentals of Statistical Physics and Thermodynamics

6.3 Classical Interatomic and Intermolecular Potentials

6.4 Classical Molecular Dynamics Simulations

6.5 Liquids, Soft Matter and Polymers

6.6 Monte Carlo Method

Problems

7 Computational Methods on Mesoscopic/ Macroscopic Scale

7.1 Example: Meso- and Macroscale Shock-Wave Experiments with Ceramics

7.2 Statistical Methods: Voronoi Tesselations and Power Diagrams for Modeling Microstructures of Ceramics

7.3 Dissipative Particle Dynamics

7.4 Ginzburg-Landau/Cahn-Hiliard Field Theoretic Mesoscale Simulation Method

7.5 Bridging Scales: Soft Particle Discrete Elements for Shock Wave Applications

7.6 Bridging Scales: Energetic Links between MD and FEM

7.7 Physical Theories for Macroscopic Phenomena: The Continuum Approach

7.8 Continuum Theory

7.9 Theory of Elasticity

7.10 Bridging Scale Application: Crack Propagation in a Brittle Specimen

8 Perspectives in Multiscale Materials Modeling

A Further Reading

General Physics

Programming Techniques

Journals and Conferences on Multiscale Materials Modeling and Simulation

B Mathematical Definitions

C Sample Code for the Main Routine of a MD Simulation

D A Sample Makefile

E Tables of Physical Constants

E.1 International System of Units (SI or mksA System)

E.2 Conversion Factors of Energy

List of Algorithms

List of Boxes

Solutions

Problems of Chapter 2

Problems of Chapter 3

Problems of Chapter 4

References

Index