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Computational Multiscale Modeling of Fluids and Solids Theory and Applications

:	Martin Oliver Steinhauser
:	Computational Multiscale Modeling of Fluids and Solids Theory and Applications
:	Springer-Verlag
:	9783662532249
:	2
:	CHF 125.70
:

:	Allgemeines, Lexika
:	English

:	419
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

T e idea of the book is to provide a comprehensive overview of computational physics methods and techniques, that are used for materials modeling on different length and time scales. Each chapter first provides an overview of the basic physical principles which are the basis for the numerical and mathematical modeling on the respective length-scale.
The book includes the micro-scale, the meso-scale and the macro-scale, and the chapters follow this classification. The book explains in detail many tricks of the trade of some of the most important methods and techniques that are used to simulate materials on the perspective levels of spatial and temporal resolution. Case studies are included to further illustrate some methods or theoretical considerations. Example applications for all techniques are provided, some of which are from the author's own contributions to some of the research areas.
The second edition has been expanded by new sections in computational models on meso/macroscopic scales for ocean and atmosphere dynamics. Numerous applications in environmental physics and geophysics had been added.

Prof. Dr. Martin Oliver Steinhauser
Fraunhofer Ernst-Mach-Institute for High-Speed Dynamics (EMI),
Eckerstrasse 4
79104 Freiburg
Germany

	Preface to the 2nd Edition	6
	Preface to the 1st Edition	8
	Contents	14
	List of Algorithms	19
	List of Boxes	20
	Part I Fundamentals	21
	1 Introduction	22
	1.1 Physics on Different Length- and Timescales	24
	1.1.1 Electronic/Atomic Scale	25
	1.1.2 Atomic/Microscopic Scale	26
	1.1.3 Microscopic/Mesoscopic Scale	26
	1.1.4 Mesoscopic/Macroscopic Scale	29
	1.2 What are Fluids and Solids?	29
	1.3 The Objective of Experimental and Theoretical Physics	32
	1.4 Computer Simulations -- A Review	33
	1.4.1 A Brief History of Computer Simulation	36
	1.4.2 Computational Materials Science	44
	1.5 Suggested Reading	46
	2 Multiscale Computational Materials Science	48
	2.1 Some Terminology	51
	2.2 What Is Computational Material Science on Multiscales?	52
	2.2.1 Experimental Investigations on Different Length Scales	53
	2.3 What Is a Model?	56
	2.3.1 The Scientific Method	57
	2.4 Hierarchical Modeling Concepts Above the Atomic Scale	64
	2.4.1 Example: Principle Model Hierarchies in Classical Mechanics	66
	2.4.2 Structure-Property Paradigm	67
	2.4.3 Physical and Mathematical Modeling	67
	2.4.4 Numerical Modeling and Simulation	75
	2.5 Unifications and Reductionism in Physical Theories	76
	2.5.1 The Four Fundamental Interactions	78
	2.5.2 The Standard Model	80
	2.5.3 Symmetries, Fields, Particles and the Vacuum	82
	2.5.4 Relativistic Wave Equations	89
	2.5.5 Suggested Reading	96
	2.6 Computer Science, Algorithms, Computability and Turing Machines	97
	2.6.1 Recursion	100
	2.6.2 Divide-and-Conquer	102
	2.6.3 Local Search	105
	2.6.4 Simulated Annealing and Stochastic Algorithms	107
	2.6.5 Computability, Decidability and Turing Machines	108
	2.6.6 Efficiency of Algorithms	118
	2.6.7 Suggested Reading	125
	3 Mathematical and Physical Prerequisites	128
	3.1 Introduction	129
	3.2 Sets and Set Operations	132
	3.2.1 Cartesian Product, Product Set	136
	3.2.2 Functions and Linear Spaces	137
	3.3 Topological Spaces	145
	3.3.1 Charts	152
	3.3.2 Atlas	153
	3.3.3 Manifolds	155
	3.3.4 Tangent Vectors and Tangent Space	157
	3.3.5 Covectors, Cotangent Space and One-Forms	160
	3.3.6 Dual Spaces	165
	3.3.7 Tensors and Tensor Spaces	167
	3.3.8 Affine Connections and Covariant Derivative	172
	3.4 Metric Spaces and Metric Connection	175
	3.5 Riemannian Manifolds	178
	3.5.1 Riemannian Curvature	179
	3.6 The Problem of Inertia and Motion: Coordinate Systems in Physics	181
	3.6.1 The Special and General Principle of Relativity	182
	3.6.2 The Structure of Spacetime	186
	3.7 Relativistic Field Equations	187
	3.7.1 Relativistic Hydrodynamics	188
	3.8 Suggested Reading	190
	4 Fundamentals of Numerical Simulation	193
	4.1 Basics of Ordinary and Partial Differential Equations in Physics	193
	4.1.1 Elliptic Type	198
	4.1.2 Parabolic Type	200
	4.1.3 Hyperbolic Type	201
	4.2 Numerical Solution of Differential Equations	203
	4.2.1 Mesh-Based and Mesh-Free Methods	204
	4.2.2 Finite Difference Methods	209
	4.2.3 Finite Volume Method	212
	4.2.4 Finite Element Methods	215
	4.3 Elements of Software Design	217
	4.3.1 Software Design	220
	4.3.2 Writing a Routine	223
	4.3.3 Code-Tuning Strategies	226
	4.3.4 Suggested Reading	229
	Part II Computational Methods on Multiscales	231
	5 Computational Methods on Electronic/Atomistic Scale	233
	5.1 Introduction	233
	5.2 Ab-Initio Methods	235
	5.3 Physical Foundations of Quantum Theory	238
	5.3.1 A Short Historical Account of Quantum Theory	239
	5.3.2 A Hamiltonian for a Condensed Matter System	242
	5.3.3 The Born--Oppenheimer Approximation	242
	5.4 Density Functional Theory	245
	5.5 Car--Parinello Molecular Dynamics	246
	5.5.1 Force Calculations: The Hellmann--Feynman Theorem	248
	5.5.2 Calculating the Ground State	249
	5.6 Solving Schrödinger's Equation for Many-Particle Systems: ƒ	251
	5.6.1 The Hartree--Fock Approximation	252
	5.7 What Holds a Solid Together?	262
	5.7.1 Homonuclear Diatomic Molecules	263
	5.8 Semi-empirical Methods	265
	5.8.1 Tight-Binding Method	267
	5.9 Bridging Scales: Quantum Mechanics (QM) - Molecular Mechanics (MM)	271
	5.10 Concluding Remarks	272
	6 Computational Methods on Atomistic/Microscopic Scale	274
	6.1 Introduction	274
	6.1.1 Thermod