Computational Physics: Selected Methods Simple Exercises Serious Applications - Tapa blanda

Sinopsis

Random Number Generation.- 1 Introduction.- 2 The Miracle Number 16807.- 3 Bit Strings of Kirkpatrick-Stoll.- 4 A Modern Example.- 5 Problems.- 6 Summary.- References.- A Few Exercises with Random Numbers.- Monte Carlo Simulations of Spin Systems.- 1 Introduction.- 2 Spin Models and Phase Transitions.- 2.1 Models and Observables.- 2.2 Phase Transitions.- 3 The Monte Carlo Method.- 3.1 Estimators and Autocorrelation Times.- 3.2 Metropolis Algorithm.- 3.3 Cluster Algorithms.- 3.4 Multicanonical Algorithms for First-Order Transitions.- 4 Reweighting Techniques.- 5 Applications to the 3D Heisenberg Model.- 5.1 Simulations for T>Tc.- 5.2 Simulations near Tc.- 6 Concluding Remarks.- Appendix: Program Codes.- References.- Metastable Systems and Stochastic Optimization.- 1 An Introduction to Complex Systems.- 2 Dynamics in Complex Systems.- 2.1 Thermal Relaxation Dynamics: The Metropolis Algorithm.- 2.2 Thermal Relaxation Dynamics: A Marcov Process.- 2.3 Thermal Relaxation Dynamics: A Simple Example.- 3 Modeling Constant-Temperature Thermal Relaxation.- 3.1 Coarse-Graining a Complex State Space.- 3.2 Tree Dynamics.- 3.3 A Serious Application: Aging Effects in Spin Glasses.- 4 Stochastic Optimization: How to Find the Ground State of Complex Systems.- 4.1 Simulated Annealing.- 4.2 Optimal Simulated Annealing Schedules: A Simple Example.- 4.3 Adaptive Annealing Schedules and the Ensemble Approach to Simulated Annealing.- 5 Summary.- Appendix: Examples and Exercises (with S. Schubert).- References.- Modelling and Computer Simulation of Granular Media.- 1 The Physics of Granular Media.- 1.1 What are Granular Media?.- 1.2 Stress Distribution in Granular Packing: Arching.- 1.3 Dilatancy, Fluidization and Collisional Cooling.- 1.4 Stick-and-Slip Motion and Self-Organized Criticality (with S. Dippel).- 1.5 Segregation, Convection, Heaping (with S. Dippel).- 2 Molecular Dynamics Simulations I: Soft Particles.- 2.1 General Remarks.- 2.2 Normal Force.- 2.3 Tangential Force.- 2.4 Detachment Effect.- 2.5 Brake Failure Effect (with J. Schäfer).- 3 Molecular Dynamic Simulations II: Hard Particles (with J. Schäfer).- 3.1 Event-Driven Simulation.- 3.2 Collision Operator.- 3.3 Limitations.- 4 Contact Dynamics Simulations (with L. Brendel and F. Radjai).- 4.1 General Remarks.- 4.2 Contact Laws and Equations of Motion.- 4.3 Iterative Determination of Forces and Accelerations.- 4.4 Results.- 5 The Bottom-to-Top Restructuring Model.- 5.1 The Algorithm and its Justification (with E. Jobs).- 5.2 Simulation of a Rotating Drum (with T. Scheffler and G. Baumann).- 6 Conclusion.- References.- Algorithms for Biological Aging.- 1 Introduction.- 2 Concepts and Models.- 3 Techniques.- 4 Results.- References.- Simulations of Chemical Reactions.- 1 Introduction.- 2 The Basic Kinetic Approach.- 3 Numerical and Analytical Approaches for Reactions Under Diffusion.- 4 Reactions in Layered Systems.- 5 Reactions Under Mixing.- 6 Reactions Controlled by Enhanced Diffusion.- References.- Random Walks on Fractals.- 1 Introduction.- 2 Deterministic Fractals.- 2.1 The Koch Curve.- 2.2 The Sierpinski Gasket.- 3 Random Fractals.- 3.1 The Random-Walk Trail.- 3.2 Self-Avoiding Walks.- 3.3 Percolation.- 4 The "Chemical Distance" ?.- 5 Random Walks on Fractals.- 5.1 Root Mean Square Displacement R(t).- 5.2 The Mean Probability Density.- 6 Biased Diffusion.- 7 Numerical Approaches.- 7.1 Generation of Percolation Clusters.- 7.2 Simulation of Random Walks.- 8 Description of the Programs.- References.- Multifractal Characteristics of Electronic Wave Functions in Disordered Systems.- 1 Electronic States in Disordered Systems.- 2 The Anderson Model of Localization.- 3 Calculation of the Eigenvectors.- 4 Description of Multifractal Objects.- 5 Multifractal Analysis of the Wave Functions.- 6 Computation of the Multifractal Characteristics.- 7 Topical Results of the Multifractal Analysis.- References.- Transfer-Matrix Methods and Finite-Size Scaling for Disordered Systems.- 1 Introduction.- 2

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