Anagnostopoulos K.N. Computational Physics - A Practical Introduction to Computational Physics and Scientific Computing

Athens: National Technical University of Athens and K.N. Anagnostopoulos, 2014. - 682p.The book is an introduction to the computational methods used in physics, but also in other scientific fields. It is addressed to an audience that has already been exposed to the introductory level of college physics, usually taught during the first two years of an undergraduate program in science and engineering.The book starts with very simple problems in particle motion and ends with an in-depth discussion of advanced techniques used in Monte Carlo simulations in statistical mechanics. The level of instruction rises slowly, while discussing problems like the diffusion equation, electrostatics on the plane, quantum mechanics and random walks. The book aims to provide the students with the background and the experience needed in order to advance to high performance computing projects in science and engineering. But it also tries to keep the students motivated by considering interesting applications in physics, like chaos, quantum mechanics, special relativity and the physics of phase transitions.The Computer
The Operating System
Filesystem
Commands
Looking for Help
Text Processing Tools – Filters
Programming with Emacs
Calling Emacs
Interacting with Emacs
Basic Editing
Cut and Paste
Windows
Files and Buffers
Modes
Emacs Help
Emacs Customization
The Fortran Programming Language
The Foundation
Details
Arrays
Gnuplot
Shell Scripting
Kinematics
Motion on the Plane
Plotting Data
More Examples
Motion in Space
Trapped in a Box
The One Dimensional Box
Errors
The Two Dimensional Box
ApplicationsLogistic MapFixed Points and n Cycles
Bifurcation Diagrams
The Newton-Raphson Method
Calculation of the Bifurcation Points
Liapunov ExponentsMotion of a Particle
Numerical Integration of Newton’s Equations
Prelude: Euler Methods
Runge–Kutta Methods
A Program for the th Order Runge–Kutta
Comparison of the Methods
The Forced Damped Oscillator
The Forced Damped Pendulum
Appendix: On the Euler–Verlet Method
Appendix: 2-nd order Runge–Kutta MethodPlanar Motion
Runge–Kutta for Planar Motion
Projectile Motion
Planetary Motion
Scattering
Rutherford Scattering
More Scattering Potentials
More ParticlesMotion in Space
Adaptive Stepsize Control for Runge–Kutta Methods
Motion of a Particle in an EM Field
Relativistic MotionElectrostatics
Electrostatic Field of Point Charges
The Program – Appetizer and Desert
The Program – Main Dish
The Program - Conclusion
Electrostatic Field in the Vacuum
Results
Poisson EquationDiffusion EquationHeat Conduction in a Thin Rod
Discretization
The Program
Results
Diffusion on the Circle
AnalysisThe Anharmonic OscillatorCalculation of the Eigenvalues of Hnm (λ)
Results
The Double Well PotentialTime Independent Schrödinger EquationThe Infinite Potential Well
Bound States
Measurements
The Anharmonic Oscillator - Again
The Lennard–Jones PotentialThe Random Walker
(Pseudo)Random Numbers
Using Pseudorandom Number Generators
Random WalksMonte Carlo Simulations
Statistical Physics
Entropy
Fluctuations
Correlation Functions
Sampling
Simple Sampling
Importance Sampling
Markov Processes
Detailed Balance ConditionSimulation of the d = 2 Ising Model
The Ising Model
Metropolis
Implementation
The Program
Towards a Convenient User Interface
Thermalization
Autocorrelations
Statistical Errors
Errors of Independent Measurements
Jackknife
Bootstrap
Appendix: Autocorrelation Function
Appendix: Error Analysis
The Jackknife Method
The Bootstrap Method
Comparing the MethodsCritical Exponents
Critical Slowing Down
Wolff Cluster Algorithm
Implementation
The Program
Production
Data Analysis
Autocorrelation Times
Temperature Scaling
Finite Size Scaling
Calculation of βc
Studying Scaling with Collapse
Binder Cumulant
Appendix: Scaling
Binder Cumulant
Scaling
Finite Size Scaling
Appendix: Critical Exponents
Definitions
Hyperscaling Relations