Computational Physics : Problem Solving with Computers

by Landau, Rubin H.; P?ez, Manuel J.; Bordeianu, Cristian C.

• ISBN13: 9783527406265
• ISBN10: 3527406263
• Edition: 2nd
• Format: Paperback
• Copyright: 2007-09-04
• Publisher: Wiley-VCH

Summary

This second edition provides an even broader survey of the techniques of computational physics and science. It features new chapters on visualisation, wavelet analysis, and data compression, molecular dynamics, and computational fluid dynamics, an expanded treatment of Fourier analysis to incorporate wavelet analysis and filtering, broader coverage of partial differential equations to include fluid dynamics, realistic waves, and shock waves, as well as a more extensive treatment of computational biology and complex systems. From the reviews of the first edition: "Landau and Paez's book would be an excellent choice for a course on computational physics which emphasizes computational methods and programming." - American Journal of Physics

Author Biography

Rubin H. Landau, PhD, is a professor in the Department of Physics at Oregon State University in Corvallis. He teaches courses in computational physics, helps direct the Northwest Alliance for Computational Science and Engineering, and has been using computers in theoretical physics research for the past 30 years. The author of more than 70 refereed publications, he has also authored the books Quantum Mechanics II, A Scientist's and Engineer's Guide to Workstations and Supercomputers, and the first edition of Computational Physics, all of them available from Wiley.

Manuel J. Páez;, PhD, is a professor in the Department of Physics at the University of Antioquia in Medellín, Colombia. He teaches courses in computational physics, programming, and nuclear physics. He and Professor Landau have conducted pioneering computational investigations in the interactions of mesons and nucleons with nuclei.

Cristian C. Bordeianu received his physics degree from Bucharest University, Romania, and his M.Sc. degree in Computer Science from "A.I.Cuza" University in Jassy, Romania. He is currently completing work towards a Ph.D. degree in Nuclear Physics at Bucharest University. He has over ten years of experience in developing Computational Physics educational software for high schools and University curricula. His current research interests include chaotic dynamics in nuclear multifragmentation and plasma of quarks and gluons.

Table of Contents

Introduction

Computational Physics and Computational Science

How to Use this Book

Computing Software Basics

Making Computers Obey

Computer Languages

Programming Warmup

Shells, Editors, and Programs

Limited Range and Precision of Numbers

Number Representation

IEEE Floating Point Numbers

Over/Underflows Exercise

Machine Precision

Determine Your Machine Precision

Structured Program Design

Summing Series

Numeric Summation

Good and Bad Pseudocode

Assessment

Errors and Uncertainties in Computations

Living with Errors

Types of Errors

Model for Disaster: Subtractive Cancellation

Subtractive Cancellation Exercises

Model for Roundoff Error Accumulation

Errors in Spherical Bessel Functions (Problem)

Numeric Recursion Relations (Method)

Implementation and Assessment: Recursion Relations

Experimental Error Determination

Errors in Algorithms

Minimizing the Error

Error Assessment

Object-Oriented Programming: Kinematics

Problem: Superposition of Motions

Theory: Object-Oriented Programming

Theory: Newton's Laws, Equation of Motion

OOP Method: Class Structure

Implementation: Uniform 1D Motion, unim1d.cpp

Assessment: Exploration, shms.cpp

Integration

Problem: Integrating a Spectrum

Quadrature as Box Counting (Math)

Algorithm: Trapezoid Rule

Algorithm: Simpson's Rule

Integration Error

Algorithm: Gaussian Quadrature

Empirical Error Estimate (Assessment)

Experimentation

Higher Order Rules

Differentiation

Problem 1: Numerical Limits

Method: Numeric

Forward Difference

Central Difference

Extrapolated Difference

Error Analysis

Error Analysis (Implementation and Assessment)

Second Derivatives

Trial and Error Searching

Quantum States in SquareWell

Trial-and-Error Root Finding via Bisection Algorithm

1 Bisection Algorithm Implementation

Newton-Raphson Algorithm

Matrix Computing and N-D Newton Raphson

Two Masses on a String

Classes of Matrix Problems

Data Fitting

Fitting Experimental Spectrum

Fitting Exponential Decay

Theory: Probability and Statistics

Least-Squares Fitting

Appendix: Calling LAPACK from C

Deterministic Randomness

Random Sequences

Monte Carlo Applications

A RandomWalk

Radioactive Decay

Implementation and Visualization

Integration by Stone Throwing

Integration by Rejection

High-Dimensional Integration

Integrating Rapidly Varying Functions

Thermodynamic Simulations: Ising Model

Statistical Mechanics

An Ising Chain (Model)

The Metropolis Algorithm

Computer Hardware Basics: Memory and CPU

High-Performance Computers

The Central Processing Unit

High-Performance Computing: Profiling and Tuning

Rules for Optimization

Programming for Data Cache

Differential Equation Applications

UNIT I. Free Nonlinear Oscillations

Nonlinear Oscillator

Math: Types of Differential Equations

Dynamical Form for ODEs

ODE Algorithms

Solution for Nonlinear Oscillations

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