9780131469907

Computational Physics

by ;
  • ISBN13:

    9780131469907

  • ISBN10:

    0131469908

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 7/21/2005
  • Publisher: Pearson

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Supplemental Materials

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Summary

Contains a wealth of topics to allow instructors flexibility in the choice of topics and depth of coverage: Examines projective motion with and without realistic air resistance. Discusses planetary motion and the three-body problem. Explores chaotic motion of the pendulum and waves on a string. Includes topics relating to fractal growth and stochastic systems. Offers examples on statistical physics and quantum mechanics. Contains ample explanations of the necessary algorithms students need to help them write original programs, and provides many example programs and calculations for reference.

Author Biography

Nicholas Giordano obtained his B.S. at Purdue University and his Ph.D. at Yale University. He has been on the faculty at Purdue since 1979, served as an Assistant Dean of Science from 2000-2003, and is currently the Hubert James Distinguished Professor of Physics. His research interests include electrical conduction, superconductivity, and magnetism in ultra-small metallic structures, along with musical acoustics and the physics of the piano. Ideas for this book grew out of the course on computational physics that he developed and taught in the early 1990s. Professor Giordano earned a Computational Science Education Award from the Department of Energy in 1997, and in 2004 was named Indiana Professor of the Year by the Carnegie Foundation for the Advancement of Teaching and the Council for the Advancement and Support of Education.

Hisao Nakanishi earned his B.S. from Brown University and his Ph.D. from Harvard University. His Ph.D. research concerned scaling and universality in a geometric phase transition called percolation and he has been interested in scale-invariance ever since. During his first postdoctoral work at Cornell he was introduced to the problem of surface critical phenomena such as wetting phase transitions, and later at the University of California, Santa Barbara, he started working on the statistics of diffusion and polymers in earnest. .In 1992 Professor Nakanishi was a part of the team that won a Gordon Bell Prize for the application of parallel computing to a problem in polymer statistics. More recently he has also put on another hat as a developer of a computer-based interactive exercise system which is used by a few thousand students at Purdue each year.

Table of Contents

Preface ix
About the Authors xii
A First Numerical Problem
1(17)
Radioactive Decay
1(1)
A Numerical Approach
2(1)
Design and Construction of a Working Program: Codes and Pseudocodes
3(8)
Testing Your Program
11(1)
Numerical Considerations
12(2)
Programming Guidelines and Philosophy
14(4)
Realistic Projectile Motion
18(30)
Bicycle Racing: The Effect of Air Resistance
18(7)
Projectile Motion: The Trajectory of a Cannon Shell
25(6)
Baseball: Motion of a Batted Ball
31(5)
Throwing a Baseball: The Effects of Spin
36(8)
Golf
44(4)
Oscillatory Motion and Chaos
48(46)
Simple Harmonic Motion
48(6)
Making the Pendulum More Interesting: Adding Dissipation, Non-linearity, and a Driving Force
54(4)
Chaos in the Driven Nonlinear Pendulum
58(8)
Routes to Chaos: Period Doubling
66(4)
The Logistic Map: Why the Period Doubles
70(5)
The Lorenz Model
75(7)
The Billiard Problem
82(6)
Behavior in the Frequency Domain: Chaos and Noise
88(6)
The Solar System
94(35)
Kepler's Laws
94(7)
The Inverse-Square Law and the Stability of Planetary Orbits
101(6)
Precession of the Perihelion of Mercury
107(6)
The Three-Body Problem and the Effect of Jupiter on Earth
113(5)
Resonances in the Solar System: Kirkwood Gaps and Planetary Rings
118(5)
Chaotic Tumbling of Hyperion
123(6)
Potentials and Fields
129(27)
Electric Potentials and Fields: Laplace's Equation
129(14)
Potentials and Fields Near Electric Charges
143(5)
Magnetic Field Produced by a Current
148(3)
Magnetic Field of a Solenoid: Inside and Out
151(5)
Waves
156(25)
Waves: The Ideal Case
156(9)
Frequency Spectrum of Waves on a String
165(4)
Motion of a (Somewhat) Realistic String
169(5)
Waves on a String (Again): Spectral Methods
174(7)
Random Systems
181(54)
Why Perform Simulations of Random Processes?
181(2)
Random Walks
183(5)
Self-Avoiding Walks
188(7)
Random Walks and Diffusion
195(6)
Diffusion, Entropy, and the Arrow of Time
201(5)
Cluster Growth Models
206(6)
Fractal Dimensionalities of Curves
212(6)
Percolation
218(11)
Diffusion on Fractals
229(6)
Statistical Mechanics, Phase Transitions, and the Ising Model
235(35)
The Ising Model and Statistical Mechanics
235(4)
Mean Field Theory
239(5)
The Monte Carlo Method
244(2)
The Ising Model and Second-Order Phase Transitions
246(13)
First-Order Phase Transitions
259(5)
Scaling
264(6)
Molecular Dynamics
270(33)
Introduction to the Method: Properties of a Dilute Gas
270(15)
The Melting Transition
285(9)
Equipartition and the Fermi-Pasta-Ulam Problem
294(9)
Quantum Mechanics
303(54)
Time-Independent Schrodinger Equation: Some Preliminaries
303(4)
One Dimension: Shooting and Matching Methods
307(16)
A Matrix Approach
323(3)
A Variational Approach
326(7)
Time-Dependent Schrodinger Equation: Direct Solutions
333(12)
Time-Dependent Schrodinger Equation in Two Dimensions
345(4)
Spectral Methods
349(8)
Vibrations, Waves, and the Physics of Musical Instruments
357(32)
Plucking a String: Simulating a Guitar
357(5)
Striking a String: Pianos and Hammers
362(5)
Exciting a Vibrating System with Friction: Violins and Bows
367(5)
Vibrations of a Membrane: Normal Modes and Eigenvalue Problems
372(10)
Generation of Sound
382(7)
Interdisciplinary Topics
389(67)
Protein Folding
389(16)
Earthquakes and Self-Organized Criticality
405(13)
Neural Networks and the Brain
418(18)
Real Neurons and Action Potentials
436(9)
Cellular Automata
445(11)
APPENDICES
A Ordinary Differential Equations with Initial Values
456(13)
A.1 First-Order, Ordinary Differential Equations
456(4)
A.2 Second-Order, Ordinary Differential Equations
460(4)
A.3 Centered Difference Methods
464(3)
A.4 Summary
467(2)
B Root Finding and Optimization
469(10)
B.1 Root Finding
469(3)
B.2 Direct Optimization
472(1)
B.3 Stochastic Optimization
473(6)
C The Fourier Transform
479(14)
C.1 Theoretical Background
479(2)
C.2 Discrete Fourier Transform
481(2)
C.3 Fast Fourier Transform (FFT)
483(3)
C.4 Examples: Sampling Interval and Number of Data Points
486(2)
C.5 Examples: Aliasing
488(2)
C.6 Power Spectrum
490(3)
D Fitting Data to a Function
493(7)
D.1 Introduction
493(1)
D.2 Method of Least Squares: Linear Regression for Two Variables
494(3)
D.3 Method of Least Squares: More General Cases
497(3)
E Numerical Integration
500(12)
E.1 Motivation
500(1)
E.2 Newton-Cotes Methods: Using Discrete Panels to Approximate an Integral
500(4)
E.3 Gaussian Quadrature: Beyond Classic Methods of Numerical Integration
504(2)
E.4 Monte Carlo Integration
506(6)
F Generation of Random Numbers
512(8)
F.1 Linear Congruential Generators
512(4)
F.2 Nonuniform Random Numbers
516(4)
G Statistical Tests of Hypotheses
520(7)
G.1 Central Limit Theorem and the Χ2 Distribution
521(2)
G.2 Χ2 Test of a Hypothesis
523(4)
H Solving Linear Systems
527(14)
H.1 Solving A x = b, b, b ≠ 0
528(7)
H.1.1 Gaussian Elimination
528(2)
H.1.2 Gauss-Jordan elimination
530(1)
H.1.3 LU decomposition
531(2)
H.1.4 Relaxational method
533(2)
H.2 Eigenvalues and Eigenfunctions
535(6)
H.2.1 Approximate Solution of Eigensystems
537(4)
Index 541

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