Monte-Carlo Simulation (2022) [Stevens] [9781032280776]
Author(s): Alan Stevens
Publisher: CRC Press
Year: 2022
Language: English
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
About the Author
Chapter 1: The Basic Idea
1.1. Introduction
Chapter 2: Buffon’s Needle
2.1. Background
2.2. Computer Simulation
2.3. Features of the Simulation
2.4. Precision
2.5. Physical Simulation
2.6. Buffon’s Formula
2.7. Exercises
Chapter 3: Areas and Integrals
3.1. Temperature Profile
3.2. Simulation
3.3. Sample Mean Method
3.4. Higher Dimensions
3.5. Exercises
Chapter 4: Thermal Radiation
4.1. Radiation View Factor
4.2. Simulation
4.3. Precision
4.4. Exercises
Chapter 5: Bending Beams
5.1. Neutral Axis Offset
5.2. Simulation
5.3. Precision
5.4. Exercises
Chapter 6: Torus Segment
6.1. Volume of a Segment of Torus
6.2. Simulation
6.3. Precision
6.4. Exercises
Chapter 7: Radiation Shielding
7.1. Diffusion
7.2. Gamma-Ray Shielding
7.3. Build-up Factor and Energy Distribution
7.4. Simulation
7.5. Build-up Factors
7.6. Exercises
Chapter 8: Stressed Cylinder
8.1. Buckling Probability
8.2. Simulation
8.3. Precision
8.4. Wilks’ Method
8.5. Exercises
Chapter 9: Linear Resistive Networks
9.1. Circuit Analysis by Random Walk
9.2. Single-Node Simulation
9.3. Unit-Resistance Cube Simulation
9.4. Heat Conduction Simulation
9.5. Exercises
Chapter 10: Magnetic Phase Transitions
10.1. Ising Spin Model
10.2. Physical Properties
10.3. The Gibbs and Metropolis Algorithms
10.4. Simulation
10.5. Exercises
Chapter 11: Polymer Chains
11.1. Polymers
11.2. Simulation
11.3. Precision
11.4. Exercises
Chapter 12: Solutions To Selected Exercises
12.1. Exercise 2.7.4
12.2. Exercise 3.5.2
12.3. Exercise 4.4.1
12.4. Exercise 5.4.2
12.5. Exercise 6.4.2
12.6. Exercise 7.6.2
12.7. Exercise 8.4.2
12.8. Exercise 9.5.1
12.9. Exercise 10.5.3
12.10. Exercise 11.4.3
Appendix A: Random Numbers
A.1. Introduction
A.2. Uniformly Distributed Random Numbers
A.3. Normally Distributed Random Numbers
Appendix B: Variance Reduction
B.1. Introduction
B.2. Importance Weighting
B.3. Antithetic Variates
B.4. Control Variates
Index
