Rongpeng Li and Aiichiro Nakano

Simulation with Python

Develop Simulation and Modeling in Natural Sciences, Engineering, and Social Sciences

Rongpeng Li
Los Angeles, CA, USA
Aiichiro Nakano
Los Angeles, CA, USA
ISBN 978-1-4842-8184-0e-ISBN 978-1-4842-8185-7
https://doi.org/10.1007/978-1-4842-8185-7
© Rongpeng Li and Aiichiro Nakano 2022
Apress Standard
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The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Apress imprint is published by the registered company APress Media, LLC, part of Springer Nature.

The registered company address is: 1 New York Plaza, New York, NY 10004, U.S.A.

To Yan, for everything.

—Ron

Introduction

This book is a small gift to a younger me, probably in high school or even earlier. This book is by no means written for seasoned researchers or professionals. It should be treated as the first bite of ice cream which makes you want more.

This book contains several scientific simulation topics, ranging from physics, biology, and even finance. The approach is very gentle and newcomer friendly. I tried to remove the majority of the complexity that I would learn with the knowledge and scientific training I already had. Instead, I did my best to keep the most important essence in each topic. The persona in my mind is a young and curious student who just got the first computer and learned some basic programming, probably from the older brother. This student, pictured as a younger me, would be able to follow the content of this book without any difficulty and get amazed by the beautiful visualizations and scientific conclusions.

Each topic in this book is rather independent. According to the level of technical difficulty and required background knowledge, I categorize the chapters into three groups. Readers can start with any chapter.

Easy:

Chapter 1: Calculating Pi with Monte Carlo Simulation

Chapter 4: Balls in a 2-D Box, a Simple Physics Engine

Medium:

Chapter 2: Markov Chain, a Peek into the Future

Chapter 3: Multi-armed Bandits, Probability Simulation, and Bayesian Statistics

Chapter 7: Rock, Scissors, and Paper: Multi-agent Simulation

Chapter 8: Disease Spreading, Simulating COVID-19 Outbreak

Chapter 9: Misinformation Spreading and Simulations on a Graph

Hard:

Chapter 5: Percolation, Threshold, and Phase Change

Chapter 6: Queuing System: How Stock Trades Are Made

I hope you enjoy this book as much as I do.

Acknowledgments

Rongpeng Li would like to thank all his previous students for the inspiration of this book, from readers at local libraries to learners in his Zoom classroom.

Table of Contents
Chapter 1:​ Calculating Pi with Monte Carlo Simulation1
Background1
The Wise Persons’ Competition1
Estimating Pi by Sprinkling Grains2
Exercise10
Contain the Goat!10
What Randomness?​11
Exercise18
Summary18
Chapter 2:​ Markov Chain, a Peek into the Future19
Weather Forecasting19
Eigenstates of Markov Chains25
Exercise27
Markov Chain Applications27
A Random Walk That Has an End28
Sonnet Written by Drunk Shakespeare31
Exercise36
Summary37
Chapter 3:​ Multi-armed Bandits, Probability Simulation, and Bayesian Statistics39
Random Pick and Naive Greedy Approach40
Greedy-Epsilon:​ Greedy but Not Always44
An Improved Greedy-Epsilon Algorithm45
Exercise46
The Bayesian Way, a Primer on Bayesian Statistics47
Exercise53
Summary54
Chapter 4:​ Balls in a 2-D Box, a Simple Physics Engine55
One Ball in a 2-D Box55
Physics Law of Motion57
Collision Detection60
Exercise65
Multiple Balls in a 2-D Box65
Update of Positions and Velocity upon Collision65
Collision Detection in Multiple-Ball Scenario74
Exercise75
Summary76
Chapter 5:​ Percolation, Threshold, and Phase Change77
Problem Introduction78
Percolation and the Critical Probability82
An Analytical Solution for the 1-D Case82
A Simulation for the 2-D Case83
Exercise90
Another Interesting Statistic in 2-D Grid Percolation90
Exercise93
Summary94
Chapter 6:​ Queuing System:​ How Stock Trades Are Made95
Trading Process Fundamentals95
The Order Book96
Create the Interfaces and Determine the Data Schema98
Implement Order Book Logic102
Hook the Bots and Engine Together107
Exercises and Extension Ideas109
Multiple Bots109
An Informed Bot110
Order Book Visualization110
Order Cancellation Support110
Stop Orders Support110
Summary110
Chapter 7:​ Rock, Scissors, and Paper:​ Multi-agent Simulation111
Community Formation on a Street112
Exercise116
How to Win a Global Rock, Paper, and Scissors Contest116
Exercise125
Summary126
Chapter 8:​ Disease Spreading, Simulating COVID-19 Outbreak127
Simplifying the Real World127
The SI Model129
Exercise133
The SIR Model133
Exercise137
Summary137
Chapter 9:​ Misinformation Spreading and Simulations on a Graph139
Model the Social Network139
Simulate Misinformation Spreading143
Simple Cases144
Misinformation Spreading on Different Networks152
Exercise161
Summary161
Index163
About the Authors
Rongpeng Li

A photo of Rongpeng Li.

is the business intelligence team lead at Unit21. He was a senior data scientist and data science instructor at Unit21. Rongpeng Li graduated from USC with two masters, one in physics and another in electrical engineering. He is a keen educator. He authored one statistics book derived from his voluntary services in the data community.
 
Aiichiro Nakano

A photo of Aiichiro Nakano.

(advisory author) is a professor of computer science and physics and astronomy with joint appointments in quantitative and computational biology and collaboratory for advanced computing and simulations at the University of Southern California. He received a PhD in physics from the University of Tokyo, Japan. His research areas are scalable scientific algorithms, high-end parallel supercomputing, scientific visualization and informatics, and computational materials science. He is a Fellow of the American Physical Society.
 
About the Technical Reviewer
Kacie Webster

A photo of Kacie Webster.

is currently a data analyst in the telecommunications industry. After graduating from San Diego State University with a degree in statistics and economics, she completed a data science bootcamp where she gained the skills to become a data professional. As Kacie continues her journey, she enjoys the constant growth and change that comes with the data world.
 
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