Table of Contents

CONTENTS FOR SECOND EDITION



Preface

1: OVERVIEW

Module 1.1 Overview of Computational Science

  • Projects
  • References

Module 1.2 The Modeling Process

  • Introduction
  • Model Classifications
  • Steps of the Modeling Process
  • Exercises
  • References

2: SYSTEM DYNAMICS PROBLEMS WITH RATE PROPORTIONAL TO AMOUNT

Module 2.1 System Dynamics Tool—Tutorial 1

  • Downloads
  • Introduction

Module 2.2 Unconstrained Growth and Decay

  • Introduction
  • Rate of Change
  • Differential Equation
  • Difference Equation
  • Simulation Program
  • Analytical Solution Introduction
  • Analytical Solution—Explanation with Indefinite Integrals (Optional)
  • Analytical Solution—Explanation with Derivatives (Optional)
  • Completion of the Analytical Solution
  • Further Refinement
  • Unconstrained Decay
  • Reports for System Dynamics Models
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • Reference

Module 2.3 Constrained Growth

  • Introduction
  • Carrying Capacity
  • Revised Model
  • Equilibrium and Stability
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 2.4 System Dynamics Tool: —Tutorial 2

  • Download
  • Introduction

Module 2.5 Drug Dosage

  • Downloads
  • Introduction
  • One-Compartment Model of Single Dose
  • One-Compartment Model of Repeated Doses
  • Mathematics of Repeated Doses
  • Sum of Finite Geometric Series
  • Two-Compartment Model
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

3: FORCE AND MOTION

Module 3.1 Modeling Falling and Skydiving

  • Downloads
  • Introduction
  • Acceleration, Velocity, and Position
  • Physics Background
  • Friction During Fall
  • Modeling a Skydive
  • Assessment of the Skydive Model
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 3.2 Modeling Bungee Jumping

  • Downloads
  • Introduction
  • Physics Background
  • Vertical Springs
  • Modeling a Bungee Jump
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 3.3 Tick Tock—The Pendulum Clock

  • Download
  • Introduction
  • Simple Pendulum
  • Linear Damping
  • Pendulum Clock
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 3.4 Up, Up, and Away—Rocket Motion

  • Download
  • Introduction
  • Physics Background
  • System Dynamics Model
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

4: SYSTEM DYNAMICS MODELS WITH INTERACTIONS

Module 4.1 Competition

  • Download
  • Community Relations
  • Competition Introduction to Competition
  • Modeling Competition
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 4.2 Predator-Prey Models

  • Download
  • Introduction
  • Lotka-Volterra Model
  • Particular Situations
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 4.3 Modeling the Spread of SARS—Containing Emerging Disease

  • Downloads
  • Introduction
  • SIR Model
  • SARS Model
  • Reproductive Number
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 4.4 Modeling a Persistent Plague—Malaria

  • Download
  • Introduction
  • Background Information
  • Analysis of Problem
  • Formulating a Model: Gather Data
  • Formulating a Model: Make Simplifying Assumptions
  • Formulating a Model: Determine Variables and Units
  • Formulating a Model: Establish Relationships
  • Formulating a Model: Determine Equations and Functions
  • Solving the Model
  • Verifying and Interpreting the Model’s Solution
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 4.5 Enzyme Kinetics—A Model of Control

  • Download
  • Introduction
  • Enzymatic Reactions
  • Differential Equations
  • Model
  • Moles vs. Molar
  • Results
  • Michaelis-Menten Equation
  • Results
  • Modeling Inhibition
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

5: COMPUTATIONAL ERROR

Module 5.1 Computational Toolbox—Tools of the Trade: Tutorial 1

  • Download
  • Introduction

Module 5.2 Errors

  • Introduction
  • Data Errors
  • Modeling Errors
  • Implementation Errors
  • Precision
  • Absolute and Relative Errors
  • Round-off Error
  • Overflow and Underflow
  • Arithmetic Errors
  • Error Propagation
  • Violation of Numeric Properties
  • Comparison of Floating Floating-Point Numbers
  • Truncation Error
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

6: SIMULATION TECHNIQUES

Module 6.1 Computational Toolbox—Tools of the Trade: Tutorial 2

  • Download
  • Introduction

Module 6.2 Euler’s Method

  • Download
  • Introduction
  • Reasoning behind Euler’s Method
  • Algorithm for Euler’s Method
  • Error
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 6.3 Runge-Kutta 2 Method

  • Introduction
  • Euler’s Estimate as a Predictor
  • Corrector
  • Runge-Kutta 2 Algorithm
  • Error
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 6.4 Runge-Kutta 4 Method

  • Introduction
  • First Estimate, ∂1, Using Euler’s Method
  • Second Estimate, ∂2
  • Third Estimate, ∂3
  • Fourth Estimate, ∂4
  • Using the Four Estimates
  • Runge-Kutta 4 Algorithm
  • Error
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

7: ADDITIONAL SYSTEM DYNAMICS PROJECTS

Module 7.1 Radioactive Chains—Never the Same Again

  • Introduction
  • Modeling the Radioactive Chain
  • Projects
  • Answers to Quick Review Questions
  • Reference

Module 7.2 Turnover and Turmoil—Blood Cell Populations

  • Introduction
  • Formation and Destruction of Blood Cells
  • Basic Model
  • Model Parameters
  • Projects
  • Answers to Quick Review Questions
  • References

Module 7.3 Deep Trouble—Ideal Gas Laws and Scuba Diving

  • Pressure
  • Ideal Gas
  • Dalton’s Law
  • Boyle’s Law
  • Charles’ Law
  • Henry’s Law
  • Rate of Absorption
  • Decompression Sickness
  • Projects
  • Answers to Quick Review Questions
  • References

Module 7.4 What Goes Around Comes Around—The Carbon Cycle

  • Introduction
  • Flow Between between Systems
  • Fossil Fuels
  • Projects
  • References

Module 7.5 A Heated Debate—Global Warming

  • Greenhouse Effect
  • Global Warming
  • Greenhouse Gases
  • Consequences
  • Projects
  • References

Module 7.6 Plotting the Future—How Will the Garden Grow?

  • The Problem
  • Project
  • Reference

Module 7.7 Cardiovascular System—A Pressure Pressure-Filled Model

  • Circulation
  • Blood Pressure
  • Nervous Systems
  • Stroke Volume
  • Venous Return
  • Systemic Vascular Resistance
  • Blood Flow
  • Projects
  • References

Module 7.8 Electrical Circuits—A Complete Story

  • Defibrillators
  • Current and Potential
  • Resistance
  • Capacitance
  • Inductance
  • Circuit for Defibrillator
  • Kirchhoff’s Voltage Law
  • Kirchhoff’s Current Law
  • Projects
  • Answers to Quick Review Questions
  • References

Module 7.10 Feeding the Problem—Antibiotic Resistance

  • Introduction
  • Projects
  • References

Module 7.11 Fueling Our Cells—Carbohydrate Metabolism

  • Glycolysis
  • Recycling NAD+s
  • Aerobic Respiration
  • Projects
  • References

Module 7.12 Mercury Pollution—Getting on Our Nerves

  • Introduction
  • Projects
  • References

Module 7.13 Managing to Eat—What’s the Catch?

  • Introduction
  • Economics Background
  • Gordon-Schaefer Fishery Production Function
  • Projects
  • Answers to Quick Review Questions
  • References

Module 7.14 Control Issues—The Operon Model

  • Proteins
  • Nucleic Acids
  • From Genes to Proteins
  • Projects
  • References

Module 7.15 Troubling Signals—Colon Cancer

  • Introduction
  • Colon Cancer
  • Modeling Crypt Dynamics
  • Projects
  • References

8: DATA-DRIVEN MODELS

Module 8.1 Computational Toolbox—Tools of the Trade: Tutorial 3

  • Download
  • Introduction

Module 8.2 Function Tutorial

  • Download
  • Introduction
  • Linear Function
  • Quadratic Function
  • Polynomial Function
  • Square Root Function
  • Exponential Function
  • Logarithmic Functions
  • Logistic Function
  • Trigonometric Functions

Module 8.3 Empirical Models

  • Downloads
  • Introduction
  • Linear Empirical Model
  • Predictions
  • Linear Regression
  • Non-Linear One-Term Model
  • Solving for y in a One-Term Model
  • Multiterm Models
  • Advanced Fitting with Computational Tools
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

9: SIMULATING WITH RANDOMNESS

Module 9.1 Computational Toolbox—Tools of the Trade: Tutorial 4

  • Download
  • Introduction

Module 9.2 Simulations

  • Download
  • Introduction
  • Disadvantages of Computer Simulations
  • Element of Chance
  • Measure of Quality
  • Simulation Development
  • Multiplicative Linear Congruential Method (Optional)
  • Different Ranges of Random Numbers
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 9.3 Random Numbers from Various Distributions

  • Downloads
  • Introduction
  • Statistical Distributions
  • Discrete Distributions
  • Normal Distributions
  • Exponential Distributions
  • Rejection Method
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 9.4 Computational Toolbox—Tools of the Trade: Tutorial 5

  • Downloads
  • Introduction

Module 9.5 Random Walk

  • Downloads
  • Introduction
  • Algorithm for Random Walk
  • Animate Path
  • Average Distance Covered
  • Relationship between Number of Steps and Distance Covered
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

10: CELLULAR AUTOMATON DIFFUSION SIMULATIONS

Module 10.1 Computational Toolbox—Tools of the Trade: Tutorial 6

  • Download
  • Introduction

Module 10.2 Diffusion: Overcoming Differences

  • Downloads
  • Introduction
  • Problem
  • Initializing the System
  • Heat Diffusion
  • Boundary Conditions
  • Applying a Function to Each Grid Point
  • Simulation Program
  • Display Simulation
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 10.3 Spreading of Fire

  • Downloads
  • Introduction
  • Problem
  • Initializing the System
  • Updating Rules
  • Periodic Boundary Conditions
  • Applying a Function to Each Grid Point
  • Simulation Program
  • Display Simulation
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 10.4 Movement of Ants—Taking the Right Steps

  • Downloads
  • Introduction
  • Analysis of Problem
  • Formulating a Model: Gather Data
  • Formulating a Model: Make Simplifying Assumptions
  • Formulating a Model: Determine Variables
  • Formulating a Model: Establish Relationships and Submodels
  • Formulating a Model: Determine Functions—Sensing
  • Formulating a Model: Determine Functions—Walking
  • Solving a Model: A Simulation
  • Verifying and Interpreting the Model’s Solution—Visualizing the Simulation
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 10.5 Biofilms—United They Stand, Divided They Colonize

  • Downloads
  • Introduction
  • The Problem
  • Nutrient Grid
  • Nutrient Boundary Conditions
  • Biofilm Initialization
  • Biofilm Boundary Conditions
  • Biofilm Growth
  • Consumption of Nutrients
  • Simulation Program
  • Display Simulation
  • Example Problem
  • Assessment of the Model
  • Computing Power
  • Projects
  • Answers to Quick Review Questions
  • References

11: AGENT-BASED MODELS

Module 11.1 Agent-Based Tool: Tutorial 1

  • Download
  • Introduction

Module 11.2 Agents of Interaction: Steering a Dangerous Course

  • Downloads
  • Introduction
  • Problem
  • Agent-Based Modeling
  • Formulating the Simulation Model
  • Overall Design of the Simulation
  • Model Environment
  • Agents and Their States
  • Agent Behaviors
  • Example Problem
  • Repeated Simulations
  • Model Refinement
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 11.3 Agent-Based Tool: Tutorial 2

  • Download
  • Introduction

Module 11.4 Introducing the Cane Toad – Able Invader

  • Download
  • Introduction
  • The Problem
  • Grid-Based Individual-Based Model
  • Model of Environment
  • Agents and Their Decictions
  • Toad’s State
  • Toad Behavior
  • Constants and Global Simulation Variables
  • Initial Environment
  • Simulation Driver
  • Phase 0: Initialization
  • Phase 1: Consumption
  • Phase 2: Movement
  • Phase 3: Complete Cycle
  • Visualization of Example Problem
  • Multiple Simulations
  • Assessment of Model
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

12: HIGH-PERFORMANCE COMPUTING

Module 12.1 Concurrent Processing

  • Introduction
  • Analogy
  • Types of Processing
  • Communication
  • Metrics
  • Exercises
  • Project
  • Answers to Quick Review Questions
  • References

Module 12.2 Parallel Algorithms

  • Introduction
  • Embarrassingly Parallel Algorithm: Adding Two Vectors
  • Data Partitioning: Adding Numbers
  • Divide and Conquer: Adding Numbers
  • Parallel Random Number Generator
  • Sequential Algorithm for the N-Body Problem
  • Barnes-Hut Algorithm for the N-Body Problem
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

13: MATRIX MODELS

Module 13.1 Computational Toolbox—Tools of the Trade: Tutorial 7

  • Download
  • Introduction

Module 13.2 Matrices for Population Studies—Linked for Life

  • Downloads
  • Population Matrices and High High-Performance Computing
  • Vectors
  • Vector Addition
  • Multiplication by a Scalar
  • Dot Product
  • Matrices
  • Scalar Multiplication and Matrix Sums
  • Matrix Multiplication
  • Square Matrices
  • Matrices and Systems of Equations
  • Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 13.3 Time after Time—Age- and Stageuctured Models

  • Downloads
  • Introduction
  • The Problem
  • Ageuctured Model
  • Leslie Matrices
  • Age Distribution Over over Time
  • Projected Population Population-Growth Rate
  • Stage Structured Model
  • Algorithms
  • Sensitivity Analysis for the Age Structured Example
  • Sensitivity Analysis for the Stage Structured Example
  • Applicability of Leslie and Lefkovitch Matrices
  • Need for High-Performance Computing
  • Nimrod
  • Exercises
  • Answers to Selected Exercises
  • Projects
  • Answers to Quick Review Questions
  • References

Module 13.5 The Next Flu Pandemic: Old Enemy—New Identity

  • Downloads
  • Introduction
  • The Problem
  • Graphs
  • Paths
  • Clustering
  • Bipartite Graphs
  • Matrix Representation of Graphs
  • People-Location Graphs
  • Minimal Dominating Set
  • Degree Distribution
  • Clustering Coefficient
  • Example Problems
  • Assessment of Model
  • Computing Power
  • Projects
  • Answers to Quick Review Questions
  • References

14: ADDITIONAL CELLULAR AUTOMATA, AGENT-BASED AND MATRIX PROJECTS

Module 14.1 Polymers—Strings of Pearls

  • Introduction
  • Simulations
  • Projects
  • References

Module 14.2 Solidification—Let’s Make It Crystal Clear!

  • Introduction
  • Projects
  • References

Module 14.3 Foraging—Finding a Way to Eat

  • Introduction
  • Simulations
  • Projects
  • References

Module 14.4 Pit Vipers—Hot Bodies, Dead Meat

  • Introduction
  • Simulations of Heat Diffusion
  • Projects
  • References

Module 14.5 Mushroom Fairy Rings—Growing in Circles

  • Introduction
  • What Are Fungi?
  • What Do Fungi Look Like?
  • How Do Fungi Feed Themselves?
  • How Do Fungi Reproduce?
  • How Do Fungi Grow?
  • The Problem
  • How Do Fairy Rings Get Started?
  • Initializing the System
  • Updating Rules Display the Simulation
  • Display the Simulation Updating Rules
  • Projects
  • References

Module 14.6 Spread of Disease—Sharing Bad News

  • Introduction
  • Exercise
  • Projects
  • References

Module 14.7 HIV—The Enemy Within

  • The Developing Epidemic
  • Attack on the Immune System
  • Plan of Attack
  • Simulation of the Attack
  • Projects
  • References

Module 14.8 Predator-Prey—”Catch Me If You Can”

  • Introduction
  • Projects
  • References

Module 14.9 Clouds—Bringing It All Together

  • Introduction
  • Projects
  • References

Module 14.10 Fish Schooling—Hanging Together, Not Separately

  • Introduction
  • Simulations
  • Projects
  • References

Module 14.11 Spaced Out—Native Plants Lose to Exotic Invasives

  • Introduction
  • Competition for Space
  • Projects
  • References

Module 14.12 Re-Solving the Problems with Cellular Automaton Simulations

  • Introduction
  • Simulations
  • Projects

Module 14.13 Re-Solving the Problems with Agent-Based Simulations

  • Introduction
  • Projects

Module 14.14 Computational Code-Breaking—Deciphering Our Own Mysteries

  • Bioinformatics
  • Mutations
  • Locating Genes with Markov Chains
  • GeneMark
  • Projects
  • Answers to Quick Review Questions
  • References

Module 14.15 Social Networks—Value in Being Well- Connected

  • Introduction
  • Projects
  • References

Glossary

Answers to Selected Exercises

Index