contentsassets.press.princeton.edu/chapters/c10291.pdfcontents preface xxiii 1 overview module 1.1...

CONTENTS

Preface xxiii

1 OVERVIEWModule 1.1 Overview of Computational Science 3

Projects 6References 6

Module 1.2 The Modeling Process 7Introduction 7Model Classifications 8Steps of the Modeling Process 9Exercises 11References 12

2 SYSTEM DYNAMICS PROBLEMS WITH RATE PROPORTIONAL TO AMOUNTModule 2.1 System Dynamics Tool—Tutorial 1 15

Download 15Introduction 15

Module 2.2 Unconstrained Growth and Decay 17Introduction 17Rate of Change 17Differential Equation 19Difference Equation 20Simulation Program 24Analytical Solution: Introduction 25Analytical Solution: Explanation with Indefinite Integrals (Optional) 26Analytical Solution: Explanation with Derivatives (Optional) 26Completion of the Analytical Solution 27Further Refinement 28Unconstrained Decay 28Reports for System Dynamics Models 30Exercises 31Projects 32Answers to Quick Review Questions 33Reference 33

Module 2.3 Constrained Growth 34Introduction 34Carrying Capacity 35Revised Model 36Equilibrium and Stability 39

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viii Contents

Exercises 39Projects 41Answers to Quick Review Questions 42References 43

Module 2.4 System Dynamics Tool—Tutorial 2 44Download 44Introduction 44

Module 2.5 Drug Dosage 45Downloads 45Introduction 45One-Compartment Model of Single Dose 46One-Compartment Model of Repeated Doses 48Mathematics of Repeated Doses 50Sum of Finite Geometric Series 53Two-Compartment Model 54Exercises 54Projects 55Answers to Quick Review Questions 56References 57

3 FORCE AND MOTION

Module 3.1 Modeling Falling and Skydiving 61Downloads 61Introduction 61Acceleration, Velocity, and Position 62Physics Background 65Friction during Fall 68Modeling a Skydive 70Assessment of the Skydive Model 72Exercises 72Projects 73Answers to Quick Review Questions 76References 77

Module 3.2 Modeling Bungee Jumping 78Downloads 78Introduction 78Physics Background 79Vertical Springs 81Modeling a Bungee Jump 84Exercises 86Projects 87Answers to Quick Review Questions 88References 88

Module 3.3 Tick Tock—The Pendulum Clock 90Download 90Introduction 90





Contents ix

Simple Pendulum 91Linear Damping 94Pendulum Clock 94Exercises 95Projects 96Answers to Quick Review Questions 97References 97

Module 3.4 Up, Up, and Away—Rocket Motion 99Download 99Introduction 99Physics Background 100System Dynamics Model 102Exercises 104Projects 105Answers to Quick Review Questions 107References 107

4 SYSTEM DYNAMICS MODELS WITH INTERACTIONSModule 4.1 Competition 111

Download 111Community Relations 111Introduction to Competition 111Modeling Competition 112Exercises 115Projects 116Answers to Quick Review Questions 117References 117

Module 4.2 Predator-Prey Models 118Download 118Introduction 118Lotka-Volterra Model 119Particular Situations 121Exercises 125Projects 125Answers to Quick Review Questions 129References 130

Module 4.3 Modeling the Spread of SARS— Containing Emerging Disease 131

Downloads 131Introduction 131SIR Model 132SARS Model 136Reproductive Number 141Exercises 142Projects 143Answers to Quick Review Questions 145References 146





x Contents

Module 4.4 Modeling a Persistent Plague—Malaria 147Download 147Introduction 147Background Information 148Analysis of Problem 149Formulating a Model: Gather Data 150Formulating a Model: Make Simplifying Assumptions 150Formulating a Model: Determine Variables and Units 151Formulating a Model: Establish Relationships 152Formulating a Model: Determine Equations and Functions 153Solving the Model 155Verifying and Interpreting the Model’s Solution 157Exercises 159Projects 159Answers to Quick Review Questions 161References 162

Module 4.5 Enzyme Kinetics—A Model of Control 164Download 164Introduction 164Enzymatic Reactions 165Differential Equations 166Model 167Moles vs. Molar 167Results 168Michaelis-Menten Equation 169Modeling Inhibition 172Exercises 173Projects 174Answers to Quick Review Questions 176References 177

5 COMPUTATIONAL ERRORModule 5.1 Computational Toolbox—Tools of the Trade: Tutorial 1 181


Module 5.2 Errors 182Introduction 182Data Errors 182Modeling Errors 182Implementation Errors 183Precision 183Absolute and Relative Errors 185Round-off Error 186Overflow and Underflow 187Arithmetic Errors 188Error Propagation 189





Contents xi

Violation of Numeric Properties 192Comparison of Floating-Point Numbers 193Truncation Error 194Exercises 196Projects 197Answers to Quick Review Questions 199References 200

6 SIMULATION TECHNIQUES

Module 6.1 Computational Toolbox—Tools of the Trade: Tutorial 2 203Download 203Introduction 203

Module 6.2 Euler’s Method 204Download 204Introduction 204Reasoning behind Euler’s Method 204Algorithm for Euler’s Method 206Error 207Exercises 209Projects 209Answers to Quick Review Questions 210References 211

Module 6.3 Runge-Kutta 2 Method 212Introduction 212Euler’s Estimate as a Predictor 212Corrector 212Runge-Kutta 2 Algorithm 215Error 216Exercises 217Projects 217Answers to Quick Review Questions 217References 217

Module 6.4 Runge-Kutta 4 Method 218Introduction 218First Estimate, ∂1, Using Euler’s Method 218Second Estimate, ∂2 219Third Estimate, ∂3 221Fourth Estimate, ∂4 223Using the Four Estimates 225Runge-Kutta 4 Algorithm 226Error 227Exercises 228Projects 228Answers to Quick Review Questions 228References 229





xii Contents

7 ADDITIONAL SYSTEM DYNAMICS PROJECTS Overview 231

Module 7.1 Radioactive Chains—Never the Same Again 233Introduction 233Modeling the Radioactive Chain 233Projects 235Answers to Quick Review Questions 236Reference 236

Module 7.2 Turnover and Turmoil—Blood Cell Populations 237Introduction 237Formation and Destruction of Blood Cells 237Basic Model 238Model Parameters 238Projects 240Answers to Quick Review Questions 241References 242

Module 7.3 Deep Trouble—Ideal Gas Laws and Scuba Diving 243Pressure 243Ideal Gas 244Dalton’s Law 244Boyle’s Law 245Charles’s Law 246Henry’s Law 247Rate of Absorption 248Decompression Sickness 249Projects 249Answers to Quick Review Questions 250References 251

Module 7.4 What Goes Around Comes Around—The Carbon Cycle 252Introduction 252Flow between Systems 252Fossil Fuels 253Projects 254References 255

Module 7.5 A Heated Debate—Global Warming 256Greenhouse Effect 256Global Warming 257Greenhouse Gases 257Consequences 257Projects 258References 259

Module 7.6 Plotting the Future—How Will the Garden Grow? 261The Problem 261Project 262Reference 263





Contents xiii

Module 7.7 Cardiovascular System—A Pressure-Filled Model 264Circulation 264Blood Pressure 265Nervous Systems 265Stroke Volume 265Venous Return 266Systemic Vascular Resistance 266Blood Flow 266Projects 267References 268

Module 7.8 Electrical Circuits—A Complete Story 270Defibrillators 270Current and Potential 270Resistance 272Capacitance 273Inductance 274Circuit for Defibrillator 274Kirchhoff’s Voltage Law 275Kirchhoff’s Current Law 277Projects 278Answers to Quick Review Questions 279References 279

Module 7.9 Transmission of Nerve Impulses— Learning from the Action Potential Heroes 281

Introduction 281The Neuron—Basic Structure and Function 282Initiating an Action Potential 283Hodgkin and Huxley Model 285Projects 286References 288

Module 7.10 Feeding the Problem—Antibiotic Resistance 290Introduction 290Projects 291References 295

Module 7.11 Fueling Our Cells—Carbohydrate Metabolism 297Glycolysis 297Recycling NAD+s 298Aerobic Respiration 299Projects 299References 300

Module 7.12 Mercury Pollution—Getting on Our Nerves 301Introduction 301Projects 302References 305





xiv Contents

Module 7.13 Managing to Eat—What’s the Catch? 307Introduction 307Economics Background 308Gordon-Schaefer Fishery Production Function 312Projects 313Answers to Quick Review Questions 315References 315

Module 7.14 Control Issues—The Operon Model 317Proteins 317Nucleic Acids 317From Genes to Proteins 321Projects 324References 324

Module 7.15 Troubling Signals—Colon Cancer 326Introduction 326Colon Cancer 327Modeling Crypt Dynamics 327Projects 332References 332

8 DATA-DRIVEN MODELSModule 8.1 Computational Toolbox—Tools of the Trade: Tutorial 3 337


Module 8.2 Function Tutorial 338Download 338Introduction 338Linear Function 339Quadratic Function 340Polynomial Function 342Square Root Function 343Exponential Function 343Logarithmic Functions 345Logistic Function 347Trigonometric Functions 348

Module 8.3 Empirical Models 352Downloads 352Introduction 353Linear Empirical Model 353Predictions 355Linear Regression 356Nonlinear One-Term Model 357Solving for y in a One-Term Model 363Multiterm Models 366Advanced Fitting with Computational Tools 368





Contents xv

Exercise 368Projects 368Answers to Quick Review Questions 370References 370

9 SIMULATING WITH RANDOMNESSModule 9.1 Computational Toolbox—Tools of the Trade: Tutorial 4 375


Module 9.2 Simulations 376Download 376Introduction 376Disadvantages of Computer Simulations 377Element of Chance 377Measure of Quality 380Simulation Development 380Multiplicative Linear Congruential Method (Optional) 382Different Ranges of Random Numbers 383Exercises 385Projects 386Answers to Quick Review Questions 388References 388

Module 9.3 Random Numbers from Various Distributions 390Downloads 390Introduction 390Statistical Distributions 390Discrete Distributions 393Normal Distributions 396Exponential Distributions 398Rejection Method 400Exercises 401Projects 402Answers to Quick Review Questions 403References 403

Module 9.4 Computational Toolbox—Tools of the Trade: Tutorial 5 404

Downloads 404Introduction 404

Module 9.5 Random Walk 405Downloads 405Introduction 405Algorithm for Random Walk 406Animate Path 408Average Distance Covered 410Relationship between Number of Steps and Distance Covered 412Exercises 412





xvi Contents

Projects 413Answers to Quick Review Questions 414References 414

10 CELLULAR AUTOMATON DIFFUSION SIMULATIONSModule 10.1 Computational Toolbox—Tools of the Trade: Tutorial 6 417


Module 10.2 Diffusion—Overcoming Differences 418Downloads 418Introduction 418Problem 419Initializing the System 419Heat Diffusion 421Boundary Conditions 423Applying a Function to Each Grid Point 426Simulation Program 428Display Simulation 429Exercises 431Projects 431Answers to Quick Review Questions 434References 434

Module 10.3 Spreading of Fire 435Downloads 435Introduction 435Problem 436Initializing the System 436Updating Rules 437Periodic Boundary Conditions 439Applying a Function to Each Grid Point 441Simulation Program 441Display Simulation 442Exercises 443Projects 445Answers to Quick Review Questions 446References 446

Module 10.4 Movement of Ants—Taking the Right Steps 448Downloads 448Introduction 448Analysis of Problem 449Formulating a Model: Gather Data 449Formulating a Model: Make Simplifying Assumptions 450Formulating a Model: Determine Variables 450Formulating a Model: Establish Relationships and Submodels 451Formulating a Model: Determine Functions—Sensing 452Formulating a Model: Determine Functions—Walking 454





Contents xvii

Solving a Model—A Simulation 455Verifying and Interpreting the Model’s Solution—Visualizing the Simulation 456Exercises 458Projects 458Answers to Quick Review Questions 460References 460

Module 10.5 Biofilms—United They Stand, Divided They Colonize 462

Downloads 462Introduction 462The Problem 463Nutrient Grid 464Nutrient Boundary Conditions 465Biofilm Initialization 465Biofilm Boundary Conditions 466Biofilm Growth 467Consumption of Nutrients 471Simulation Program 472Display Simulation 473Example Problem 474Assessment of the Model 474Computing Power 479Projects 479Answers to Quick Review Questions 482References 482

11 AGENT-BASED MODELSModule 11.1 Agent-Based Tool: Tutorial 1 487


Module 11.2 Agents of Interaction: Steering a Dangerous Course 488

Downloads 488Introduction 488Problem 489Agent-Based Modeling 489Formulating the Simulation Model 490Overall Design of the Simulation 491Model Environment 492Agents and Their States 494Agent Behaviors 495Example Problem 502Repeated Simulations 503Model Refinement 505Exercise 508Projects 508





xviii Contents

Answers to Quick Review Questions 509References 510

Module 11.3 Agent-Based Tool: Tutorial 2 511Download 511Introduction 511

Module 11.4 Introducing the Cane Toad— Able Invader 512

Download 512Introduction 512The Problem 514Grid-Based Individual-Based Model 514Model of Environment 515Agents 516Toad’s State 516Toad Behavior 517Constants and Global Simulation Variables 518Initial Environment 518Simulation Driver 520Phase 0: Initialization 520Phase 1: Consumption 522Phase 2: Movement 524Phase 3: Complete Cycle 527Visualization of Example Problem 528Multiple Simulations 529Assessment of Model 529Exercise 532Projects 532Answers to Quick Review Questions 537References 538

12 HIGH-PERFORMANCE COMPUTING

Module 12.1 Concurrent Processing 543Introduction 543Analogy 545Types of Processing 547Communication 548Metrics 550Exercises 552Project 552Answers to Quick Review Questions 552References 553

Module 12.2 Parallel Algorithms 555Introduction 555Embarrassingly Parallel Algorithm: Adding Two Vectors 556Data Partitioning: Adding Numbers 558Divide and Conquer: Adding Numbers 561





Contents xix

Parallel Random Number Generator 564Sequential Algorithm for the N-Body Problem 566Barnes-Hut Algorithm for the N-Body Problem 570Exercises 574Projects 576Answers to Quick Review Questions 577References 579

13 MATRIX MODELSModule 13.1 Computational Toolbox—Tools of the Trade: Tutorial 7 583


Module 13.2 Matrices for Population Studies—Linked for Life 584Downloads 584Population Matrices and High-Performance Computing 584Vectors 586Vector Addition 588Multiplication by a Scalar 588Dot Product 589Matrices 590Scalar Multiplication and Matrix Sums 591Matrix Multiplication 592Square Matrices 595Matrices and Systems of Equations 596Exercises 598Projects 603Answers to Quick Review Questions 605References 606

Module 13.3 Time after Time—Age- and Stage-Structured Models 608Downloads 608Introduction 608The Problem 610Age-Structured Model 611Leslie Matrices 613Age Distribution over Time 614Projected Population-Growth Rate 615Stage-Structured Model 619Algorithms 620Sensitivity Analysis for the Age-Structured Example 621Sensitivity Analysis for the Stage-Structured Example 622Applicability of Leslie and Lefkovitch Matrices 622Need for High-Performance Computing 623Exercises 624Projects 626Answers to Quick Review Questions 637References 637





xx Contents

Module 13.4 Probable Cause—Modeling with Markov Chains 640Introduction 640Problems from Psychology to Genetics 642Probability 642Transition Matrix 645Exercises 650Projects 651Answers to Quick Review Questions 656References 657

Module 13.5 The Next Flu Pandemic—Old Enemy, New Identity 659Downloads 659Introduction 659The Problem 660Graphs 661Paths 665Clustering 666Bipartite Graphs 668Matrix Representation of Graphs 669People-Location Graphs 671Minimal Dominating Set 674Degree Distribution 677Clustering Coefficient 680Example Problems 681Assessment of Model 682Computing Power 682Projects 683Answers to Quick Review Questions 689References 689

14 ADDITIONAL CELLULAR AUTOMATA, AGENT-BASED AND MATRIX PROJECTS

Overview 691

Module 14.1 Polymers—Strings of Pearls 693Introduction 693Simulations 695Projects 696References 697

Module 14.2 Solidification—Let’s Make It Crystal Clear! 699Introduction 699Projects 700References 702

Module 14.3 Foraging—Finding a Way to Eat 703Introduction 703Simulations 704Projects 705References 708





Contents xxi

Module 14.4 Pit Vipers—Hot Bodies, Dead Meat 709Introduction 709Projects 709References 710

Module 14.5 Mushroom Fairy Rings—Growing in Circles 711Introduction 711What Are Fungi? 712What Do Fungi Look Like? 712How Do Fungi Feed Themselves? 713How Do Fungi Reproduce? 713How Do Fungi Grow? 713The Problem 713How Do Fairy Rings Get Started? 714Initializing the System 715Updating Rules 716Display the Simulation 717Projects 718References 719

Module 14.6 Spread of Disease—Sharing Bad News 720Introduction 720Exercise 720Projects 720

Module 14.7 HIV—The Enemy Within 723The Developing Epidemic 723Attack on the Immune System 724Plan of Attack 725Simulation of the Attack 726Projects 726References 728

Module 14.8 Predator-Prey—“Catch Me If You Can” 730Introduction 730Projects 731References 734

Module 14.9 Clouds—Bringing It All Together 736Introduction 736Projects 737References 740

Module 14.10 Fish Schooling—Hanging Together, Not Separately 741Introduction 741Simulations 742Projects 742References 743

Module 14.11 Spaced Out—Native Plants Lose to Exotic Invasives 745Introduction 745Competition for Space 747





xxii Contents

Projects 748References 750

Module 14.12 Re-Solving the Problems with Cellular Automaton Simulations 751

Introduction 751Projects 751

Module 14.13 Re-Solving the Problems with Agent-Based Simulations 753

Introduction 753Projects 753

Module 14.14 Computational Code-Breaking— Deciphering Our Own Mysteries 757

Bioinformatics 757Mutations 758Locating Genes with Markov Models 758GeneMark 762Projects 763Answers to Quick Review Questions 768References 768

Module 14.15 Social Networks—Value in Being Well Connected 770Introduction 770Projects 772References 775

Glossary 777Answers to Selected Exercises 801Index 807





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