Mathematical Modeling of Earth's Dynamical Systems: A Primer available in Paperback
Mathematical Modeling of Earth's Dynamical Systems: A Primer
- ISBN-10:
- 0691145148
- ISBN-13:
- 9780691145143
- Pub. Date:
- 04/17/2011
- Publisher:
- Princeton University Press
- ISBN-10:
- 0691145148
- ISBN-13:
- 9780691145143
- Pub. Date:
- 04/17/2011
- Publisher:
- Princeton University Press
Mathematical Modeling of Earth's Dynamical Systems: A Primer
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Overview
Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables.
This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus.
Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems.
- Step-by-step lessons for representing complex Earth systems as dynamical models
- Explains geologic processes in terms of fundamental laws of physics and chemistry
- Numerical solutions to differential equations through the finite difference technique
- A philosophical approach to quantitative problem-solving
- Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more
- Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html
Product Details
ISBN-13: | 9780691145143 |
---|---|
Publisher: | Princeton University Press |
Publication date: | 04/17/2011 |
Edition description: | New Edition |
Pages: | 248 |
Product dimensions: | 5.00(w) x 7.90(h) x 0.90(d) |
About the Author
Table of Contents
Preface xiChapter 1: Modeling and Mathematical Concepts 1Pros and Cons of Dynamical Models 2An Important Modeling Assumption 4Some Examples 4Example I: Simulation of Chicxulub Impact and Its Consequences 5Example II: Storm Surge of Hurricane Ivan in Escambia Bay 7Steps in Model Building 8Basic Definitions and Concepts 11Nondimensionalization 13A Brief Mathematical Review 14Summary 22
Chapter 2: Basics of Numerical Solutions by Finite Difference 23First Some Matrix Algebra 23Solution of Linear Systems of Algebraic Equations 25General Finite Difference Approach 26Discretization 27Obtaining Difference Operators by Taylor Series 28Explicit Schemes 29Implicit Schemes 30How Good Is My Finite Difference Scheme? 33Stability Is Not Accuracy 35Summary 37Modeling Exercises 38
Chapter 3: Box Modeling: Unsteady, Uniform Conservation of Mass 39Translations 40Example I: Radiocarbon Content of the Biosphere as a One-Box Model 40Example II: The Carbon Cycle as a Multibox Model 48Example III: One-Dimensional Energy Balance Climate Model 53Finite Difference Solutions of Box Models 57The Forward Euler Method 57Predictor-Corrector Methods 59Stiff Systems 60Example IV: Rothman Ocean 61Backward Euler Method 65Model Enhancements 69Summary 71Modeling Exercises 71
Chapter 4: One-Dimensional Diffusion Problems 74Translations 75Example I: Dissolved Species in a Homogeneous Aquifer 75Example II: Evolution of a Sandy Coastline 80Example III: Diffusion of Momentum 83Finite Difference Solutions to 1-D Diffusion Problems 86Summary 86Modeling Exercises 87
Chapter 5: Multidimensional Diffusion Problems 89Translations 90Example I: Landscape Evolution as a 2-D Diffusion Problem 90Example II: Pollutant Transport in a Confined Aquifer 96Example III: Thermal Considerations in Radioactive Waste Disposal 99Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems 101An Explicit Scheme 102Implicit Schemes 103Case of Variable Coefficients 107Summary 108Modeling Exercises 109
Chapter 6: Advection-Dominated Problems 111Translations 112Example I: A Dissolved Species in a River 112Example II: Lahars Flowing along Simple Channels 116Finite Difference Solution Schemes to the Linear Advection Equation 122Summary 126Modeling Exercises 128
Chapter 7: Advection and Diffusion (Transport) Problems 130Translations 131Example I: A Generic 1-D Case 131Example II: Transport of Suspended Sediment in a Stream 134Example III: Sedimentary Diagenes Influence of Burrows 138Finite Difference Solutions to the Transport Equation 143QUICK Scheme 144QUICKEST Scheme 146Summary 147Modeling Exercises 147Chapter 8: Transport Problems with a Twist: The Transport of Momentum 151Translations 152Example I: One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers’ Equation) 152An Analytic Solution to Burgers’ Equation 157Finite Difference Scheme for Burgers’ Equation 158Solution Scheme Accuracy 160Diffusive Momentum Transport in Turbulent Flows 163Adding Sources and Sinks of Momentum: The General Law of Motion 165Summary 166Modeling Exercises 167
Chapter 9: Systems of One-Dimensional Nonlinear Partial Differential Equations 169Translations 169Example I: Gradually Varied Flow in an Open Channel 169Finite Difference Solution Schemes for Equation Sets 175Explicit FTCS Scheme on a Staggered Mesh 175Four-Point Implicit Scheme 177The Dam-Break Problem: An Example 180Summary 183Modeling Exercises 185
Chapter 10: Two-Dimensional Nonlinear Hyperbolic Systems 187Translations 188Example I: The Circulation of Lakes, Estuaries, and the Coastal Ocean 188An Explicit Solution Scheme for 2-D Vertically Integrated Geophysical Flows 197Lake Ontario Wind-Driven Circulation: An Example 202Summary 203Modeling Exercises 206Closing Remarks 209References 211Index 217
What People are Saying About This
"Written by two of the leading researchers in the field, Mathematical Modeling of Dynamical Systems is a must-read for all geoscientists, and not just students. This excellent primer offers bite-size gems of insight into the world of quantitative geosciences applications, covers both mathematical and modeling concepts, and offers practical exercises to build expertise. Course notes and methodologies will be improving across our academies."—James P. M. Syvitski, executive director, Community Surface Dynamics Modeling System"This wonderful, timely, and necessary book is a real winner. I appreciated the amazing range of geoscience topics as well as the book's structure—each of the chapters begins with an abstract-like summary preview, followed by examples of translations, before delving more deeply into topics. The authors should be congratulated for a brilliant book and pedagogical milestone."—Gidon Eshel, Bard College"I am impressed with the overall philosophy of the book. The authors' definition of modeling is quite lucid and there is a useful breadth to the problems presented. The book's approach is pedagogically valuable for geoscience students, and fills a niche that exists between the more traditional geophysics math methods and Earth system dynamics."—Stephen Griffies, physical scientist, NOAA Geophysical Fluid Dynamics Lab