Mathematical Modeling of Earth's Dynamical Systems: A Primer

Princeton University Press
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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
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About the author

Rudy Slingerland and Lee Kump are professors of geosciences at Pennsylvania State University. Slingerland is the coauthor of Simulating Clastic Sedimentary Basins. Kump is the coauthor of The Earth System.
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Additional Information

Publisher
Princeton University Press
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Published on
Mar 28, 2011
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Pages
248
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ISBN
9781400839117
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Language
English
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Genres
Mathematics / Applied
Science / Earth Sciences / General
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Content Protection
This content is DRM protected.
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Available on Android devices
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Eligible for Family Library

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Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. In Analysis of Evolutionary Processes, Fabio Dercole and Sergio Rinaldi have written the first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones. The book shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics.

After introducing the basics of evolutionary processes and classifying available modeling approaches, Dercole and Rinaldi give a detailed presentation of the derivation of the AD canonical equation, an ordinary differential equation that focuses on evolutionary processes driven by rare and small innovations. The authors then look at important features of evolutionary dynamics as viewed through the lens of AD. They present their discovery of the first chaotic evolutionary attractor, which calls into question the common view that coevolution produces exquisitely harmonious adaptations between species. And, opening up potential new lines of research by providing the first application of AD to economics, they show how AD can explain the emergence of technological variety.



Analysis of Evolutionary Processes will interest anyone looking for a self-contained treatment of AD for self-study or teaching, including graduate students and researchers in mathematical and theoretical biology, applied mathematics, and theoretical economics.

Hidden away in foggy, uncharted rain forest valleys in Northern California are the largest and tallest organisms the world has ever sustained–the coast redwood trees, Sequoia sempervirens. Ninety-six percent of the ancient redwood forests have been destroyed by logging, but the untouched fragments that remain are among the great wonders of nature. The biggest redwoods have trunks up to thirty feet wide and can rise more than thirty-five stories above the ground, forming cathedral-like structures in the air.

Until recently, redwoods were thought to be virtually impossible to ascend, and the canopy at the tops of these majestic trees was undiscovered. In The Wild Trees, Richard Preston unfolds the spellbinding story of Steve Sillett, Marie Antoine, and the tiny group of daring botanists and amateur naturalists that found a lost world above California, a world that is dangerous, hauntingly beautiful, and unexplored.

The canopy voyagers are young—just college students when they start their quest—and they share a passion for these trees, persevering in spite of sometimes crushing personal obstacles and failings. They take big risks, they ignore common wisdom (such as the notion that there’s nothing left to discover in North America), and they even make love in hammocks stretched between branches three hundred feet in the air.

The deep redwood canopy is a vertical Eden filled with mosses, lichens, spotted salamanders, hanging gardens of ferns, and thickets of huckleberry bushes, all growing out of massive trunk systems that have fused and formed flying buttresses, sometimes carved into blackened chambers, hollowed out by fire, called “fire caves.” Thick layers of soil sitting on limbs harbor animal and plant life that is unknown to science. Humans move through the deep canopy suspended on ropes, far out of sight of the ground, knowing that the price of a small mistake can be a plunge to one’s death.

Preston’s account of this amazing world, by turns terrifying, moving, and fascinating, is an adventure story told in novelistic detail by a master of nonfiction narrative. The author shares his protagonists’ passion for tall trees, and he mastered the techniques of tall-tree climbing to tell the story in The Wild Trees—the story of the fate of the world’s most splendid forests and of the imperiled biosphere itself.
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Interweaving physics, astronomy, chemistry, geology, and biology, this sweeping account tells Earth’s complete story, from the synthesis of chemical elements in stars, to the formation of the Solar System, to the evolution of a habitable climate on Earth, to the origin of life and humankind. The book also addresses the search for other habitable worlds in the Milky Way and contemplates whether Earth will remain habitable as our influence on global climate grows. It concludes by considering the ways in which humankind can sustain Earth’s habitability and perhaps even participate in further planetary evolution.

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Leading schools that have ordered, recommended for reading, or adopted this book for course use:

Arizona State University Brooklyn College CUNY Columbia University Cornell University ETH Zurich Georgia Institute of Technology Harvard University Johns Hopkins University Luther College Northwestern University Ohio State University Oxford Brookes University Pan American University Rutgers University State University of New York at Binghamton Texas A&M University Trinity College Dublin University of Bristol University of California-Los Angeles University of Cambridge University Of Chicago University of Colorado at Boulder University of Glasgow University of Leicester University of Maine, Farmington University of Michigan University of North Carolina at Chapel Hill University of North Georgia University of Nottingham University of Oregon University of Oxford University of Portsmouth University of Southampton University of Ulster University of Victoria University of Wyoming Western Kentucky University Yale University
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