Continuum Mechanics in the Earth Sciences

Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical insights, the book surveys solid, fluid and gas dynamics. In later review chapters, it explores new aspects of the field emerging from nonlinearity and dynamical complexity and provides a brief introduction to computational modeling. Simple, yet rigorous, derivations are used to review the essential mathematics. The author emphasizes the full three-dimensional geometries of real-world examples, enabling students to apply this in deconstructing solid earth and planet-related problems. Problem sets and worked examples are provided, making this a practical resource for graduate students in geophysics, planetary physics and geology and a beneficial tool for professional scientists seeking a better understanding of the mathematics and physics within Earth sciences.

Preface; Acknowledgements; 1. Some mathematical essentials; 2. Stress principles; 3. Deformation and motion; 4. Fundamental laws and equations; 5. Linear elastic solids; 6. Classical fluids; 7. Geophysical fluid dynamics; 8. Computation in continuum mechanics; 9. Nonlinearity in the Earth; References; Index.

William I. Newman is a Professor in the Department of Earth and Space Sciences as well as the Departments of Physics and Astronomy, and Mathematics at the University of California, Los Angeles, where he has taught for over 30 years. A unifying feature of his research is the role of chaos and complexity in nature, in applications ranging from geophysics to astrophysics as well as mathematical, statistical and computational modeling in condensed matter physics, climate dynamics and theoretical biology. Professor Newman is a former member of the Institute for Advanced Study in Princeton, a John Simon Guggenheim Memorial Foundation Fellow and has held appointments as the Stanislaw Ulam Distinguished Scholar at the Center for Nonlinear Studies, Los Alamos National Laboratory and as the Morris Belkin Visiting Professor in Computational and Applied Mathematics at the Weizmann Institute of Science, Israel. For six months he also worked with colleagues in the Russian Academy of Sciences in Moscow on modeling earthquake events. He has served in an editorial capacity for the Journal of Geophysical Research and Nonlinear Processes in Geophysics and has held elective office as chair of the Division of Dynamical Astronomy of the American Astronomical Society.