This IMA Volume in Mathematics and its Applications CHAOTIC PROCESSES IN THE GEOLOGICAL SCIENCES is based on the proceedings of a workshop which was an integral part of the 1989- 90 IMA program on "Dynamical Systems and their Applications". The workshop was intended to be an arena for scientific exchanges between earth scientists and mathematical researchers, especially with experts in dynamical systems. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell and David Yuen for organizing the meeting. We especially thank David Yuen for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the Minnesota Supercomputer Institute, the National Science Foundation, and the Office of Naval Research. A vner Friedman Willard Miller, Jr. PREFACE The problems in geological sciences have many nonlinearities from the nature of the complicated physical laws which give rise to strongly chaotic behavior. Foremost and most visible are earthquakes and volcanic eruptions, more subtle are the time dependent variations of the Earth's magnetic fields and motions of the surface plates.

Klappentext

The subject matter of chaos and nonlinear dynamics has begun to spread to the geological sciences in the last several years. The articles in this book are from a workshop held at the University of Minnesota in June 1990 in which well-renowned geophysicists, geologists and applied mathematicians were in attendance. There were three areas of focus in the workshop: thermal convection as applied to the earth's mantle, magmatic dynamics and processes in geodynamo. The nonlinear nature of convection was discussed especially in light of recent advances made in the physics community of the phenomenon of hard-turbulent convection. This book is useful for graduate students and researchers in geophysics, applied mechanics, and applied mathematics. It should also be of interest to workers in other areas of thermal convection.

Inhalt
Turbulent thermal convection.- Spherical symmetry-breaking bifurcations and thermal convection in the earth's mantle.- Convection and chaos.- Strongly chaotic Newtonian and non-Newtonian mantle convection.- Routes to chaos in the solid earth.- Mantle phase transitions, layered chaotic convection and the viscosity of the deep mantle.- Vigorous motions in magma chambers and lava lakes.- The eruption and spreading of lava.- Modeling transport processes in nonlinear systems: The example of solidification and convection.- Convection in porous media with thermal and chemical buoyancy: A comparison of two models for solute dispersion.- Dynamo theory.- Theory of the geodynamo and core-mantle coupling.- Nonlinear dynamical models for earthquakes and frictional sliding.- The spatial structure of isotropic turbulence and the related three-dimensional graphics problems.- Other titles and abstracts.