A Graduate Student's Persepective on designing a nonlinear dynamics course for geoscience

Paul Riley, University of Wisconsin - Madison

I am coming into this conference from a slightly different angle than most of the participants: I am still a graduate student who has not yet taught a course on nonlinear, dynamic systems. My research centers around how fractures self-organize into recognizable patterns, with an emphasis on developing methodologies to quantify said organization. I greatly enjoy not only my research, but also the fundamental theory behind my research (i.e., what exactly is a self-organizing system). I am admittedly biased from my research, but I believe that a greater understanding of how patterns exist in the natural world can be done through a course on nonlinear dynamics in the geosciences. Although I have taken mathematics courses on nonlinear systems, I have not had the chance to see how the topic is approached in geoscience classes. My involvement in this conference is based on the premise that I hope to teach such a course in the near future.

Nonlinear dynamics includes the fields of fractal analysis, chaos theory, and self-organization (Baas, 2002). Largely, applications in the geosciences have been in the field of hydrology (see Sivakumar (2000) for a complete review) and geomorphology (e.g. Sapozhnikov et al., 1998; Baas, 2002), but also include stylolite spacing/agate banding (Wang and Merino, 1990; Merino, 1992), stick-slip fault behavior (Feder and Feder, 1991), plate organization (Anderson, 1999), and biogeochemistry. My research suggests an applicability to fracture organization, as well. Thus, nonlinear dynamics covers a diverse suite of topics within the geosciences. Consequently, teaching this subject should require a knowledge about the range in nonlinear dynamical geoscience systems. A problem arises when we, as researchers, center too much on topics of our own interest, and ignore the range of topics that may be of interest to a diverse student body. I am interested in learning how others have approached teaching topics in nonlinear dynamics that are outside their realm of expertise.

Despite the range of nonlinear dynamical systems that exist in the geosciences, understanding the fundamental theory of self-organizing and chaotic systems should be a unifying theme of courses teaching these topics. Whether this is through cellular automata models, observing changes in a predator-prey model, or through hands-on construction of a fractal pattern, I believe there should be some basic knowledge that students should possess upon completion of any nonlinear dynamics course. I am interested to see what teaching methods instructors have used to address the fundamentals of nonlinear dynamical systems.

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