Modeling environmental complexity

Lectures: 2 sessions / week, 1.5 hours / session

Students should have completed 18.03SC Differential Equations or its equivalent and have some familiarity with partial differential equations.

This course provides an introduction to the study of environmental phenomena that exhibit both organized structure and wide variability—i.e., complexity. Emphasis is on the development of quantitative theoretical models, with special attention given to macroscopic continuum or statistical descriptions of microscopic dynamics. Concepts and problems include the microdynamics and macrodynamics of random walks and fluid flow; extreme deviations and anomalous diffusion; geological and ecological networks; percolation theory; dynamical origin of fractals and scale invariance; the origin and complex kinetics of biogeochemical cycles.

Through focused study of a variety of physical, biological, and chemical problems in conjunction with theoretical models, students learn a series of lessons with wide applicability to understanding the structure and organization of the natural world. Such lessons include: How complexity can derive from simple dynamics; why fractals are ubiquitous in the natural world; and generic consequences of complex biogeochemical kinetics. Students will also acquire specific skills, including: The statistical analysis of data with wide variability; how to use computer simulations to reveal fundamental phenomena; and how to construct a minimal model of a complex system that provides informative answers to precise questions. A unifying theme is the relation of macroscopic complexity to microscopic dynamics.

There are 3 project-oriented problem sets. A final, independent project on a topic of the student's choice is due at the end of the term, including a written report and an oral presentation. There is no exam.

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