Time: ARR
Instructor: W. Horsthemke, FOSC 313
Last updated January 11, 2006
For complete information about this class, please consult the First-Day Handout in the Handouts section below.
Course Description:
This course covers transport and chemical kinetics, with special
emphasis on temporal and spatial pattern formation in nonlinear
chemical systems.
The class will acquaint students with the basic theoretical ideas
and experimental tools of chemical pattern formation.
Background: Patterns are ubiquitous in nature, ranging from the spiral structure of galaxies to banded rocks to the stripes of the zebra to the one-cellular algae Acetabularia. Though temporal and spatial patterns in chemistry were sporadically reported in the literature during the first half of this century, the field of chemical pattern formation only took off in 1968. At a conference in Prague that year, the work of Belousov and Zhabotinskii on oscillating chemical reactions, done in Moscow in the fifties and early sixties, became widely known to western scientists. It was realized at that time that their work could be understood in the framework of dissipative structures, whose theory was being developed by the Brussels school. Also, Turing's seminal 1952 article "The Chemical Basis of Morphogenesis" was "rediscovered". In this work, Turing proposed a theory of chemical spatial pattern formation and its application to biological patterns. The field of oscillating reactions received a further boost in 1972, when Noyes and coworkers at the University of Oregon elucidated the chemical mechanism of the Belousov-Zhabotinskii reaction. In the mid-seventies, the Bordeaux group pioneered the use of the CSTR (continuous-flow stirred tank reactor) for the study of chemical oscillations and chaos. This tool has become an invaluable device in the field of oscillatory reactions. Then in the early eighties, Epstein, De Kepper, and coworkers at Brandeis University discovered systematic ways to design new oscillating chemical reactions. In 1987, the Austin group developed the CFUR (continuous-flow unstirred reactor) as the spatial analogue to the CSTR. Chemical patterns persist in a CFUR as long as the feed of the reactor is maintained. Turing patterns, stationary spatial chemical patterns, were first observed in a CFUR in 1990 by the Bordeaux group.
The course will begin with a four week review of Chemical Kinetics and students will attend CHEM 6114 Chemical Kinetics.
Handouts are available in Adobe's Portable Document Format (PDF).
First Day: First-Day Handout (Syllabus) AdvPChemhndout2006.pdf
Visit the Picture Gallery of the Nonlinear Dynamics Group at the University of Leeds to see pictures of spatial patterns in the Belousov-Zhabotinskii reaction.
Visit Aric Hagberg's website at The Center for Nonlinear Studies at Los Alamos for animations of reaction-diffusion patterns.
Some good introductory articles are: