Instructor: W. Horsthemke, FOSC 313
Last updated November 20, 2013
For complete information about this class, please consult the First-Day Handout in the Handouts section below.
This course covers transport and chemical kinetics, with special
emphasis on temporal and spatial pattern formation in nonlinear
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 the last 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.
Handouts are available in Adobe's Portable Document Format (PDF).
First Day: First-Day Handout (Syllabus) AdvPChemhndout2013.pdf
Set 1: Review of elementary kinetics (Atkins 9th ed.; Chap. 21: 21.1 – 21.7, Chap 23: 23.2(a),
Set 2: Transport processes: Molecules in motion (Atkins 9th ed.; Chap. 20: 20.1 – 20.4, 20.8 – 20.11) AdvPChemSet2.pdf
Set 3: History of nonlinear chemical phenomena AdvPChemSet3.pdf
Set 4: Well-stirred reactors I (bistability): One-variable pool chemical models – Schlögl model I, Schlögl model II, Verhulst model AdvPChemSet4.pdf
Set 5: Well-stirred reactors II (oscillations): Two-variable pool chemical models – Lotka-Volterra model, Brusselator AdvPChemSet5.pdf
Set 6.Well-stirred reactors III (bistability, oscillations): Two-variable CSTR model – Gray-Scott model AdvPChemSet6.pdf
Set 7. Well-stirred reactors IV (models of oscillating reactions): Oregonator model of the Belousov-Zhabotinsky reaction; Lengyel-Epstein model of the chlorite-iodide malonic acid reaction and chlorine dioxide-iodine-malonic acid reaction AdvPChemSet7.pdf
Set 8. Reaction-diffusion systems: Turing instability; front propagation AdvPChemSet8.pdf
John Pojman's site Nonlinear Chemical Dynamics Movies: Links to various movies about nonlinear phenomena. Special Feature: The complete version, all 20 minutes, of the wonderful movie "Never Say Never" about the history of the BZ reaction produced by Moscow State Television in 1982 (dubbed in English).
Brandeis group: Various movies of pattern formation in reaction-diffusion systems.
Ray Kapral, U. Toronto: Pattern Formation in the Sel'kov Model.
Aric Hagberg's website at The Center for Nonlinear Studies at Los Alamos: animations of numerical simulations of various phenomena in reaction-diffusion systems.
Some good introductory articles are:
R is not only a powerful environment for statistical analysis and graphing data, it also provides a high-level programming language for scientific computing. R is an excellent tool for solving kinetic rate equations and for modeling nonlinear chemical systems. R is open source and is available free-of-charge for all three major platforms: Macintosh, Windows, and Linux.
1. Download and install the appropriate R binary from The Comprehensive R Archive Network (CRAN).
2. Download and install the free and open-source front end RStudio, a powerful editor and superb integrated development environment for R.
3. The R binary installs only the base system. To solve kinetic rate equations and to model nonlinear phenomena in chemistry, biology, ecology, etc., you need to install additional packages using the R application. Go to the menu item "Packages," and click "Install package(s)." The wording of the menu items may differ slightly, depending on the platform and version. Make sure that "Install dependencies" is checked. You can also use RStudio to install packages. Do not download package binaries directly from CRAN using the package URL provided below.
Useful Packages for Chemical Kinetics and Nonlinear Dynamics:
Literature for Scientific Computing and Mathematical Modeling with R: