Physics 313 Course Syllabus

Fall Semester, 2008

Professor Henry Greenside

Welcome

The topics discussed in this course differ from year to year with the instructor. This year (2008), the course will follow closely chapters in a forthcoming textbook Pattern Formation and Dynamics of Nonequilibrium Systems by M. Cross and H. Greenside, and will also discuss some of the science and mathematics associated with networks. Some goals of the course will be the following:

1. To study some experiments that represent significant broadly applicable insights about pattern formation and spatiotemporal dynamics. We will discuss experiments on fluid systems, chemical reaction-diffusion systems and excitable media such as heart tissue.

2. To learn some mathematical theory and techniques for analyzing pattern-forming systems: linear stability methods, amplitude equations, Lyapunov spectra, and correlation functions.

3. To study the derivation and analysis of simplified mathematical models (partial differential equations and coupled map lattices) that help to develop intuition and to make quantitative predictions concerning pattern formation.

4. To understand some of the recent advances in understanding networks: their empirical structure and how the structure of a network affects the overall dynamics when the nodes are dynamical systems.

Prerequisites

Occasionally you will need to run (and perhaps to modify) simple computer programs in Mathematica or a similar high-level language.

Please talk with me at the beginning of the semester if you have any questions about whether your background is adequate for Physics 313.

Time and Place

Changes in the class schedule will be posted on the Announcements section of the 313 home page, which you should bookmark and look at before each class.

Office Hours

To set up a meeting, you can send e-mail to the address hsg@phy.duke.edu or call me at my office number 660-2548.

Feel free to send me e-mail at any time. I am often logged on in the evenings and on the weekends and will be glad to discuss the course or homework with you.

Computer Accounts

Lectures and homework assignments will be available respectively through the URLs Lectures and Assignments while class-related files such as data sets, computer code, and multimedia will be made available through the the Miscellaneous Files link from the 313 home page. Copyrighted restricted files will be available through the URL Protected Files.

Grading

There is no final examination.

As is appropriate for a 300-level research seminar, the emphasis will be on discussion and critical thinking rather than the lecture-homework-exam format of an undergraduate class. Given this, your active class participation throughout the semester will be essential. You will occasionally be asked to go to the blackboard to sketch or to work out some argument, you will be challenged in class to defend your thinking by appropriate reasoning or by references to material covered in the lectures and reading.

I expect all members of the class to read and to think about the assigned material before lecture and to come prepared to ask questions and to discuss the material in class. If you don't understand something during lecture or from the assigned reading, please don't be shy, ask questions! If something catches your interest and you want to learn more, ask questions. Talking with me outside of lecture is also one way to participate in class. I want to see evidence of your actively trying to learn about the course material.

You are allowed to collaborate on the homework assignments (this is realistic, scientists collaborate all the time in research) but as much as possible you should attempt the assignments on your own since you will learn the most that way. Whether or not you collaborate, you must write up your homework on your own, in your own words, and with your own understanding. You must also acknowledge explicitly at the beginning of your homework anyone who gave you substantial help, e.g., classmates, myself, or other people. (Again, scientists usually acknowledge in their published articles colleagues that helped to carry out the research.) Failure to write your homeworks in your own words and failure to acknowledge help when given can lead to severe academic penalties so please play by the rules.

Your main two goals in writing up your homework are to be clear (so that I can understand what you have written) and to demonstrate insight. Writing clearly means using readable handwriting. You should avoid tiny script and avoid trying to cram many sentences and equations onto a single page. Leave plenty of space between symbols and between lines of equations and leave plenty of space between the ending of one homework problem and the beginning of the next. Spread your answer out over many pages if necessary; paper is cheap compared to your time to complete the assignments and compared to my time to grade your assignments.

Demonstrating insight means using complete sentences that explain what you are doing and why (e.g., as you proceed with some mathematical derivation). Cryptic brief answers like ``yes'', ``no'', ``24'', or ``f(x)'' will not be given credit. Your homework must show that you understand how you got your answer and that you appreciate the significance of your answer. A well-written complete answer is one that you will be able to understand yourself a month after you have written the answer, even if you don't remember the original question.

Please pay attention to details as you write your assignments. All symbols should be given names the first time you introduce them, e.g., say ``the momentum p'' or ``the flux F'' instead of just using the symbols p and F. Physical units should be given for any answer that is a physical quantity, e.g., say ``the angular momentum was A=0.02 J-sec'' or ``the angle was µ=0.32 radians.'' Numerical answers should have the minimum number of significant digits that is consistent with the given data. For example, if you have a product or ratio of numbers of which the least accurate number has two significant digits, the final answer should have only two significant digits. Graphs should have their axes clearly labeled by the corresponding variables and by the variables' physical units. Each graph should have a title that explains the graph's purpose. A good way to learn how to write effectively is to imitate the style of published articles, e.g., those published in Physical Review Letters .

If you write a computer program to obtain answers for an assignment, please include a copy of the program with that assignment.

Late homeworks are not accepted. If you think you will not be able to hand in your homework by its due date, please get in touch with me as soon as possible---at least three days before the due date---and explain what the situation is.

References

The following are supplementary references. Easier references are:

• The Self-Made Tapestry: Pattern Formation in Nature by Philip Ball (Oxford U. Press, 1999). A non-technical and pictorial survey of recent advances in pattern formation, perhaps the best first book to learn about pattern-forming systems. A review of this book is available here.

• Mathematical Models In Biology by Leah Edelstein-Keshet (Random House, 1988). An excellent pedagogical book that discusses the mathematics of pattern formation from a biologist's point of view. The book is somewhat more elementary than the level of this course but good supplementary reading, especially for those who want to see a clear detailed discussion and motivation of topics such as linear stability and diffusion.

• Fearful Symmetry: Is God a Geometer? by Ian Stewart and Martin Golubitsky (Penguin Books, England, 1992). A non-technical paperback that gives an entertaining and insightful discussion about symmetry breaking, with an emphasis on nonequilibrium systems.

• Pattern Formation Outside of Equilibrium by Michael Cross and Pierre Hohenberg, Reviews of Modern Physics, Volume 65(3):851--1112 (1993). A remarkably broad and deep survey of the pattern formation literature as of 1993. An excellent place to look for connections to experiments and further examples and applications of pattern formation.

• An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos by Irving R. Epstein and John A. Pojman (Oxford U. Press, New York, 1998). A pedagogical graduate-level book on pattern formation and dynamics of chemical systems. Has recipes for experiments to try out.

• Chaos in Dynamical Systems by Edward Ott (Cambridge University Press, 1993). This is an advanced discussion of chaos theory, with many explicit examples worked out with impressive insight.

• Physical Fluid Dynamics, Second Edition by D. J. Tritton (Oxford, 1988). A gentle and enjoyable introduction to fluid dynamics. Students with no prior knowledge of fluid dynamics will want to look here first.

• Fluid Mechanics, Second Edition by L. D. Landau and E. M. Lifshitz (Pergamon Press, 1987). A definitive and classic (but challenging) reference on fluid dynamics, written from a physicist's point of view.

• Practical Numerical Algorithms for Chaotic Systems by T. S. Parker and L. O. Chua (Springer-Verlag, 1989). Discusses numerical methods for analyzing nonlinear dynamical systems, although primarily for lower-dimensional ones.

• Principles of Condensed Matter Physics by P. M. Chaikin and T. C. Lubensky (Cambridge University Press, 1995). Explains how condensed matter physicists have learned to think about many equilibrium systems and their phase transitions. This style of thinking has strongly influenced many areas of nonequilibrium physics research.