Nonlinear Physics: Modeling Chaos and Complexity

Announcements:

• Project materials DUE 5 PM Tuesday 8 June.
• Materials: Project Presentation (PDF), Project Report (PDF), and running(!) Python Code (Please zip components into a single compressed file).
• Send email to Prof. Crutchfield at ``chaos at ucdavis.edu'' with the materials attached or with a URL to website from which they can be downloaded.

Instructor: Professor Jim Crutchfield (Physics and CSC)
Assistant: Benny Brown
WWW: http://csc.ucdavis.edu/~chaos/courses/nlp/

Upper Division catalog number: Physics 150, Special Topics (CRN 76103)
Units: 4
Graduate catalog number: Physics 250 Section 4, Special Topics (CRN 83105)
Units: 3
Times and Locations:
Tu 0210-0330 PM: 185 Physics
Th 0210-0330 PM: 2118 Mathematical Sciences Building
Office hours:
Crutchfield: Wed 0300-0400 PM, 1109 MSB
Brown: Tu 0100-0200 PM, 1106 MSB

Poster: [JPG].

This is a course on computational science methods. The goal is for you to learn how to build powerful computing tools that help you do science.

The course explores the origins of intrinsic unpredictability (deterministic chaos) and the emergence of structure (self-organization) in natural complex systems. This will be developed using dynamical systems theory and focus on analyzing periodic and chaotic behaviors and bifurcations between them. In addition to this physics track, the parallel theme is constructing exploration tools for nonlinear processes. That is, in addition to developing the mathematics of qualitative dynamics, this is also a practical class. Students will design and build interactive tools for simulating and visualizing complex systems using Python. We will also make a field trip to the KeckCAVES sensory immersive visualization lab (keckcaves.org).

Outline: (Course Syllabus [PDF] [HTML] )

• Weeks 1-2: Qualitative Dynamics
• Weeks 3-4: Bifurcations
• Weeks 5-8: Visualizing and Quantifying Unpredictability
• Weeks 9-end: Projects.

Complex systems to be analyzed:

• Low-dimensional chaos and routes to chaos
• Spatially extended systems, as time and interest permit

Audience: Upper division undergraduates and graduate students in physics, mathematics, computer science, engineering, mathematical biology, and theoretical neuroscience. Others also welcome. Please see the Prerequisites in the syllabus linked above.

Reference materials:

• Books:
  • Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, S. H. Strogatz, Second Edition, Addison-Wesley, Reading, Massachusetts (2001).
  • Learning Python, M. Lutz, Fourth Edition, O'Reilly Media, New York (2009). This edition covers Python 2.6 and Python 3.X. We'll use Python 2.6 in the course. An electronic version is on reserve at the library. Go there, select Course Reserves Catalog. Select Instructor, enter Crutchfield. This will bring up a page with a link to the electronic version.
• Lecture Notes on Dynamics.
• Python Programming Labs.
• Python Installation.
• Computing Tutorials.
• Nonlinear Physics Reader.
• Supplemental Readings for reference documents, historical background, projects, programming, and amusement.
• Supplemental Software Tools.

Course Work (Grading):

1. Class Accounts:
   • Set up your account on the math computing lab machines here, using course number 998Z.
   • Those with existing Math department accounts need not get a separate one to use the lab.
2. Weekly Assigned Readings.
3. Weekly Problem Sets: Dynamics (30%) and Python Programming (30%).
4. Research Project: 40%.