| schedule: | Mo, We: 16:00 - 17:15 @ GMCS-307 |
| Instructor: | Dr. Ricardo Carretero | ||
| Lectures: |
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| Office Hours: | Mo, We: 12:00 - 1:00 @ GMCS-577 (or by appointment) | ||
| E-mail: |
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Word format of this sullabus: [ doc ]
Important dates:
Wed, Sep. 03: First lecture.
Mon, Sep. 22: Last day to adjust schedule (adds, drops, etc.)
Wed, Nov. 05: Last day to form project teams and choose project.
Wed, Dec. 10: Last lecture: project presentations.
Mon, Dec. 15: Project presentations (15:30-17:30)
Top: Pattern on a cone snail shell created by accretion of calcified material as the shell matures. Bottom: Cellular automaton model (coupled cell dynamics) recreating the shell pattern structure. For more pictures of cone snails click here. Description:
Ever wondered what are the mechanisms behind the pattern formation of the intricate and beautiful patterns in zebras, leopards, fish, shells, etc.? What is behind the structure of convection cells in burners, mixed fluids, liquid crystals and the Sun's atmosphere? Amazingly, the trigger for different families of patterns in a wide range of disciplines such as Biology, Chemistry and Physics, can be traced down to relatively simple mathematical models. This course aims to give the basis for the study of pattern formation using spatio-temporal models. Examples from Physics, Chemistry and Biology will motivate the mathematical models and theory. Audience: The course is intended for senior undergra-duate and graduate students in Mathematics, Computational Science, Engineering, Physics, Chemistry, Biology, etc. Examples from interdisciplinary areas will be covered. Most of the concepts and examples will be supplemented with Matlab-based codes. As part of the course, students will be given access to a computer laboratory to complete the computer-based coursework. A final project, based on individual interests, accompanied with an oral presentation will be required.
This course forms part of the MS in Applied Mathematics with concentration in Dynamical Systems offered by the Nonlinear Dynamical Systems (NLDS) group. For detailed information about this program visit: http://nlds.sdsu.edu/ [Graduate Programs] [MS]
Textbooks:
- Spatio-temporal Pattern Formation, with examples from Physics, Chemistry, and Material Science. D. Walgraef, Springer 1996.
- A New Kind of Science, S. Wolfram, Wolfram, 2002.
- Additional material will be drawn from several reference books and journal articles.
Prerequisites:
Good knowledge of Calculus is the minimum requirement. Familiarity with elementary Differential Equations and Linear Algebra is desirable. Computer experience is also desirable.
Topics to be covered:
Linear stability, Rayleigh-Bérnard, Cross-Hohenberg classification. One dimensional patterns, bifurcations, Ginzburg-Landau. Two dimensional patterns, Newell-Whitehead-Segel equation, multiple scales, square and hexagonal patterns, defects. Swift-Hohenberg, complex Ginzburg Landau and Kuramoto-Sivashinsky equations. Spatio-temporal chaos. Granular systems.
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