M635 PATTERN FORMATION

SYLLABUS

POLICIES

ASSIGNMENTS

FINAL PROJECTS

COURSE MATERIAL


                    M635 Pattern Formation / Syllabus

Office: GMCS 503
Office Hours: T TH 1PM - 2PM
e-mail: apalacios AT mail.sdsu.edu

Textbook
Pattern Formation. An Introduction to Methods
Author: Rebecca Hoyle
Publisher: Cambridge University Press 2006.


Course Outline

  1. Overview of Pattern-Forming Systems
    • What are natural patterns?
    • Convection
    • Reaction Diffusion Systems
    • Faraday Waves

  2. Mathematical Background
    • Bifurcation theory
    • Normal Forms
    • Bifurcations in Symmetric Systems
    • The Equivariant Branching Lemma

  3. Lattice Patterns
    • Bifurcations on a lattice
    • Roll/stripe solutions
    • The Kuppers-Lortz instability
    • Hopf bifurcation on a lattice






  1. Spatial Modulation
    • Envelope equations
    • Envelope equations and symmetries
    • Free energies
    • Ginzburg-Landau equation
    • Schrodinger equation

  2. Instabilities of Stripes and Travelling Plane Waves
    • Universal instabilities of stripes
    • The Eckhaus instability
    • The zigzag instability
    • Phase dynamics

  3. Selected Topics
    • Defects
    • Dislocation of a roll pattern
    • Spirals
    • Spiral defect chaos

 


References

[1] Pattern Formation and Dynamics in Nonequilibrium Systems. Michael Cross and Henry Greenside
  [2] Mathematical Biology II: Spatial Models and Biomedical Applications. J.D. Murray
  [3] Spatio-temporal Pattern Formation, with examples from Physics, Chemistry, and Material Science. D. Walgraef






Grading Scale
A
90% and above
B
80% and above
C
65% and above
D 55% and above

 

Grading
Homework
45 %
Midterm Exam
30 %
Final Project ( topics )
25 %

 

 





*Note: Exam dates listed above are tentative and will be confirmed in class. The instructor reserves the right to change these dates if considered necessary.

  • Exams, Homework, and Quizzes are considered individual work. Copying someone else work is considered cheating and will be penalized.
  • Quizzes may or may not be announced. If a quiz is given at the beginning of class and you are late, you will not be able to take this quiz earlier.If a quiz is given at the end of the hour, you will not be able to take this quiz earlier.



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