Both Caltech and Non-Caltech students will be considered

Project Title:

Analysis of Patterns in Spatiotemporal Chaos

Project Description:

The project is to analyse the structure of the patterns occurring in systems showing spatiotemporal chaos i.e. complexity in both spatial structure and temporal dynamics, in particular experimental systems and numerical models showing "stripe" phases (e.g. Rayleigh-Benard convection and models thereof). The project will be to develop methods to quantify the visual appearance of the patterns, in particular the defect structures such as spirals or dislocations, and the large scale morphology. Methods to be used may include spectral filtering, empirical projection, and pursuing analogies with finger-print characterization. The project will involve analytic development of the methodology and numerical implementation.

Background Information:

Although chaos - the complex time dynamics in simple dynamical systems - is now quite well undertood, the complex dynamics of systems with many dynamical degrees of freedom developing rich spatial structures (spatiotemporal chaos) is much less well understood. There are many laboratory experiments, and potential applications to widespread phenomena, such as the atmosphere, structures in materials, non-linear optics and others. A major problem is the quantitative characterization of the dynamical spatial patterns. This project aims to develop tools to do this.

Literature references or articles that may provide more information on the project:

http://www.cco.caltech.edu/~mcc/Science, 263, 1569 (1994 Mar 18) Rev. Mod. Phys. 65, 851 (1993)

Requirements (skills, specific coursework, academic major, year in school, etc.):

The student should be comfortable with either C or Fortran, and know what a Fourier transform is.

Research Sponsor Name: Michael Cross
E-Mail: mcc@styx.caltech.edu
Division: Physics, Mathematics and Astronomy
Telephone: (818) 395-4320
Address: M/C 114-36

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