Project Title: Periodic Cellular Automata

Project Description:

The project is to study almost periodic cellular automata which can be used to simulate, among other things, fluids in almost periodic media. The subject has been initiated by A. Hof (McMaster University) and myself during summer 1994. We met many open questions. One exciting thing is that we can evolve infinite aperiodic fluid configurations which obstacles in any dimension with finitely many data.

Nature of the work:

  1. Since we want to show that this scheme is of practical value in hydrodynamical problems, this SURF project emphases on experimental and computational work simulating fluids (we have done already simulations with Mathematica but would like to see fast simulations for 2D or 3D fluids).
  2. Literature work and interaction with other divisions at Caltech. What problems in hydrodynamics, earth sciences, astrophysics can be treated better with this method.
  3. The project is concerned with pure mathematical and physical problems in the domain of topological dynamics and/or percolation theory and/or spectral theory of dynamical systems and/or turbulence in fluid mechanics and/or statistical mechanics of particle systems.

Background Information:

Simulation of a 3D FLUIDS with discrete elements is CPU-time and memory consuming. The same problems have also lattice gas automata, special cellular automata designed for fluid dynamics. Having a lattice of 1000 X 1000 X 1000 grids needs already giga bytes of data in order to store only one configuration. We have shown in (Hof-Knill) that defining configurations with few data and allows efficient processing over reasonable time.

Requirements:

The sponsor requires that interested students meet the following requirements: Good experience in a fast language like C for Fortran. Preknowledge in cynamical systems and/or fluid dynamics is helpful. Important is mathematical and physical interest and the ability to do careful experimental work in an exciting domain.

This opportunity is for:

Caltech students only

Research Sponsor

Sponsor: Oliver Knill
Division: PMA
Mail Code: 253-37
Phone: 4325
E-mail: knill@cco.caltech.edu