ffmSlice

This repository holds the Matlab/Octave scripts which were used in the in-slice integration of the Kuramoto-Sivashinsky system in Budanur et al. (2014).

Quick start

In order to test the code on your system, start a Matlab or Octave instance in ffmSice/scripts/ and run ks_statesp_red or ks_statesp_full. When runs, ks_statesp_red and ks_statesp_full produces Matlab/Octave-equivalents of Figure 2 b and Figure 2 a of Budanur et al. (2014) respectively.

Tested on

Octave 3.8.1, and Matlab R2013b

File descriptions

ffmSlice/scripts/

• Lg.m : SO(2) generator

• LieEl.m : SO(2) element

• SliceCond.m : Slice condition

• slicep.m : Slice fixing point (0,1,0,0,...)

• vel.m : Velocity function in real representation

• vksred.m : Reduced velocity function in real representation

• gradV.m : KS stability matrix in real representation

• gradVred.m : KS reduced stability matrix

• ksETDRK4.m : KS solver in full state space

• ksETDRK4red.m : KS solver in the first-mode slice

• ks_statesp_red.m : Computes the unstable manifold of TW_1 on the first Fourie mode slice, and plots it on a state space projection along with TW_2, and RPO_{33.50} (arXiv: 1405.1096, Fig 2.b).

• ks_statesp_full.m : Same with ks_statesp_red.m, but trajectories are computed in the full state space, in addition, group orbits of TW_1 and TW_2 are drawn (arXiv: 1405.1096, Fig 2.a).

ffmSlice/docs/

• docSlice.tex: Latex document which explains implementation details of the in-slice integration of Kuramoto-Sivashinsky system. pdflatex docSlice

• def.tex: Definitions used in docSlice.tex

License

MIT license

Copyright (c) 2014 Nazmi Burak Budanur, http://cns.physics.gatech.edu/~burak