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Stationary coexistence of hexagons and rolls via rigorous computations
J.B. van den Berg, A. Deschênes, J.-P. Lessard and J.D. Mireles James
SIAM Journal on Applied Dynamical Systems, 14 (2), 942–979, 2015
PDF doi:10.1137/140984506 Publication [21]
Files
Codes and data accompanying the paper, reproducing the computer-assisted proofs it reports.
- proofs.zip (93 KB)
proofs/ — 17 files (137 KB)
- 00_read_me (898 B)
- DF_hex.m (4.8 KB)
- DF_hex_int.m (5.2 KB)
- F_hex_int.m (2.7 KB)
- approx_sol_hex2neg_rolls.mat (2.0 KB)
- approx_sol_hex2pos_rolls.mat (2.0 KB)
- convertToPoly_2DTo4D_dual.m (816 B)
- cubic_sumFFT_int.m (873 B)
- hex_aposteriori.m (5.9 KB)
- intval_fft.m (1.7 KB)
- manifolds_hex2neg_rolls.mat (22 KB)
- manifolds_hex2pos_rolls.mat (47 KB)
- matrixNorm.m (231 B)
- proof_hex2neg_rolls.m (20 KB)
- proof_hex2pos_rolls.m (20 KB)
- quadratic_sumFFT.m (280 B)
- quadratic_sumFFT_int.m (705 B)
The scripts are written in MATLAB; the rigorous parts require the interval arithmetic package INTLAB to be installed and started.