Simulation data for toppling and height probabilities in sandpiles

Data collection method:

This dataset contains simulation data in 2d, 3d, 5d, and 32d in folders named sandpile_data_xd. In 2d, we simulate the sandpile model in a box size of 2L x 2L both with periodic boundary conditions for systems with L = 512, 1024, 2048, and 4096 with sample sizes 2 × 10^7, 1.5 × 10^7, 3 × 10^6, and 7.5 × 10^5, and with Dirichlet boundary conditions for systems with L = 512, 1024, 2048, 4096, and 8192 with sample sizes 6 × 10^7, 3 × 10^7, 7.5 × 10^6, 4 × 10^6, and 10^6, respectively. The characteristics simulated include the toppling probability, the number of waves, and the height probability at the origin. In 3d, we generate the data of the toppling probability with Dirichlet boundary conditions for systems with L = 32, 64, 128, and 256 with sample sizes 8 × 10^7, 2 × 10^7, 4.5 × 10^6, and 4 × 10^6. In 5d, we simulate the toppling probability using hashing in the box with radius L = 32. The number of samples taken was 4 × 10^7, with approximately 400 samples discarded due to a full hashtable. In 32d, we simulate the height probability at the origin using hashing for a system with L = 128 with a sample size 4 × 10^6. We check our results in two ways to confirm that our methods give results consistent with earlier work. One uses the data to agree with some exponents in the earlier work in 2d and 3d. In 2d, the data are in out files called xxxsink-cluster-origin-aaa with L = xxx, and the overall averages are in text files named by s-origin-2d-average and s-distinct-origin-2d-average. In 3d, the data are in out files called 3d-xxxsink-cluster-origin with L =xxx, and the overall averages are in text files called s-origin-3d-average and s-distinct-origin-3d-average. On the other hand, we check that our methods yield the known height probabilities in 2d with L = 4096 in Dirichlet boundary conditions. The data used are in the text files called probability4096sink-aaa, and the overall average height probability is in the text file named probability4096sink-average. The number of samples generated in each file is 5 x 10^4. There are 80 files in total, so the total sample size is 4 x 10^6.