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Studies on phase-transitions in the reaction-diffusion layer

Context

We study the robstness of the phase transition that occurs in a stochastic Greenberg-Hastings CA. We are interested in finding how the critical transmission probability varies when changing the model: introducing defects in the topology (MLR and HR), lenghtening the refractory period M.

Numerical Results with "classical" computing devices

Changing the value of M
HR MLR TOPO Mval L pTc plot
0 0 TV4 2 800 0.4246 open plot
0 0 TV4 3 800 0.4246 open plot
0 0 TV4 4 400 0.4600 open plot
0 0 TV4 5 800 0.4600 open plot
0 0 TV4 6 800 0.4775 open plot
0 0 TV4 7 800 0.4775 open plot
0 0 TV4 8 800 0.4879 open plot
0 0 TV4 9 800 0.4879 open plot
0 0 TV4 10 800 0.4947 open plot


Adding Missing links
HR MLR TOPO Mval L pTc plot
0 0 TV4 4 400 0.4600 open plot
0 10 TV4 4 800 0.5051 open plot
0 20 TV4 4 800 0.5605 open plot
0 30 TV4 4 400 0.6308 open plot
0 40 TV4 4 1200 0.721 open plot


Adding Holes
HR MLR TOPO Mval L pTc plot
0 0 TV4 4 400 0.4600 open plot
10 0 TV4 4 800 0.5155 open plot
20 0 TV4 4 800 0.5876 open plot
30 0 TV4 4 800 0.685 open plot
40 0 TV4 4 1200 0.824 open plot


Varying the topology
HR MLR TOPO Mval L pTc plot
0 0 THX 2 800 0.2740 open plot
0 0 THX 3 800 0.2965 open plot
0 0 THX 4 800 0.3110 open plot
0 0 THX 5 800 0.3205 open plot
0 0 THX 6 800 0.3272 open plot
0 0 THX 7 800 0.3322 open plot


HR MLR TOPO Mval L pTc plot
0 0 TM8 4 400 0.2300 open plot
0 0 TM8 5 400 0.2375 open plot
0 0 TCI1 4 800 0.7833 open plot
0 0 TCI2 4 800 0.1484 open plot
0 0 TCI3 4 800 0.0602 open plot
0 0 TCI4 4 800 0.03265 open plot
0 0 TCI5 4 800 0.0206 open plot


Different topology, same results
HR MLR TOPO Mval L pTc plot
0 0 TV5 4 800 0.4600 open plot
0 0 FV4 4 800 0.4602 open plot
0 0 FM8 4 800 0.2299 open plot
0 0 TM9 4 800 0.2297 open plot


Other Topologies, with errors
HR MLR TOPO Mval L pTc plot
0 10 THX 4 400 0.3420 open plot
0 10 TM8 4 400 0.2519 open plot


Topology codes : V4 = 4-von Neumann, M8 = 8-Moore, HX = 6-Hexagonal, CI = circular

Numerical Results with FPGA

TOPO M plot
T4 2 Click to open the plot
T4 3 Click to open the plot
T4 4 Click to open the plot
T4 5 Click to open the plot
T4 6 Click to open the plot
T4 7 Click to open the plot
T4 8 Click to open the plot
T4 9 Click to open the plot
T4 10 Click to open the plot
T4 11 Click to open the plot
T4 12 Click to open the plot
T4 13 Click to open the plot
T4 14 Click to open the plot
TOPO M plot
T8 2 Click to open the plot
T8 3 Click to open the plot
T8 4 Click to open the plot
T8 5 Click to open the plot
T8 6 Click to open the plot
T8 7 Click to open the plot
T8 8 Click to open the plot
T8 9 Click to open the plot
T8 10 Click to open the plot
T8 12 Click to open the plot
T8 14 Click to open the plot

Last Update : July 2010