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Thermal activation

Hereby results with the "old" SCPM model can be found for thermal activation.

Paramters

The simulations share the following paramters:

The flowstress-distribution was exponential, with average 1
the left and right flowstresses were the same
left and right movements were thermally activated; if a site with positive tau_sc ( = tau_int + tau_ext) is activated thermally, then it creates a positive deformation, and negative otherwise
the propability that a cell is activated is $P_{\to} + P_{\leftarrow} = \frac{e^{- β (τ_{f} - τ_{s c})} + e^{- β (τ_{f} + τ_{s c})}}{Z},$ where Z is the sum of the nominator over all the cells.
Simulation size: 256 x 256

Differences were:

the applied plastic strain have or don't have upper limit (limited_1 or max deformation)
the beta paramater in the propability (1 or 10)
the applied constant external stress

Stress strain curve (not thermal)

Without thermal activation, the external stress was increased from 0, and the increasement was stopped during an avalanche. This curve is to illustrate the stress and strain values.

Strain - step curve (thermal)

For the thermally activated simulations, the strain - step curves are plotted. An upper limit for the strain and for the step are set. For the "max deformation" simulations, the inital strain value is higher, but the slopes seem to be the same.

Z decreasement (thermal)

It could be interesting, how Z decreases. Because the average of the flow stress is increasing (even chosing from the same distribution), Z decreases too at even 0 external stress. The lower the temperature is, the faster the curve tends to 0.

Avalanche size distribution (not thermal and thermal)

The main reason to introduce unlimited strain size was to eliminate the peaks in the avalanche size distibutions at the multiple values of the strain unit. At simulations limited_1, note the peak at avalanche size 1 for example. The size distribution has no lower-limit, as the local stress can be arbitrary small, and strain in chose in such a way to decrease the stress to 0.

For not thermally activated simulations, it seems that the exponent rather tends to -1.3. For thermally activated simulations, go further.

For thermally activated simulations, when the deformation is limited, the size distribution is not useful:

The picture is better for "max deformation", especially for higher temperature values. Simulations with beta = 0.1 is on the way.