Depinning Olympics [paper and game!]

A one dimensional elastic string driven by a uniform force in a random medium is a minimal model for a field driven domain wall in a large family of thin-film ferromagnetic materials. 

The motion of the elastic string at zero temperature is characterized by a depinning threshold fc, such that if the driving is f<fc the string is blocked after a transient, while for f>fc it slides and never stops, acquiring a well defined and finite steady-state average velocity.

At finite temperature, thermal activation allows the string to have a finite average velocity at all finite driving forces however.

As a result, the mean velocity is an interesting function v(T,f) which presents a creep regime for f<fc, a depinning region for f>~fc, and a flow regime for f>>fc. The depinning transition was recently characterized experimentally by L. J. Albornoz et al. in thin-film ferrimagnets at very low temperatures.

Now it is your turn to find a depinning transition!

The applet below numerically simulates the motion of the elastic string with quenched disorder (not shown) and lets you adjust the temperature T and the uniform driving force f. We challenge you to find the best approximation to the sample critical threshold fc. Put your best value in the comments and compete for a medal!

Once you get fc it is nice to appreciate the roughness change of the string as you approach it. This geometrical change is well described in average by a correlation length which diverges at we approach fc from above, and it is related with the typical size of the "avalanches" (large rearrangements between almost blocked configurations). 

If you did a good effort to calculate fc you may appreciate that it is a difficult and delicate task, due to the slowing down as you approach it. This is a serious difficulty for large systems! Fortunately, we have at our disposal a very efficient numerical method, which succeeds by avoiding solving the actual dynamics. Similarly, efficient numerical methods exist for tackling the ultra-slow creep dynamics.