Separate Bond Angle Distributions for certain Normalized Force ranges

[andyletzhang]

We see from plots from the summer that forces tend slightly stronger at periodic peaks - forces are angle-dependent (non-isotropic). Following up on this, is the angle distribution force-dependent? Do very strong forces distribute the same way as very weak ones?

[andyletzhang]

Creating the infrastructure to this isn't difficult, but deciding with what values to bin our forces is. My first impulse is to divide into a few logarithmic bins between the minimum and maximum value:

We see the orange (medium force) bin regularly sandwiched between the outer bins, which suggests some meaningful trend. We're seeing a slight increase in peak strength for strong forces (which tend to involve pins), so let's add some more bins to isolate the strong forces:

The trend holds up pretty well over five bins. Forces larger than 8 clearly belong to unusually strong force chains, and what we see here is that these are very unlikely to form at 90 or 180 degree angles. I think this makes sense: chains need to involve pins, so they can't run in straight lines in the spaces between them in which case there would be no chance of contact. This also might be telling us that chains don't usually form directly between two adjacent pins, although that's not a direct conclusion we can draw from this single plot.

Here's the same treatment on our trusty tri64 dataset:

Edit: I'm realizing after looking at the lower limit that my bin-drawing formula was using e^x in all places but one: the lower limit had a log₁₀ in it which cut off the weakest forces. Leaving this as is since everything these plots show is still valid.

Something TODO: binning for high forces, it probably makes sense to scale via power law since we're leaning toward that curve characterizing the distribution of the fat tail.