Some actionable Force Distribution sanity checks
andyletzhang opened this issue · comments
- plot force distribution histograms on loglog axes for very weak forces, both for all data and for only weakest pressure data, to make sure our buckler power scaling correlations make sense as pins increase.
- plot <f> against pressure for each trial. We expect a linear scaling here, pressure being distributed evenly through a system, although this may change at high pin densities (depends on how the algorithm determines pressure... P may be literally equivalent to <f>).
- Compare mean force <f>, peak normalized force f*/<f>, and power law exponent in a certain pressure range against pin density on the x axis.
Loglog plots of force distributions are difficult to parse. Will have to see if anyone has meaningful insights next Thursday.
<f> vs. pressure looks promising; we see slopes increase as pins are added, which appears to indicate the presence of localized strong force chains which don't factor into the pressure (one random 100-pin trial which we've cut out of our dataset has a mean force at medium pressure with a mean force 6 times too large; probably indicating an outlier particle trapped between pins clustered close together).
We're seeing unusual behavior with λ scaling: we would hope that plotting against λ resolves some of the variation between different lattice geometries, but we still see two different curves for square and triangle lattices.
The peaks as they're arranged here correspond to our intuition: if at each pin number triangle lattices have slightly higher pin densities than their square counterparts, then peak force scales inversely with λ. But turns out given the conditions of our simulations (rs is smaller for each triangle simulation) that pin density is actually lower for triangle lattices at each pin number, so the correlation doesn't hold as we would like.
