Substitute α for λ in cell 3.7

Question

Substitute α for λ in cell 3.7

andyletzhang opened this issue 4 years ago · comments

α is a ratio of total area which is occupied by pins.

andyletzhang · Answer 1 · Thu Nov 05 2020 23:53:49 GMT+0800 (China Standard Time)

So what exactly is α?
We're quantifying the average area of a particle compared to the area of a region around each pin, which will depend on the geometry of a pin lattice. The average area of a particle is just πr_avg², and the area per pin is ga², where g=1 for a square lattice and √(3)/2 for a triangular lattice.

Altogether:
$\frac{\text{area per particle}}{\text{area belonging to pin}}=\pi\frac{(1^2+1.4^2)}{2g}\frac{r_s^2}{a^2}$

andyletzhang · Answer 2 · Wed Nov 11 2020 04:23:17 GMT+0800 (China Standard Time)

Using α shifts triangle data to the right compared to the squared data since α scales with λ²/g, and g_squ<g_tri. Unfortunately the data still falls short of merging into a single curve: for the same pin numbers, looks like our datasets have near-identical α values.