Manuscript VII-F@1 · VII-F.tex · section · 2d81c03f

One-sided edge laws

Cellulation and the isolated particle event › One-sided edge laws · lines 807–832

The changing boundary in the half-sector $ξ \geq η$ obeys

10 ξ + η = 15 s .

Its Euclidean normal velocity with respect to the parameter $s$ is

\frac{15}{101} .

In the other half-sector, the analogous equation is $ξ + 10 η = 15 s$ . The rays, bisectors, and outer crest have fixed spatial directions.

The endpoint laws are

B_{i}^{'} = \frac{3}{2} v_{i}, C_{i}^{'} = \frac{15}{11} (v_{i} + v_{i + 1}),

and the outgoing length derivatives follow directly from Proposition prop:lengths. Before the event, all finite edge lengths are constant.

These are slicing-parameter laws, not matter-velocity laws.

Displayed formulas in this passage

unlabeled · line 810
$10 ξ + η = 15 s .$
unlabeled · line 814
$\frac{15}{101} .$
unlabeled · line 822
$B_{i}^{'} = \frac{3}{2} v_{i}, C_{i}^{'} = \frac{15}{11} (v_{i} + v_{i + 1}),$