nx_ice_distribution.nx

nx_ice_distribution.nx -- THE CRYSTAL SIZE DISTRIBUTION, and the coupling that nx_ice_recrystal had to assert because it did not have one. ===== WHY THIS EXISTS ============================================ nx_ice_recrystal models cycling damage as V_new = V_old * (1 + phi * G) where phi is the fraction of ice MASS that melts and refreezes on an excursion -- derived honestly from the freezing curve -- and G is a geometric coupling that was ASSERTED. That constant was flagged as the organ's weak point, and it deserved the flag: it converts "this much mass moved" into "the mean diameter grew this much", which is a statement about the crystal size distribution, and the organ had no distribution. ★IT IS NOT A FREE PARAMETER. Given a distribution the whole step is exact arithmetic: 1. Gibbs-Thomson orders the melting -- the smallest crystals have the highest surface curvature, the most depressed local melting point, and therefore go first. The order is physics, not a modelling choice. 2. Remove the smallest crystals until their cumulative MASS reaches phi * M. Count how many crystals that took. 3. That mass refreezes onto the survivors, so total mass is unchanged while the count has fallen. 4. Mean volume is mass over count, so it rises by exactly N / N'. ★★THE WHOLE POINT IS THAT THE NUMBER FRACTION IS NOT THE MASS FRACTION. Small crystals are numerous and light. Removing a given fraction of the MASS removes a much larger fraction of the COUNT, because it takes many small crystals to make up that mass. A model that quietly equates the two -- which is what a coupling of 1.0 does -- therefore UNDER-STATES how much the mean size grows per cycle. Under-stating damage is the direction that says a product is fine when it is not. So this organ computes the coupling instead of asserting it, and dist_coupling_error_permil measures how wrong the assertion was. ===== WHAT REMAINS ASSERTED ======================================