Fragment redistribution function

This function specifies the fraction of disrupted mass assigned to each fragment size interval. A self-similar law depends on fragment-to-parent size ratios, rather than an absolute size. In logarithmic bins its translation invariance gives the constant processed mass flux of the interior steady collisional cascade. In a removal-dominated interval, it instead sets the fragment source spectrum.

If fragments are injected with number spectrum $S_N(D)\propto D^{-{\alpha }_r}$ and escape faster than they collide, steady balance gives $n(D)=S_N(D)t_y(D)$. Thus $t_y\propto D^{\gamma }$ changes the differential number index to ${\alpha }_r-\gamma$. A removed population with size-independent subsequent lifetime retains the source index ${\alpha }_r$.