Rate equation and scaling for fragmentation with mass loss

Abstract

A linear rate equation describes fragmentation with continuous and discrete mass loss typified by consumption of porous reactive solids and two-phase heterogeneous solids. For a massdependent fragmentation rate x and a continuous-mass-loss rate ex ", o ya -1 & 0 yields a

Scaling in animal group-size distributions

“…Other exponents can be obtained with more complicated combinations of aggregation and breakup kernels, even in the mean-field case (29)(30)(31). But some of the most interesting predictions of the model are related to the effective dimension d of the space in which animals move.…”

Global Solvability of a Fragmentation-Coagulation Equation With Growth and Restricted Coagulation

“…by surface deposition or dissolution in chemical applications, see e.g. [10] or by birth or division processes in biological ones, see e.g. [1,16].…”

Appearance of dust in fragmentations

“…In particular, when τ (x) = x α , some dust appears if and only if α < 0. This last result was found independently and for some particular functions ν by some physicists [8], [15] in the 80's (they called the loss of mass to dust phenomenon "shattering"). More recently, Jeon [14] and Fournier and Giet [10] investigated the problem for fragmentation equations, which, restricted to our context, correspond to the case where ν is binary (i.e.…”

“…We also mention the papers [9], [8], [15], [6], [10], and [13] for discussions on the appearance of dust for some different classes of deterministic and random fragmentations.…”