An explicit solutions to a discrete fragmentation model

Abstract. The discrete binary fragmentation equation is solved explicitly far a model where tnenetrateoibreakupoiaparlicie oishek, o,,equals(k- lj/(k+l),andthedaughter-ri~e distribution b,lx equals 2 / ( k- 1). This system is closely related to a model of polymer degradation considered by Simha, in which ax = I and b,, * is as above. In the continuum limit, both of these models go over to a continuous fragmentation model in which all particles break with an equal rate, a ( x) = I, and the daughter-size distribution is uniform, b(yl x) = Z/x, which is at the borderline of the shattering transition. 1