Kinetics of fragmentation-annihilation processes.

We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, non-linear process, fragments react at collision to produce an inert species, causing loss of mass. We analyse these systems in the reaction-limited regime by solving a continuous model within the mean-field approximation. The rate of fragmentation, for a particle of mass x to break into fragments of masses y and x− y, has the form x (λ > 0), and the annihilation rate is constant and independent of the masses of the reactants. We find that the asymptotic regime is characterized by the annihilation of small-mass clusters, with the cluster-density decaying as in pure-annihilation and the average cluster-mass as in pure-fragmentation. The results are compared with those for a model with linear mass-loss (i.e. with a sink rather than a reaction). We also study more complex models, in which the processes of fragmentation and annihilation are controlled by mutually-reacting catalysts. Both pairand linearannihilation are considered. Depending on the specific model and initial densities of the catalysts, the time-decay of the cluster-density can now be very unconventional and even non-universal. The interplay between the fragmentation and annihilation processes and the existence of a scaling regime are determined by the asymptotic behaviour of the average-mass and of the mass-density, which may either decay indefinitely or tend to a constant value. We discuss further developments of this class of models and their potential applications. PACS: 05.20.-y, 02.50.Ey, 82.20.-w email: [email protected]. Address from April 1, 1996: Biomathematics & Statistics Scotland, The University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Edinburgh EH9 3JZ, UK. email: [email protected]