Dynamics of infinite-range ballistic aggregation

Abstract

The authors calculate the width of the growing interface of ballistic aggregation in the limit in which the range of the sticking interaction between the particles becomes infinite. They derive a scaling form for the width, and they compute the short- and long-time exponents finding nu =3/4 and alpha =1/2. Furthermore, they find that the crossover exponent defining the argument of the scaling function is gamma =1/2. They compare these exact results with computer simulations, finding excellent agreement. They also discuss the relation of these results to those of ordinary finite-range ballistic aggregation. Finally, they present a simple expression for the density of all ballistic aggregation clusters, regardless of the range of the interaction, which agrees with known results and interpolates between the infinite- and finite-range cases.