Breakdown of Kolmogorov scaling in models of cluster aggregation with   deposition
  The steady state of the model of cluster aggregation with deposition is characterized by a constant flux of mass directed from small masses towards large masses. It can therefore be studied using phenomenological theories of turbulence, such as Kolmogorov's 1941 theory. On the other hand, the large scale behavior of the aggregation model in dimensions lower than or equal to two is governed by a perturbative fixed point of the renormalization group flow, which enables an analytic study of the scaling properties of correlation functions in the steady state. In this paper, we show that the correlation functions have multifractal scaling, which violates linear Kolmogorov scaling. The analytical results are verified by Monte Carlo simulations. 
Colm Connaughton and R. Rajesh and Oleg Zaboronski