Constant flux relation for aggregation models with desorption and fragmentation

We study mass fluxes in aggregation models where mass transfer to large scales by aggregation occurs alongside desorption or fragmentation. Two models are considered: (1) a system of diffusing, aggregating particles with influx and outflux of particles (in-out model); and (2) a system of diffusing aggregating particles with fragmentation (chipping model). Both these models can exist in phases where probability distributions are power laws. In these power law phases, we argue that the two point correlation function should have a certain homogeneity exponent. These arguments are based on the exact constant flux scaling valid for simple aggregation with input. Predictions are compared with Monte Carlo simulations.