Random relative motion aggregation

The solution of the partial differential equation (3.3.43) written for P(r", t + t) subject to the initial condition (3.3.44) and boundary conditions (3.3.45) and (3.3.46) is readily obtained. However, since the time scale of random relative motion may be viewed as being considerably smaller than that of aggregation, the preceding diffusion process may be construed to have reached steady state. The steady-state version of (3.3.43) written for... 

Particles, chains, aggregates and floes were allowed to move in space according to their respective diffusion coefficients recomputed at each step from their masses and conformations. Brownian motion was represented by random walks. The number of random walks during a unit of (relative) time was proportional to the diffusion coefficients of the moving entities. The link between the relative and physical time was made by correlating the mean displacement of a reference particle (not participating in the aggregation process) and its diffusion coefficients. 

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