and sectional methods. In the multi-variate case, however, when two or more properties (such as size, shape, composition, etc.) are introduced, one has to seek special approximation methods that suffer less from curse of dimensionality. Approximation based on Gaussian radial basis functions has been successfully applied to the coagulation equation in more than one dimension. When the accuracy of the solution is not of primary importance, stochastic particle (Monte Carlo) methods are an attractive alternative. Condensation-driven aggregation In addition to aggregation, particles may also grow in size by condensation, deposition or by accretion. Hassan and Hassan recently proposed a condensation-driven aggregation (CDA) model in which aggregating particles keep growing continuously between merging upon collision. The CDA model can be understood by the following reaction scheme where denotes the aggregate of size at time and is the elapsed time. This reaction scheme can be described by the following generalized Smoluchowski equation Considering that a particle of size grows due to condensation between collision time equal to inverse of by an amount i.e. One can solve the generalized Smoluchowski equation for constant kernel to give which exhibits dynamic scaling. A simple fractal analysis reveals that the condensation-driven aggregation can be best described fractal of dimension The th moment of is always a conserved quantity which is responsible for fixing all the exponents of the dynamic scaling. Such conservation law has also been found in Cantor set too. See also Einstein–Smoluchowski relation Flocculation Smoluchowski factor Williams spray equation References Differential equations Statistical mechanics