Particle accumulation on fractals

Sometimes, as in the case of particle segregation on fractals (e.g., the planar Sierpinski gasket discussed in Section 6.1) this effect indeed is self-evident [88-90]. Its analytical treatment for particle accumulation was presented in [91, 92] we reproduce here simple mesoscopic estimates following these papers. Particle concentrations obey the kinetic equations 

As it was shown in [16, 93] the concentration of particles is determined mainly by the behaviour of the difference of the species concentrations Z = Ca - Cb which satisfies the linear kinetic equation 

In computer experiments [88, 89] the total numbers of A and B particles created in a system per unit time are equal, so (Z x,t)) = 0. Its second 

The accuracy of this approximation will be estimated further. Here we shall study the behaviour of the quantity Z ) only. 

The investigation of the behaviour of Z(r, t) in a finite system is a difficult problem due to the fact that the boundary conditions for (7.3.3) are unknown for fractal systems although one can use some scaling arguments based on the knowledge of the properties of the infinite system. In the case of the independent production of different particles we obtain 

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