Fractal dimension and degree of order in sequential deposition of mixture

We present a number of models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power law p(x) similar to alpha x(alpha-1), x less than or equal to 1. We explicitly obtain the scaling function in the case of random sequential adsorption and show that the pattern created in the long-time limit becomes scale invariant. This pattern can be described by a unique exponent, the fractal dimension. In addition, we introduce an external tuning parameter beta to describe the correlated sequential deposition of a mixture of particles where the degree of correlation is determined by beta, while beta = 0 corresponds to the random sequential deposition of a mixture. We show that the fractal dimension of the resulting pattern increases as beta increases and reaches a constant nonzero value in the limit beta --> infinity when the pattern becomes perfectly ordered or nonrandom fractals.