Mk. Hassan, FRACTAL DIMENSION AND DEGREE OF ORDER IN SEQUENTIAL DEPOSITION OF MIXTURE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(5), 1997, pp. 5302-5310
We present a number of models describing the sequential deposition of
a mixture of particles whose size distribution is determined by the po
wer law p(x) similar to alpha x(alpha-1), x less than or equal to 1. W
e explicitly obtain the scaling function in the case of random sequent
ial adsorption and show that the pattern created in the long-time limi
t becomes scale invariant. This pattern can be described by a unique e
xponent, 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 determin
ed by beta, while beta = 0 corresponds to the random sequential deposi
tion of a mixture. We show that the fractal dimension of the resulting
pattern increases as beta increases and reaches a constant nonzero va
lue in the limit beta --> infinity when the pattern becomes perfectly
ordered or nonrandom fractals.