Scaling behavior of jamming fluctuations upon random sequential adsorption

It is shown that the fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) (<InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\sigma_{\theta_J}$</EquationSource> </InlineEquation>), decay with the lattice size according to the power-law <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\sigma_{\theta_J} \propto L^{-1/\nu_{J}}$</EquationSource> </InlineEquation>, with <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\nu_{J}=\frac{2}{2D - d_{\rm f}}$</EquationSource> </InlineEquation>,where D is the dimension of the substrate and <InlineEquation ID="Equ4"> <EquationSource Format="TEX">$d_{\rm f}$</EquationSource> </InlineEquation> is the fractal dimension of the set of sites belonging to the substrate where the RSA process actually takes place. This result is in excellent agreement with the figure recently reported by Vandewalle et al. [Eur. Phys. J. B <Emphasis Type="Bold">14, 407 (2000)], namely <InlineEquation ID="Equ5"> <EquationSource Format="TEX">$\nu_{J}=1.0 \pm 0.1$</EquationSource> </InlineEquation> for the RSA of needles with D=2 and <InlineEquation ID="Equ6"> <EquationSource Format="TEX">$d_{\rm f}=2$</EquationSource> </InlineEquation>, that gives <InlineEquation ID="Equ7"> <EquationSource Format="TEX">$\nu_{J}=1$</EquationSource> </InlineEquation>. Furthermore, our prediction is in excellent agreement with different previous numerical results. The derived relationships are also confirmed by means of extensive numerical simulations applied to the RSA of dimers on both stochastic and deterministic fractal substrates. Copyright Springer-Verlag Berlin/Heidelberg 2003