A Generalized Model for Disordered Random Sequential Adsorption with Charge-Dependent Deposition
We generalize a one-dimensional random sequential adsorption model (RSA) of charged unit segments in which the deposition position follows a beta kernel determined by the charges bounding the available gap and those of the incoming particle. The interaction parameter \(0\leq\lambda<1\) interpolates between uniform car parking and strongly localized deposition. We derive a four component generating function equation that provides exact recursions for the complete occupation statistics, although only the mean and variance are analyzed in detail here. Exact finite-shell solutions serve as benchmarks for the Gauss--Jacobi quadrature and Monte Carlo simulations. We prove that, although boundary charges affect finite size behavior, the four boundary states have the same asymptotic mean and variance densities, consequently, we prove that the jammed density is self-averaging. Numerical results show that charge selectivity increases the coverage, especially for mixtures dominated by opposite endpoint charges, which also exhibit strongly reduced fluctuations near \(\lambda=1\). The model provides a tractable connection between uniform RSA, dynamically generated disorder, and interaction-driven deposition.