AI 中文总结
该研究推广了带电单元的随机序列吸附（RSA）模型，推导四分量生成函数方程，证明堵塞密度自平均，发现电荷选择性可提升覆盖率并降低λ=1附近的波动，建立了均匀RSA等的可处理联系。
AI 中文摘要
我们推广了带电单元段的一维随机序列吸附（RSA）模型，其中沉积位置遵循β核，该β核由可用间隙边界的电荷以及入射粒子的电荷决定。相互作用参数\boldsymbol{0≤λ<1}在均匀停车模型和强局域沉积之间插值。我们推导了一个四分量生成函数方程，该方程为完整的占据统计提供了精确的递推关系，尽管此处仅详细分析了均值和方差。精确的有限壳层解可作为高斯-雅可比求积法和蒙特卡洛模拟的基准。我们证明，尽管边界电荷会影响有限尺寸行为，但四种边界态具有相同的渐近均值和方差密度，因此，我们证明堵塞密度是自平均的。数值结果表明，电荷选择性可提高覆盖率，尤其是对于以相反端点电荷为主的混合物，这些混合物在\boldsymbol{λ=1}附近的波动也会显著降低。该模型在均匀RSA、动态生成的无序以及相互作用驱动的沉积之间建立了可处理的联系。
英文摘要
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 \(0\leqλ<1\) 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 \(λ=1\). The model provides a tractable connection between uniform RSA, dynamically generated disorder, and interaction-driven deposition.
