Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of elongated objects deposited on two-dimensional honeycomb lattices. The depositing particle is modeled as a linear array of length $k$ (so-called $k$-mer), maximizing the distance between first and last monomers in the chain. The separation between $k$-mer units is equal to the lattice constant. Hence, $k$ sites are occupied by a $k$-mer when adsorbed onto the surface. The adsorption process starts with an initial configuration, where all lattice sites are empty. Then, the sites are occupied following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. Jamming coverage ${\theta }_{j,k}$ and percolation threshold ${\theta }_{c,k}$ were determined for a wide range of values of $k$ ($2\le k\le 128$). The obtained results shows that $\left(i\right) {\theta }_{j,k}$ is a decreasing function with increasing $k$, being ${\theta }_{j,k\to \infty }=0.6007\left(6\right)$ the limit value for infinitely long $k$-mers; and $\left(ii\right) {\theta }_{c,k}$ has a strong dependence on $k$. It decreases in the range $2\le k<48$, goes through a minimum around $k=48$, and increases smoothly from $k=48$ up to the largest studied value of $k=128$. Finally, the precise determination of the critical exponents $\nu , \beta ,$ and $\gamma$ indicates that the model belongs to the same universality class as 2D standard percolation regardless of the value of $k$ considered.

中文翻译：

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线性晶格在蜂窝晶格上的干扰和渗透

已经进行了数值模拟和有限尺寸缩放分析，以研究沉积在二维蜂窝状晶格上的细长物体的干扰和渗滤行为。沉积粒子建模为长度的线性阵列$ķ$ （所谓的 $ķ$-mer），以最大化链中第一个和最后一个单体之间的距离。之间的分离$ķ$-mer单位等于晶格常数。因此，$ķ$ 网站被一个 $ķ$-mer吸附到表面上时。吸附过程从初始构型开始，在该构型中所有晶格​​位点均为空。然后，按照随机顺序吸附机理占据位点。当达到卡纸状态并且由于没有适当大小和形状的空位簇而无法放置更多对象时，该过程结束。干扰覆盖${\theta }_{Ĵ，ķ}$ 和渗透阈 ${\theta }_{C，ķ}$ 被确定为广泛的价值 $ķ$ （$2\le ķ\le 128$）。获得的结果表明$（\mathrm{一世}） {\theta }_{Ĵ，ķ}$ 是随着增加而减少的功能 $ķ$， 存在 ${\theta }_{Ĵ，ķ\to \infty }=0.6007（6）$ 无限长的极限值 $ķ$-mers; 和$（\mathrm{一世}\mathrm{一世}） {\theta }_{C，ķ}$ 高度依赖 $ķ$。在范围内减小$2\le ķ<48$，经过一个最小值 $ķ=48$，并从 $ķ=48$ 直到最大的研究价值 $ķ=128$。最后，精确确定关键指数$\nu ， \beta ，$ 和 $\gamma$ 表示该模型与2D标准渗流属于同一通用类，而与 $ķ$ 考虑过的。