论文标题

在一条线上部分订购的“巴黎停车问题”

"Paris car parking problem" for partially ordered discorectangles on a line

论文作者

Lebovka, Nikolai I., Tatochenko, Mykhailo O., Vygornitskii, Nikolai V., Tarasevich, Yuri Yu.

论文摘要

在数值上研究了一条线(“巴黎停车问题”)上相同伸长颗粒(圆锥形)的随机顺序吸附(RSA)。考虑了具有连续位置和定向自由度的非现场模型。在[-θ_\ text {m}中$θ\之间限制了二心序的可能取向; θ_\ text {m}] $在[1; 100] $ in In [1; 100]中的范围内变化了Discorectangles的长宽比(长度与宽度比)。此外,考虑了限制案例$ \ varepsilon = \ infty $(即,无宽度棒)。我们观察到,所考虑的问题的RSA沉积受稀疏的孔的形成(包含沿线的颗粒)的形成,这些孔被相对密集的堆栈包围(在垂直方向上填充了几乎平行的颗粒)。讨论了顺序参数变化和填料密度的动力学。 Discorectangles的部分排序显着影响干扰状态下的填料密度,$φ_\ text {j} $,并在$φ_\ text {j}(\ varepsilon)$依赖项中移动了cusps。这可以通过对粒子定向自由度与排除体积效应之间竞争的影响来解释。

The random sequential adsorption (RSA) of identical elongated particles (discorectangles) on a line ("Paris car parking problem") was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The possible orientations of the discorectanles were restricted between $θ\in [-θ_\text{m}; θ_\text{m}]$ while the aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;100]$. Additionally, the limiting case $\varepsilon=\infty$ (i.e., widthless sticks) was considered. We observed, that the RSA deposition for the problem under consideration was governed by the formation of rarefied holes (containing particles oriented along a line) surrounded by comparatively dense stacks (filled with almost parallel particles oriented in the vertical direction). The kinetics of the changes of the order parameter, and the packing density are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, $φ_\text{j}$, and shifted the cusps in the $φ_\text{j}(\varepsilon)$ dependencies. This can be explained by the effects on the competition between the particles' orientational degrees of freedom and the excluded volume effects.

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