In this study, we investigate the percolation threshold of curved linear objects, describing them as quadratic Bézier curves. Using Monte Carlo simulations, we calculate the critical number densities of the curves with different curviness. We also obtain the excluded area of the curves. When an excluded area is given, we can find the critical number density of the curves with arbitrary curviness. Apparent conductivity exponents are computed for the curves, and these values are found to be analogous to that of sticks in the percolative region for a junction resistance dominant system. These results can be used to analyze the optoelectrical performance of metal nanowire films because the high-aspect-ratio metal nanowires can be easily curved during coating.

中文翻译：

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弯曲线性物体的渗透阈值

在这项研究中，我们研究了弯曲线性对象的渗透阈值，将它们描述为二次贝塞尔曲线。使用蒙特卡洛模拟，我们计算了具有不同弯曲度的曲线的临界数密度。我们还获得了曲线的排除区域。当给出一个排除区域时，我们可以找到任意曲率的曲线的临界数密度。计算曲线的表观电导率指数，发现这些值类似于结电阻主导系统的渗透区域中的棒的电导率。这些结果可用于分析金属纳米线薄膜的光电性能，因为高纵横比的金属纳米线在涂覆过程中容易弯曲。