Purpose

The extraordinary properties of graphene render it ideal for diverse contemporary and future applications. Aiming at the investigation of certain aspects commonly overlooked in pertinent works, the authors study wave-propagation phenomena supported by graphene layers within a stochastic framework, i.e. when uncertainty in various factors affects the graphene’s surface conductivity. Given that the consideration of an increasing number of graphene sheets may increase the stochastic dimensionality of the corresponding problem, efficient surrogates with reasonable computational cost need to be developed.

Design/methodology/approach

The authors exploit the potential of generalized Polynomial Chaos (PC) expansions and develop low-cost surrogates that enable the efficient extraction of the necessary statistical properties displayed by stochastic graphene-related quantities of interest (QoI). A key step is the incorporation of an initial variance estimation, which unveils the significance of each input parameter and facilitates the selection of the most appropriate basis functions, by favoring anisotropic formulae. In addition, the impact of controlling the allowable input interactions in the expansion terms is investigated, aiming at further PC-basis elimination.

Findings

The proposed stochastic methodology is assessed via comparisons with reference Monte-Carlo results, and the developed reduced basis models are shown to be sufficiently reliable, being at the same time computationally cheaper than standard PC expansions. In this context, different graphene configurations with varying numbers of random inputs are modeled, and interesting conclusions are drawn regarding their stochastic responses.

Originality/value

The statistical properties of surface-plasmon polaritons and other QoIs are predicted reliably in diverse graphene configurations, when the surface conductivity displays non-trivial uncertainty levels. The suggested PC methodology features simple implementation and low complexity, yet its performance is not compromised, compared to other standard approaches, and it is shown to be capable of delivering valid results.

中文翻译：

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利用有效多项式模型随机研究石墨烯结构

目的

石墨烯的非凡性能使其成为各种当代和未来应用的理想选择。为了研究在相关工作中通常被忽略的某些方面，作者研究了随机框架内石墨烯层所支持的波传播现象，即当各种因素的不确定性影响石墨烯的表面电导率时。考虑到越来越多的石墨烯片的考虑可能会增加相应问题的随机尺寸，因此需要开发具有合理计算成本的有效替代方案。

设计/方法/方法

作者利用广义多项式混沌（PC）展开的潜力并开发了低成本替代方案，该替代方案可有效提取与石墨烯相关的随机感兴趣量（QoI）显示的必要统计属性。关键步骤是合并初始方差估计，它通过支持各向异性公式揭示了每个输入参数的重要性，并有助于选择最合适的基函数。此外，还研究了控制扩展项中允许的输入交互的影响，旨在进一步消除PC基础。

发现

通过与参考蒙特卡洛结果进行比较，评估了所提出的随机方法，并且所开发的简化基础模型显示出足够的可靠性，同时在计算上也比标准PC扩展便宜。在这种情况下，对具有不同数量随机输入的不同石墨烯构型进行了建模，并对它们的随机响应得出了有趣的结论。

创意/价值

当表面电导率显示出非常重要的不确定性水平时，可以在各种石墨烯配置中可靠地预测表面等离激元极化子和其他QoI的统计特性。与其他标准方法相比，建议的PC方法具有实现简单，复杂度低的特点，但其性能并未受到影响，并且可以提供有效的结果。