Thamwattana Ngamta, Cox Barry J, Hill James M
Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia.
J Phys Condens Matter. 2009 Apr 8;21(14):144214. doi: 10.1088/0953-8984/21/14/144214. Epub 2009 Mar 18.
In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques, which provides considerable insight into the underlying mechanisms of the nanoscaled oscillators. The paper presents a synopsis of the major results derived in detail by the present authors (Cox et al 2007 Proc. R. Soc. A 464 691-710 and Cox et al 2007 J. Phys. A: Math. Theor. 40 13197-208).
在本文中，我们研究了一种纳米级千兆赫兹振荡器的力学特性，该振荡器由一个在均匀同心碳纳米管环或管束中心振荡的碳分子组成。我们考虑了两种振荡分子，即碳纳米管和C(60)富勒烯。利用 Lennard-Jones 势和连续介质方法，我们得到了管束半径与构成管束的纳米管半径之间的关系，以及使纳米管束振荡器和C(60)管束振荡器产生最大振荡频率的最佳管束尺寸。虽然此前该领域的研究是通过分子动力学模拟进行的，但本文强调应用数学建模技术，这能深入洞察纳米级振荡器的潜在机制。本文概述了作者（考克斯等人，2007年，《皇家学会学报A》第464卷，691 - 710页；考克斯等人，2007年，《物理学杂志A：数学理论》第40卷，13197 - 208页）详细推导的主要结果。
