Please use this identifier to cite or link to this item:
|Title:||Determination of join regions between carbon nanostructures using variational calculus|
B. J. Cox
J. M. Hill
University of Adelaide
|Citation:||ANZIAM Journal. Vol.54, No.4 (2013), 221-247|
|Abstract:||We review the work of the present authors to employ variational calculus to formulate continuous models for the connections between various carbon nanostructures. In formulating such a variational principle, there is some evidence that carbon nanotubes deform as in perfect elasticity, and rather like the elastica, and therefore we seek to minimize the elastic energy. The calculus of variations is utilized to minimize the curvature subject to a length constraint, to obtain an Euler-Lagrange equation, which determines the connection between two carbon nanostructures. Moreover, a numerical solution is proposed to determine the geometric parameters for the connected structures. Throughout this review, we assume that the defects on the nanostructures are axially symmetric and that the into-the-plane curvature is small in comparison to that in the two-dimensional plane, so that the problems can be considered in the two-dimensional plane. Since the curvature can be both positive and negative, depending on the gap between the two nanostructures, two distinct cases are examined, which are subsequently shown to smoothly connect to each other. © Copyright ©2013 Australian Mathematical Societŷ.|
|Appears in Collections:||Scopus 2011-2015|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.