# CARMA Colloquium

## Wednesday, 24th Apr 2019

SR202, SR Building

# A/Prof Duangkamon Baowan

(Department of Mathematics, Mahidol University)

# Calculus of variations and the bending of carbon nanostructures

Calculus of variations is utilized to minimize the elastic energy arising from the curvature squared while maximizing the van der Waals energy. Firstly, the shape of folded graphene sheets is investigated, and an arbitrary constant arising by integrating the Euler–Lagrange equation is determined. In this study, the structure is assumed to have a translational symmetry along the fold, so that the problem may be reduced to a two dimensional problem with reflective symmetry across the fold. Secondly, both variational calculus technique and least squared minimization procedure are employed to determine the joining structure involved a C60 fullerene and a carbon nanotube, namely a nanobud. We find that these two methods are in reasonable overall agreement. However, there is no experimental or simulation data to determine which procedure gives the more realistic results.