Forced nano-oscillators comprising double-wailed nanotubes

Abstract

We examine a class of nano-oscillator comprising an outer carbon nanotube that isuncapped and xed, within which oscillates an inner nanotube. The inner tube is acted on byexcess van der Waals forces as well as an applied sinusoidal force, which may result from a timevarying external electric eld acting on ions functionalised to the inner nanotube. Although theequations of motion contain both a non-linear position dependence as well as a time-varyingterm; by neglecting dissipative terms and considering the solution in di erent spatial domains,we reduce the problem to one with an analytical solution which we then evolve in time, solvingfor the domain boundaries to generate a full numerical solution.We nd a frequency dependenceon the maximum extrusion distance which is suggestive that the system may be used as the basisfor an accurate frequency detection device with sensitivity in the gigahertz range. We also notethat for a xed frequency of forcing, variations in the electric eld strength lead to changesin the amplitude and frequency of the response of the oscillator. Finally, we also commentthat an analysis of the position-momentum space reveals that in general the system occupiesall combinations of position and momentum inside a total energy envelop. However, carefullychosen initial conditions may lead to highly deterministic paths, where small perturbations tothese initial condtions quickly lead to a loss of order and thus we conclude these systems exhibitchaotic behaviour in these cases.