Curved Graphene Nanoribbons: Structure and Dynamics of Carbon Nanobelts

Carbon nanoribbons (CNRs) are graphene (planar) structures with large aspect ratio. Carbon nanobelts (CNBs) are small graphene nanoribbons rolled up into spiral-like structures, i. e., carbon nanoscrolls (CNSs) with large aspect ratio. In this work we investigated the energetics and dynamical aspects of CNBs formed from rolling up CNRs. We have carried out molecular dynamics simulations using reactive empirical bond-order potentials. Our results show that similarly to CNSs, CNBs formation is dominated by two major energy contribution, the increase in the elastic energy due to the bending of the initial planar configuration (decreasing structural stability) and the energetic gain due to van der Waals interactions of the overlapping surface of the rolled layers (increasing structural stability). Beyond a critical diameter value these scrolled structures can be even more stable (in terms of energy) than their equivalent planar configurations. In contrast to CNSs that require energy assisted processes (sonication, chemical reactions, etc.) to be formed, CNBs can be spontaneously formed from low temperature driven processes. Long CNBs (length of $\sim$ 30.0 nm) tend to exhibit self-folded racket-like conformations with formation dynamics very similar to the one observed for long carbon nanotubes. Shorter CNBs will be more likely to form perfect scrolled structures. Possible synthetic routes to fabricate CNBs from graphene membranes are also addressed

Enhancing the Mass Sensitivity of Graphene Nanoresonators Via Nonlinear Oscillations: The Effective Strain Mechanism

We perform classical molecular dynamics simulations to investigate the enhancement of the mass sensitivity and resonant frequency of graphene nanomechanical resonators that is achieved by driving them into the nonlinear oscillation regime. The mass sensitivity as measured by the resonant frequency shift is found to triple if the actuation energy is about 2.5 times the initial kinetic energy of the nanoresonator. The mechanism underlying the enhanced mass sensitivity is found to be the effective strain that is induced in the nanoresonator due to the nonlinear oscillations, where we obtain an analytic relationship between the induced effective strain and the actuation energy that is applied to the graphene nanoresonator. An important implication of this work is that there is no need for experimentalists to apply tensile strain to the resonators before actuation in order to enhance the mass sensitivity. Instead, enhanced mass sensitivity can be obtained by the far simpler technique of actuating nonlinear oscillations of an existing graphene nanoresonator.Comment: published versio

Damped finite-time-singularity driven by noise

We consider the combined influence of linear damping and noise on a dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or absorbing state distribution with a peak at the singularity and a long time tail. The damping introduces a characteristic cross-over time. In the early time regime the probability distribution and first-passage-time distribution show a power law behavior with scaling exponent depending on the ratio of the non linear coupling strength to the noise strength. In the late time regime the behavior is controlled by the damping. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.Comment: 9 pages, 4 eps-figures, revtex4 fil

Raman modes of the deformed single-wall carbon nanotubes

With the empirical bond polarizability model, the nonresonant Raman spectra of the chiral and achiral single-wall carbon nanotubes (SWCNTs) under uniaxial and torsional strains have been systematically studied by \textit{ab initio} method. It is found that both the frequencies and the intensities of the low-frequency Raman active modes almost do not change in the deformed nanotubes, while their high-frequency part shifts obviously. Especially, the high-frequency part shifts linearly with the uniaxial tensile strain, and two kinds of different shift slopes are found for any kind of SWCNTs. More interestingly, new Raman peaks are found in the nonresonant Raman spectra under torsional strain, which are explained by a) the symmetry breaking and b) the effect of bond rotation and the anisotropy of the polarizability induced by bond stretching

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $\lambda$ dependence of the shape and breaking rate.Comment: 4 pages, 3 figure

Simply connected projective manifolds in characteristic p>0p>0 have no nontrivial stratified bundles

We show that simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker. The proof uses Hrushovski's theorem on periodic points.Comment: 16 pages. Revised version contains a more general theorem on torsion points on moduli, together with an illustration in rank 2 due to M. Raynaud. Reference added. Last version has some typos corrected. Appears in Invent.math

Nanoscale Weibull Statistics

In this paper a modification of the classical Weibull Statistics is developed for nanoscale applications. It is called Nanoscale Weibull Statistics. A comparison between Nanoscale and classical Weibull Statistics applied to experimental results on fracture strength of carbon nanotubes clearly shows the effectiveness of the proposed modification. A Weibull's modulus around 3 is, for the first time, deduced for nanotubes. The approach can treat (also) a small number of structural defects, as required for nearly defect free structures (e.g., nanotubes) as well as a quantized crack propagation (e.g., as a consequence of the discrete nature of matter), allowing to remove the paradoxes caused by the presence of stress-intensifications