Graphene growth on h-BN by molecular beam epitaxy

The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated. Formation of single-layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic-force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h-BN substrates. The growth is governed by the high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms.     

Sigma function solution of the initial value problem for Somos 5 sequences

The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.

     

Direct measurement of strain-induced changes in the band structure of carbon nanotubes

The effect of uniaxial strain on the optical transition energies of single-walled carbon nanotubes with known chiral indices was measured by Rayleigh scattering spectroscopy. Existing theory accurately predicts the trends in the measured strain-induced shifts, but overestimates their magnitude. Modification of the analysis to account for internal sublattice relaxation results in quantitative agreement with experiment.     

Variable electron-phonon coupling in isolated metallic carbon nanotubes observed by Raman scattering

We report the existence of broad and weakly asymmetric features in the high-energy (G) Raman modes of freely suspended metallic carbon nanotubes of defined chiral index. A significant variation in peak width (from 12 cm(-1) to 110 cm(-1)) is observed as a function of the nanotube's chiral structure. When the nanotubes are electrostatically gated, the peak widths decrease. The broadness of the Raman features is understood as the consequence of coupling of the phonon to electron-hole pairs, the strength of which varies with the nanotube chiral index and the position of the Fermi energy.     

Properties of the series solution for Painlevé I

We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation. For the general solution, explicit recursive formulae for the Taylor expansion of the tau-function around a zero are given, which are natural extensions of analogous formulae for the elliptic sigma function, as given by Weierstrass. Numerical and exact results on the symmetric solution which is singular at the origin are also presented.     

Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics

We consider a fifth-order partial differential equation (PDE) that is a generalization of the integrable Camassa–Holm equation. This fifth-order PDE has exact solutions in terms of an arbitrary number of superposed pulsons with a geodesic Hamiltonian dynamics that is known to be integrable in the two-body case N==2. Numerical simulations show that the pulsons are stable, dominate the initial value problem, and scatter elastically. These characteristics are reminiscent of solitons in integrable systems. But after demonstrating the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and obtaining negative results from Painlevé analysis and the Wahlquist–Estabrook method, we assert that this fifth-order PDE is not integrable.     

Fast centroid molecular dynamics: a force-matching approach for the predetermination of the effective centroid forces

A fast centroid molecular dynamics (CMD) methodology is proposed in which the effective centroid forces are predetermined through a force-matching algorithm applied to a standard path integral molecular dynamics simulation. The resulting method greatly reduces the computational cost of generating centroid trajectories, thus extending the applicability of CMD. The method is applied to the study of liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The static and dynamical results are compared to those obtained from full adiabatic CMD simulations and found to be in excellent agreement for all three systems; the transport properties are also compared to experiment and found to have a similar level of agreement.     

An Entire Function Defined by a Nonlinear Recurrence Relation

For the nonlinear recurrence relation it is proved that the limit exists and defines an entire function of ₂ = ₁(1-₁).     

Is the intrinsic thermoelectric power of carbon nanotubes positive?

The thermoelectric power (TEP) of single-walled carbon nanotubes (SWNTs) is extremely sensitive to gas exposure history. Samples exposed to air or oxygen have an always positive TEP, suggestive of holelike carriers. However, at fixed temperature the TEP crosses zero and becomes progressively more negative as the SWNTs are stripped of oxygen. The time constant for oxygen adsorption/desorption is strongly temperature dependent and ranges from seconds to many days, leading to apparently "variable" TEP for a given sample at a given temperature. The saturated TEP can be accounted for within a model of strong oxygen doping of the semiconducting nanotubes.