Conformal Mechanics and the Virasoro Algebra

We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.Comment: 9 pages, LaTeX. Latest version contains minor clarifications and change

Energy Controlled Edge Formation for Graphene Nano Ribbons

On the basis of first principles calculations, we report energy estimated to cut a graphene sheet into nanoribbons of armchair and zigzag configurations. Our calculations show that the energy required to cut a graphene sheet into zigzag configuration is higher than that of armchair configuration by an order of 0.174 eV. Thus, a control over the threshold energy might be helpful in designing an experiment for cutting a graphene sheet into smooth edged armchair or zigzag configurations

First-principles study of crystallographic slip modes in ω-Zr.

We use first-principles density functional theory to study the preferred modes of slip in the high-pressure ω phase of Zr. The generalized stacking fault energy surfaces associated with shearing on nine distinct crystallographic slip modes in the hexagonal ω-Zr crystal are calculated, from which characteristics such as ideal shear stress, the dislocation Burgers vector, and possible accompanying atomic shuffles, are extracted. Comparison of energy barriers and ideal shear stresses suggests that the favorable modes are prismatic 〈c〉, prismatic-II [Formula: see text] and pyramidal-II 〈c + a〉, which are distinct from the ground state hexagonal close packed α phase of Zr. Operation of these three modes can accommodate any deformation state. The relative preferences among the identified slip modes are examined using a mean-field crystal plasticity model and comparing the calculated deformation texture with the measurement. Knowledge of the basic crystallographic modes of slip is critical to understanding and analyzing the plastic deformation behavior of ω-Zr or mixed α-ω phase-Zr

Edge Configurational Effect on Band Gaps in Graphene Nanoribbons

In this Letter, we put forward a resolution to the prolonged ambiguity in energy band gaps between theory and experiments of fabricated graphene nanoribbons (GNRs). Band structure calculations using density functional theory are performed on oxygen passivated GNRs supercells of customized edge configurations without disturbing the inherent sp2 hybridization of carbon atoms. Direct band gaps are observed for both zigzag and armchair GNRs, consistent with the experimental reports. In addition, band gap values of GNRs scattered about an average value curve for a given crystallographic orientation are correlated with their width on basis of the edge configurations elucidates the band gaps in fabricated GNRs. We conclude that edge configurations of GNRs significantly contribute to band gap formation in addition to its width for a given crystallographic orientation, and would play a crucial role in band gap engineering of GNRs for future research works on fabrication of nanoelectronic devices.Comment: 5 pages, 6 figure