NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES

This note is a study of nonnegativity conditions on curvature preserved by the Ricci flow. We focus on a specific class of curvature conditions which we call non-coercive: These are the conditions for which nonnegative curvature and vanishing scalar curvature does not imply flatness. We show, in dimensions greater than 4, that if a Ricci flow invariant nonnegativity condition is satisfied by all Einstein curvature operators with nonnegative scalar curvature, then this condition is just the nonnegativity of scalar curvature. As a corollary, we obtain that a Ricci flow invariant curvature condition, which is stronger than a nonnegative scalar curvature, cannot be strictly satisfied by curvature operators (other than multiples of the identity) of compact Einstein symmetric spaces. We also investigate conditions which are satisfied by all conformally flat manifolds with nonnegative scalar curvature.

Tunability of 1/f Noise at Multiple Dirac Cones in hBN Encapsulated Graphene Devices

The emergence of multiple Dirac cones in hexagonal boron nitride (hBN)-graphene heterostructures is particularly attractive because it offers potentially better landscape for higher and versatile transport properties than the primary Dirac cone. However, the transport coefficients of the cloned Dirac cones is yet not fully characterized and many open questions, including the evolution of charge dynamics and impurity scattering responsible for them, have remained unexplored. Noise measurements, having the potential to address these questions, have not been performed to date in dual-gated hBN graphene hBN devices. Here, we present the low frequency 1/f noise measurements at multiple Dirac cones in hBN encapsulated single and bilayer graphene in dual-gated geometry. Our results reveal that the low-frequency noise in graphene can be tuned by more than two-orders of magnitude by changing carrier concentration as well as by modifying the band structure in bilayer graphene. We find that the noise is surprisingly suppressed at the cloned Dirac cone compared to the primary Dirac cone in single layer graphene device, while it is strongly enhanced for the bilayer graphene with band gap opening. The results are explained with the calculation of dielectric function using tight-binding model. Our results also indicate that the 1/f noise indeed follows the Hooge's empirical formula in hBN-protected devices in dual-gated geometry. We also present for the first time the noise data in bipolar regime of a graphene device.

Resonance cones and mode conversion in a warm magnetized bounded plasma

The warm plasma resonance cone structure of the quasistatic field produced by a gap source in a bounded magnetized slab plasma is determined theoretically. This is initially determined for a homogeneous or mildly inhomogeneous plasma with source frequency lying between the lower hybrid frequency and the plasma frequency. It is then extended to the complicated case of an inhomogeneous plasma with two internal lower hybrid layers present, which is of interest to radio frequency heating of plasmas.

In the first case, the potential is obtained as a sum of multiply reflected warm plasma resonance cones, each of which has a similar structure, but a different size, amplitude, and position. An important interference between nearby multiply-reflected resonance cones is found. The cones are seen to spread out as they move away from the source, so that this interference increases and the individual resonance cones become obscured far away from the source.

In the second case, the potential is found to be expressible as a sum of multiply-reflected, multiply-tunnelled, and mode converted resonance cones, each of which has a unique but similar structure. The effects of both collisional and collisionless damping are included and their effects on the decay of the cone structure studied. Various properties of the cones such as how they move into and out of the hybrid layers, through the evanescent region, and transform at the hybrid layers are determined. It is found that cones can tunnel through the evanescent layer if the layer is thin, and the effect of the thin evanescent layer is to subdue the secondary maxima of cone relative to the main peak, while slightly broadening the main peak and shifting it closer to the cold plasma cone line.

Energy theorems for quasistatic fields are developed and applied to determine the power flow and absorption along the individual cones. This reveals the points of concentration of the flow and the various absorption mechanisms.

Tubular graphite cones with single-crystal nanotips and their antioxygenic properties.

Tubular graphite cones (TGCs) with a single-crystal nanotip have been achieved by means of microwave plasma-assisted chemical vapor deposition using in-situ-evaporated Fe catalysts. The absence of the disorder-induced D band in Raman spectra revealed the single-crystalline feature of the nanotip. TGCs were found to stem from Fe catalytic carbon spherules on the order of 100 mum diameter, whose critical role in promoting both nucleation and plasma annealing in the formation of highly crystalline TGCs is discussed. The crystalline quality of such TGCs can be further verified by the investigation of their oxidative stability in air. All TGCs can survive up to 600 degrees C without any structural variations, and a few TGCs still survive with an anisotropic etched and stepped nanotip at temperatures up to 800 degrees C, much better than CNTs. Thus, TGCs with single crystalline nanotips are potential candidates for scanning probes in high-temperature oxygen-containing environments.

Contraction and observer design on cones

We consider the problem of positive observer design for positive systems defined on solid cones in Banach spaces. The design is based on the Hilbert metric and convergence properties are analyzed in the light of the Birkhoff theorem. Two main applications are discussed: positive observers for systems defined in the positive orthant, and positive observers on the cone of positive semi-definite matrices with a view on quantum systems. © 2011 IEEE.

Raman scattering of non-planar graphite: arched edges, polyhedral crystals, whiskers and cones

Planar graphite has been extensively studied by Raman scattering for years. A comparative Raman study of several different and less common non-planar graphitic materials is given here. New kinds of graphite whiskers and tubular graphite cones (synthetic and natural) have been introduced. Raman spectroscopy has been applied to the characterization of natural graphite crystal edge planes, an individual graphite whisker graphite polyhedral crystals and tubular graphite cones. Almost all of the observed Raman modes were assigned according to the selection rules and the double-resonance Raman mechanism. The polarization properties related to the structural features, the line shape of the first-order dispersive mode and its combination modes, the frequency variation of some modes in different carbon materials and other unique Raman spectral features are discussed here in detail.

Individual differences provide psychophysical evidence for separate on- and off-pathways deriving from short-wave cones

Distinct neural populations carry signals from short-wave (S) cones. We used individual differences to test whether two types of pathways, those that receive excitatory input (S+) and those that receive inhibitory input (S-), contribute independently to psychophysical performance. We also conducted a genome-wide association study (GWAS) to look for genetic correlates of the individual differences. Our psychophysical test was based on the Cambridge Color Test, but detection thresholds were measured separately for S-cone spatial increments and decrements. Our participants were 1060 healthy adults aged 16-40. Test-retest reliabilities for thresholds were good (ρ=0.64 for S-cone increments, 0.67 for decrements and 0.73 for the average of the two). "Regression scores," isolating variability unique to incremental or decremental sensitivity, were also reliable (ρ=0.53 for increments and ρ=0.51 for decrements). The correlation between incremental and decremental thresholds was ρ=0.65. No genetic markers reached genome-wide significance (p-7). We identified 18 "suggestive" loci (p-5). The significant test-retest reliabilities show stable individual differences in S-cone sensitivity in a normal adult population. Though a portion of the variance in sensitivity is shared between incremental and decremental sensitivity, over 26% of the variance is stable across individuals, but unique to increments or decrements, suggesting distinct neural substrates. Some of the variability in sensitivity is likely to be genetic. We note that four of the suggestive associations found in the GWAS are with genes that are involved in glucose metabolism or have been associated with diabetes.