On Ext1{\mathrm{Ext}}^1 for Drinfeld modules

Let $A={\mathbb F}_q[t]$ be the polynomial ring over a finite field ${\mathbb F}_q$ and let $\phi$ and $\psi$ be $A-$Drinfeld modules. In this paper we consider the group ${\mathrm{Ext}}^1(\phi ,\psi )$ with the Baer addition. We show that if $\mathrm{rank}\phi >\mathrm{rank}\psi$ then $\mathrm{Ext^1}(\phi,\psi)$ has the structure of a \tm module. We give complete algorithm describing this structure. We generalize this to the cases: $\mathrm{Ext^1}(\Phi,\psi)$ where $\Phi$ is a \tm module and $\psi$ is a Drinfeld module and $\mathrm{Ext^1}(\Phi, C^{\otimes e})$ where $\Phi$ is a \tm module and $C^{\otimes e}$ is the $e$-th tensor product of Carlitz module. We also establish duality between \Ext groups for \tm modules and the corresponding adjoint ${\mathbf t}^{\sigma}$-modules. Finally, we prove the existence of "\Hom-\Ext" six-term exact sequences for \tm modules and dual \tm motives. As the category of \tm modules is only additive (not abelian) this result is nontrivial

Morphology of Graphene on SiC(000-1) Surfaces

Graphene is formed on SiC(000-1) surfaces (the so-called C-face of the crystal) by annealing in vacuum, with the resulting films characterized by atomic force microscopy, Auger electron spectroscopy, scanning Auger microscopy and Raman spectroscopy. Morphology of these films is compared with the graphene films grown on SiC(0001) surfaces (the Si-face). Graphene forms a terraced morphology on the C-face, whereas it forms with a flatter morphology on the Si-face. It is argued that this difference occurs because of differing interface structures in the two cases. For certain SiC wafers, nanocrystalline graphite is found to form on top of the graphene.Comment: Submitted to Applied Physics Letters; 9 pages, 3 figures; corrected the stated location of Raman G line for NCG spectrum, to 1596 cm^-

On the forcings of the unusual Quasi-Biennial Oscillation structure in February 2016

The westerly phase of the stratospheric Quasi-Biennial Oscillation (QBO) was reversed during Northern Hemisphere winter 2015/2016 for the first time since records began in 1953. Recent studies proposed that Rossby waves propagating from the extratropics played an important role during the reversal event in 2015/2016. Building upon these studies, we separated the extratropical Rossby waves into different wavenumbers and timescales by analyzing the combined ERA-40 and ERA-Interim reanalysis zonal wind, meridional wind, vertical velocity, and potential vorticity daily mean data from 1958 to 2017. We find that both synoptic and quasi-stationary Rossby waves are dominant contributors to the reversal event in 2015/2016 in the tropical lower stratosphere. By comparing the results for 2015/2016 with two additional events (1959/1960 and 2010/2011), we find that the largest differences in Rossby wave momentum fluxes are related to synoptic-scale Rossby waves of periods from 5 to 20 d. We demonstrate for the first time, that these enhanced synoptic Rossby waves at 40 hPa in the tropics in February 2016 originate from the extratropics as well as from local wave generation. The strong Rossby wave activity in 2016 in the tropics happened at a time with weak westerly zonal winds. This coincidence of anomalous factors did not happen in any of the previous events. In addition to the anomalous behavior in the tropical lower stratosphere in 2015/2016, we explored the forcing of the unusually long-lasting westerly zonal wind phase in the middle stratosphere (at 20 hPa). Our results reveal that mainly enhanced Kelvin wave activity contributed to this feature. This was in close relation with the strong El Niño event in 2015/2016, which forced more Kelvin waves in the equatorial troposphere. The easterly or very weak westerly zonal winds present around 30–70 hPa allowed these Kelvin waves to propagate vertically and deposit their momentum around 20 hPa, maintaining the westerlies there