The KHKH-Isomorphism Conjecture and Algebraic KKKK-theory

In this article we prove that the $KH$-asembly map, as defined by Bartels and L{\"u}ck, can be described in terms of the algebraic $KK$-theory of Cortinas and Thom. The $KK$-theory description of the $KH$-assembly map is similar to that of the Baum-Connes assembly map. In very elementary cases, methods used to prove the Baum-Connes conjecture also apply to the $KH$-isomorphism conjecture

H2_2 Emission Nebulosity Associated with KH 15D

An H$_2$ emission filament is found in close proximity to the unique object KH 15D using the adaptive optics system of the Subaru Telescope. The morphology of the filament, the presence of spectroscopic outflow signatures observed by Hamilton et al., and the detection of extended H$_2$ emission from KH 15D by Deming, Charbonneau, & Harrington suggest that this filament arises from shocked H$_2$ in an outflow. The filament extends about 15" to the north of KH 15D.Comment: 11 pages, 3 figures, 1 table. Astrophysical Journal Letters, in pres

Evolution of a barotropic shear layer into elliptical vortices

When a barotropic shear layer becomes unstable, it produces the well known Kelvin-Helmholtz instability (KH). The non-linear manifestation of KH is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KH characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counter-propagating vorticity waves is solely responsible for this KH formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides possible explanation behind the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g. meddies, Stratospheric polar vortices, Jovian vortices, Neptune's Great Dark Spot and coherent vortices in the wind belts of Uranus.Comment: 7 pages, 4 figures, Accepted in Physical Review

Three-band Hubbard model for Na2_2IrO3_3: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material

Na$_2$IrO$_3$ was one of the first materials proposed to feature the Kane-Mele type topological insulator phase. Contemporaneously it was claimed that the very same material is in a Mott insulating phase which is described by the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott insulating behavior in conjunction with antiferromagnetic long-range order. Further refined experiments established antiferromagnetic order of zigzag type which is not captured by the KH model. Since then several extensions and modifications of the KH model were proposed in order to describe the experimental findings. Here we suggest that adding charge fluctuations to the KH model represents an alternative explanation of zigzag antiferromagnetism. Moreover, a phenomenological three-band Hubbard model unifies all the pieces of the puzzle: topological insulator physics for weak and KH model for strong electron-electron interactions as well as a zigzag antiferromagnet at intermediate interaction strength.Comment: 5 pages, 3 figures; v2 (as published): added discussion about kinetic energy scale C; more realistic values of C shift the zigzag AFM phase to larger values of

The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces

We show that, for a complete simplicial toric variety $X$, we can determine its homotopy \KH-theory entirely in terms of the torus pieces of open sets forming an open cover of $X$. We then construct conditions under which, given two complete simplicial toric varieties, the two spectra \KH(X) \otimes \Q and \KH(Y) \otimes \Q are weakly equivalent. We apply this result to determine the rational \KH-theory of weighted projective spaces. We next examine \K-regularity for complete toric surfaces; in particular, we show that complete toric surfaces are \K_{0}-regular. We then determine conditions under which our approach for dimension 2 works in arbitrary dimensions, before demonstrating that weighted projective spaces are not \K_{1}-regular, and for dimensions bigger than 2 are also not in general \K_{0}-regular.Comment: 14 pages. Updated version, strengthening the proofs to hold true over any regular ring. To appear in the Journal of Pure and Applied Algebr

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear

The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (DTM) which dominate at lower shearing rates. The possible application of these results in tokamaks with internal transport barrier is discussed.Comment: 4 pages, 4 figure