Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points"

Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy predictions for the decayed, late-time state. Both formulations define an entropy through a somewhat ad hoc discretization of vorticity to the "particles" of which statistical mechanical methods are employed to define an entropy, before passing to a mean-field limit. In one case, the particles are delta-function parallel "line" vortices ("points" in two dimensions), and in the other, they are finite-area, mutually-exclusive convected "patches" of vorticity which in the limit of zero area become "points." We use time-dependent, spectral-method direct numerical simulation of the Navier-Stokes equations to see if initial conditions which should relax to different late-time states under the two formulations actually do so.Comment: 21 pages, 24 figures: submitted to "Physics of Fluids

The Role of Crystal Symmetry in the Magnetic Instabilities of β\beta-YbAlB4_4 and α\alpha-YbAlB4_4

Density functional theory methods are applied to investigate the properties of the new superconductor $\beta$-YbAlB$_4$ and its polymorph $\alpha$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $\beta$-YbAlB$_4$ and $\alpha$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $\beta$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $\beta$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.Comment: 9 pages, 9 figures, 2 table

Overexpression of hypoxia-inducible factor prolylhydoxylase attenuated by HCG-induced vascular endothelial growth factor expression in luteal cells

Vascular endothelial growth factor (VEGF)-dependent angiogenesis plays a crucial role in the corpus leteum formation and their functional maintenances in mammalian ovaries. We recently reported that the activation of hypoxia-inducible factor (HIF)-1α signaling contributes to the regulation of VEGF expression in the luteal cells (LCs) in response to hypoxia and human chorionic gonadotropin (HCG). This study was designed to test the hypothesis that, HIF prolyl-dydoxylases (PHDs) express in LCs and overexpression of PHD attenuates the expression of VEGF induced by HCG in LCs. By real-time PCR and western blot analysis, we examined the expression of PHDs, confirmed the plasmid transfection and their expression and also investigated the changes of HIF-1α and VEGF expression after treatment with HCG and PHD2 transgenes. PHD2 expression was significantly higher than the others, indicating its main roles. Moreover, a significant increase of VEGF mRNA was found after HCG treatment, while this increased VEGF mRNA was also blocked by PHD2 overexpression in LCs. Further analysis also found that, this HCG-induced increase of VEGF mRNA was consistent with the level of HIF-1α protein, which is regulated by HIF prolyl-dydoxylase -mediated degradation. Taken together, our results indicated that, PHD2 mainly expressed in LCs and HCG-induced VEGF expression can be blocked by PHD2 overexpression through HIF-1α -mediated mechanism in LCs. This PHD2-mediated transcriptional activation may be one of the important mechanisms regulating VEGF expression in LCs during mammalian corpus leteum development.Key words: Hypoxia-inducible factor-1α, HIF prolyl-dydoxylase, vascular endothelial growth factor, human chorionic gonadotropin, luteal cells

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Topological quantum memory interfacing atomic and superconducting qubits

We propose a scheme to manipulate a topological spin qubit which is realized with cold atoms in a one-dimensional optical lattice. In particular, by introducing a quantum opto-electro-mechanical interface, we are able to first transfer a superconducting qubit state to an atomic qubit state and then to store it into the topological spin qubit. In this way, an efficient topological quantum memory could be constructed for the superconducting qubit. Therefore, we can consolidate the advantages of both the noise resistance of the topological qubits and the scalability of the superconducting qubits in this hybrid architecture.Comment: v2: Accepted for publication in Science China-Physics, Mechanics & Astronom

Far-infrared optical properties of the pyrochlore spin ice compound Dy2Ti2O4

Near normal incident far-infrared reflectivity spectra of [111] dysprosium titanate (Dy2Ti2O4) single crystal have been measured at different temperatures. Seven phonon modes (eight at low temperature) are identified at frequency below 1000 cm-1. Optical conductivity spectra are obtained by fitting all the reflectivity spectra with the factorized form of the dielectric function. Both the Born effective charges and the static optical primitivity are found to increase with decreasing temperature. Moreover, phonon linewidth narrowering and phonon modes shift with decreasing temperature are also observed, which may result from enhanced charge localization. The redshift of several low frequency modes is attributed to the spin-phonon coupling. All observed optical properties can be explained within the framework of nearest neighbor ferromagnetic(FM) spin ice model