Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, $B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$. Then, we prove the global wellposedness for (\textit{ANS}) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.Comment: 39 page

A nondiagrammatic calculation of the Rho parameter from heavy fermions

A simple nondiagrammatic evaluation of the nondecoupling effect of heavy fermions on the Veltman's Rho parameter is presented in detail. This calculation is based on the path integral approach, the electroweak chiral Lagrangian formalism, and the Schwinger proper time method.Comment: 11 page

Self-equilibrium and super-stability of truncated regular hexahedral and octahedral tensegrity structures

This paper presents conditions for self-equilibrium as well as super-stability of the truncated regular hexahedral and octahedral tensegrity structures. Their symmetry can be described by octahedral group in group representation theory, and furthermore, their force density matrix is analytically rewritten in the symmetry-adapted form. The condition for self-equilibrium, in terms of force densities, is found by satisfying the non-degeneracy condition for a tensegrity structure. The condition for super-stability, also in terms of force densities, is further presented by guaranteeing positive semi-definiteness of the force density matrix

Tunnelling through black rings

Hawking radiation of black ring solutions to 5-dimensional Einstein-Maxwell-dilaton gravity theory is analyzed by use of the Parikh-Wilczek tunnelling method. To get the correct tunnelling amplitude and emission rate, we adopted and developed the Angheben-Nadalini-Vanzo-Zerbini covariant approach to cover the effects of rotation and electronic discharge all at once, and the effect of back reaction is also taken into account. This constitute a unified approach to the tunnelling problem. Provided the first law of thermodynamics for black rings holds, the emission rate is proportional to the exponential of the change of Bekenstein-Hawking entropy. Explicit calculation for black ring temperatures agree exactly with the results obtained via the classical surface gravity method and the quasilocal formalism.Comment: 10 pages, V2: various modifications throughout the text, plus a lot of newly added reference

Pattern Registration Between Spherical Block-Copolymer Domains and Topographical Templates

Pattern registration is achieved in thin films of self-assembling block copolymers by using a topographical template to guide the positions of the polymer domains. The placement accuracy of the polymer domains is related to the edge roughness of the topographical template, and the ultimate placement accuracy is assessed (see Figure). For a block copolymer with spherical morphology, a registered polymer array is achieved by using a two-dimensional template

Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry

The energy spectra and the corresponding two- component spinor wavefunctions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The $s-$wave ($\kappa = 0$ state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wavefunctions for this potential and other special types of this potential are obtained. Extension of this result to $\kappa \neq 0$ state is suggested.Comment: 18 page

Petrogenesis of granitoids in the eastern section of the Central Qilian Block: Evidence from geochemistry and zircon U-Pb geochronology

The Caledonian-age Qilian Orogenic Belt at the northern margin of the Greater Tibetan Plateau comprises abundant granitoids that record the histories of the orogenesis. We report here our study of these granitoids from two localities. The Qingchengshan (QCS) pluton, which is situated in the eastern section of the Central Qilian Block, is dated at ~430–420 Ma. It has high-K calc-alkaline composition with high SiO2 (> 70 wt%), enrichment in large ion lithophile elements (LILEs), depletion in high field strength elements (HFSEs), and varying degrees of negative Sr and Eu anomalies. The granitoids in the Tongwei (TW) area, 150 km east of the QCS, are complex, the majority of which are dated at ~440 Ma, but there also exist younger, ~230 Ma intrusions genetically associated with the Qinling Orogeny. The Paleozoic TW intrusions also have high SiO2, fractionated REE (rare earth element) patterns, but a negligible Eu anomaly. The whole rock Sr-Nd-Hf isotopic compositions suggest that all these Paleozoic granitoids are consistent with melting-induced mixing of a two-component source, which is best interpreted as the combination of last fragments of subducted/subducting ocean crust with terrigenous sediments. The mantle isotopic signature of these granitoids (87Sr/86Sri: 0.7038 to 0.7100, εNd(t): −4.8 to −1.3, εHf(t): −0.7 to +4.0) reflects significant (~70 %) contribution of the ocean crust derived in no distant past from the mantle at ocean ridges with an inherited mantle isotopic signature. Partial melting of such ocean crust plus terrigenous sediments in response to the ocean closing and continental collision (between the Qilian and Alashan Blocks) under amphibolite facies conditions is responsible for the magmatism. Varying extents of fractional crystallization (±plagioclase, ±amphibole, ±garnet, ±zircon) of the parental magmas produced the observed QCS and TW granitoids. We note that sample HTC12–01 in the TW area shows an A-type or highly fractionated granite signature characterized by elevated abundances and a flat pattern of REEs, weak Nb-Ta anomaly, conspicuous negative Sr and Eu anomalies (Sr/Sr* = 0.09, Eu/Eu* = 0.22), and thus the high 87Sr/86Sr ratio (0.7851), and moderate εNd(t) (−4.9) and εHf(t) (−2.0), pointing to the significant mantle contribution. Compared with the Paleozoic granitoids, the ~230 Ma granitoids in the TW area represented by sample JPC12–02 have higher initial 87Sr/86Sr (0.7073) and lower εNd(t) (−6.2) and εHf(t) (−4.5) values, offering an ideal opportunity for future studies on tectonic effects of juxtaposition of younger orogenesis on an older orogen