Probing the anisotropic expansion from supernovae and GRBs in a model-independent way

In this paper, we study the anisotropic expansion of the universe using type Ia supernovae Union 2.1 sample and 116 long gamma-ray bursts. The luminosity distance is expanded with model-independent cosmographic parameters as a function of $z/(1+z)$ directly. Thus the results are independent of cosmology model. We find a dipolar anisotropy in the direction ($l=309.2^\circ \pm 15.8^\circ$, $b=-8.6^\circ \pm 10.5^\circ$) in galactic coordinates with a significant evidence $97.29\%$ (more than $2~\sigma$). The magnitude is $(1.37\pm 0.57) \times 10^{-3}$ for the dipole, and $(2.6\pm 2.1)\times 10^{-4}$ for the monopole, respectively. This dipolar anisotropy is more significant at low redshift from the redshift tomography analysis. We also test whether this preferred direction is caused by bulk flow motion or dark energy dipolar scalar perturbation. We find that the direction and the amplitude of the bulk flow in our results are approximately consistent with the bulk flow surveys. Therefore, bulk flow motion may be the main reason for the anisotropic expansion at low redshift, but the effect of dipolar distribution dark energy can not be excluded, especially at high redshift.Comment: 17 pages, 5 figures, 5 tables, accepted for publication in MNRA

Twistings, crossed coproducts and Hopf-Galois coextensions

Let $H$ be a Hopf algebra. Ju and Cai introduced the notion of twisting of an $H$-module coalgebra. In this note, we study the relationship between twistings, crossed coproducts and Hopf-Galois coextensions. In particular, we show that a twisting of an $H$-Galois coextension remains $H$-Galois if the twisting is invertible.Comment: 20 page

A thermodynamic theory for thermal-gradient-driven domain wall motion

Spin waves (or magnons) interact with magnetic domain walls (DWs) in a complicated way that a DW can propagate either along or against magnon flow. However, thermally activated magnons always drive a DW to the hotter region of a nanowire of magnetic insulators under a temperature gradient. We theoretically illustrate why it is surely so by showing that DW entropy is always larger than that of a domain as long as material parameters do not depend on spin textures. Equivalently, the total free energy of the wire can be lowered when the DW moves to the hotter region. The larger DW entropy is related to the increase of magnon density of states at low energy originated from the gapless magnon bound states

Low temperature latching solenoid

A magnetically latching solenoid includes a pull-in coil and a delatching coil. Each of the coils is constructed with a combination of wire materials, including material of low temperature coefficient of resistivity to enable the solenoid to be operated at cryogenic temperatures while maintaining sufficient coil resistance. An armature is spring-based toward a first position, that may extend beyond the field of force of a permanent magnet. When voltage is temporarily applied across the pull-in magnet, the induced electromagnetic forces overcome the spring force and pulls the armature to a second position within the field of the permanent magnet, which latches the armature in the pulled-in position. Application of voltage across the delatching coil induces electromagnetic force which at least partially temporarily nullifies the field of the permanent magnet at the armature, thereby delatching the armature and allowing the spring to move the armature to the first position

Projectively deformable Legendrian surfaces

Consider an immersed Legendrian surface in the five dimensional complex projective space equipped with the standard homogeneous contact structure. We introduce a class of fourth order projective Legendrian deformation called \emph{$\,\Psi$-deformation}, and give a differential geometric characterization of surfaces admitting maximum three parameter family of such deformations. Two explicit examples of maximally $\, \Psi$-deformable surfaces are constructed; the first one is given by a Legendrian map from \, \PP^2 blown up at three distinct collinear points, which is an embedding away from the -2-curve and degenerates to a point along the -2-curve. The second one is a Legendrian embedding of the degree 6 del Pezzo surface, \, \PP^2 blown up at three non-collinear points. In both cases, the Legendrian map is given by a system of cubics through the three points, which is a subsystem of the anti-canonical system.Comment: 33 page

An extension of heat hierarchy

We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra $\mathcal{A}_1$. The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.Comment: This note is incorporated into arXiv:1409.7024, arXiv:1408.324