Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source crosses the caustics. Furthermore, the discriminant of the quintic equation enables us to study changes in the number of solutions, namely in the number of images. It is shown that this discriminant can be factorized into two parts: One represents the condition that the lens equation can be reduced to a single quintic equation, while the other corresponds to the caustics.Comment: 7 pages (PTPTeX); accepted for publication in Prog. Theor. Phy

Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for the caustics and critical curves. The present formulation offers a useful way for studying galaxy lenses frequently modeled as isothermal ellipsoids.Comment: 5 pages; accepted for publication in A&

A NOVEL PT-BASED CATHODE CATALYST DESIGN BY FIRST PRINCIPLES

Joint Research on Environmental Science and Technology for the Eart

Chemistry of sprite discharges through ion-neutral reactions

International audienceWe estimate the concentration changes, caused by a single streamer in sprites, of ozone and related minor species as odd nitrogen (NOx) and hydrogen (HOx) families in the upper stratosphere and mesosphere. The streamer has an intense electric field and high electron density at its head where a large number of chemically-radical ions and atoms are produced through electron impact on neutral molecules. After propagation of the streamer, the densities of minor species can be perturbed through ion-neutral chemical reactions initiated by the relaxation of these radical products. We evaluate the production rates of ions and atoms using electron kinetics model and assuming the electric field and electron density in the streamer head. We calculate the density variations mainly for NOx, Ox, and HOx species using a one-dimensional model of the neutral and ion composition of the middle atmosphere, including the effect of the sprite streamer. Results at the nighttime condition show that the densities of NO, O3, H, and OH increase suddenly through reactions triggered by firstly produced atomic nitrogen and oxygen, and electrons just after streamer initiation. It is shown that NO and NO2 still remain for 1 h by a certain order of increase with their source-sink balance predominantly around 60 km; for other species, increases in O3, OH, HO2, and H2O2 still remain in the range of 40?70 km. From this affirmative result of long time behavior previously not presented, we emphasize that sprites would have a power to impact on local chemistry at night. We also discuss comparison with previous studies and suggestion for satellite observations

Age of the Universe: Influence of the Inhomogeneities on the global Expansion-Factor

For the first time we calculate quantitatively the influence of inhomogeneities on the global expansion factor by averaging the Friedmann equation. In the framework of the relativistic second-order Zel'dovich-approximation scheme for irrotational dust we use observational results in form of the normalisation constant fixed by the COBE results and we check different power spectra, namely for adiabatic CDM, isocurvature CDM, HDM, WDM, Strings and Textures. We find that the influence of the inhomogeneities on the global expansion factor is very small. So the error in determining the age of the universe using the Hubble constant in the usual way is negligible. This does not imply that the effect is negligible for local astronomical measurements of the Hubble constant. Locally the determination of the redshift-distance relation can be strongly influenced by the peculiar velocity fields due to inhomogeneities. Our calculation does not consider such effects, but is contrained to comparing globally homogeneous and averaged inhomogeneous matter distributions. In addition we relate our work to previous treatments.Comment: 10 pages, version accepted by Phys. Rev.

Domain walls in (Ga,Mn)As diluted magnetic semiconductor

We report experimental and theoretical studies of magnetic domain walls in an in-plane magnetized (Ga,Mn)As dilute moment ferromagnetic semiconductor. Our high-resolution electron holography technique provides direct images of domain wall magnetization profiles. The experiments are interpreted based on microscopic calculations of the micromagnetic parameters and Landau-Lifshitz-Gilbert simulations. We find that the competition of uniaxial and biaxial magnetocrystalline anisotropies in the film is directly reflected in orientation dependent wall widths, ranging from approximately 40 nm to 120 nm. The domain walls are of the N\'eel type and evolve from near-$90^{\circ}$ walls at low-temperatures to large angle [1$\bar{1}$0]-oriented walls and small angle [110]-oriented walls at higher temperatures.Comment: 5 pages, 4 figure