Scattering of Dirac Waves off Reissner-Nordström Black Holes

Dirac equation in Kerr geometry was separated by Chandrasekhar in 1976. In the present paper, the radial parts of Dirac equation in Reissner-Nordström (RN) geometry are solved. We concentrate on two cases. The first one is that the energies of the waves are greater than the height of the potential barrier and the second one is that the waves hit on the potential barrier. In each case, the reflection and transmission coefficients and the wave function are computed. We compare the solutions with several parameters to show how the properties of the scattered wave depend on these parameters.     

Fibrous Networks with Incorporated Macrocycles: A Chiral Stimuli‐Responsive Supramolecular Supergelator and Its Application to Biocatalysis in Organic Media

A new and versatile, crown ether appended, chiral supergelator has been designed and synthesized based on the bis‐urea motif. The introduction of a stereogenic center improved its gelation ability significantly relative to its achiral analogue. This low‐molecular‐weight gelator forms supramolecular gels in a variety of organic solvents. It is sensitive to multiple chemical stimuli and the sol–gel phase transitions can be reversibly triggered by host–guest interactions. The gel can be used to trap enzymes and release them on demand by chemical stimuli. It stabilizes the microparticles in Pickering emulsions so that enzyme‐catalyzed organic reactions can take place in the polar phase inside the microparticles, the organic reactants diffusing through the biphasic interface from the surrounding organic phase. Because of the higher interface area between the organic and polar phases, enzyme activity is enhanced in comparison with simple biphasic systems.     

Notable shift of ultraviolet intensity on Sn-doped ZnO nanostructure fabricated by sol–gel method

Sn-doped ZnO (SZO) thin films are deposited by sol–gel dip-coating method with Sn content at 0 at.% and 1–15 at.% with an increment of 2 at.%. The structure and luminescence of the films are investigated. X-ray diffraction results indicate that all the SZO samples show preferential orientation along the (002) direction, and the scanning electron microscope exhibits that the surface morphology of the films change from nanoparticles to nanorods with increasing Sn concentration. X-ray photoelectron spectroscopy reveals that Sn exists as valence of +4 in the matrix. The photoluminescence peaks at 381 and 398 nm are observed in all the samples. The ratio of intensity of peak at 381 nm to that of peak at 398 nm differed markedly. The intensity of peak at 398 nm might be due to the response for the Sn atoms, while the intensity of peak at 381 nm is probably related to the quantum size effect.     

Effect of graft polymer prepared by living radical polymerisation on electro-optical properties of polymer dispersed liquid crystal

In this study, a graft polymer matrix prepared by living radical polymerisation had been incorporated into polymer dispersed liquid crystals (PDLCs). The electro-optical properties of the PDLCs were investigated. The results showed that the length and density of graft chain had a great influence on the memory effect of the PDLCs. Low-driving-voltage and weak-memory-effect PDLCs could easily be obtained with a graft polymer matrix.     

Numerical Investigation on the Effects of a Precursor Wetting Film on the Displacement of Two Immiscible Phases Along a Channel

A set of numerical experiments has been conducted to study the effect of a precursor fluid layer on the motion of two phase system in a channel. This system is characterized by coupled Cahn-Hillard and Navier-Stokes system together with slip boundary conditions. The solution of the governing equation involves first the solution of Cahn-Hillard equation with semi-implicit and Mixed finite element discritization with a convex splitting scheme. The Navier-Stokes equations are then solved with a P2-P0 mixed finite element method. Three cases have been investigated; in the first the effect of different wettability scenarios with no precursor layer has been investigated. In the second scenario, the effect of the precursor layer for different wettability conditions is investigated. In the third case, the effect of the thickness of the precursor layer is investigated. It is found that, wettability conditions have considerable effect on the flow of the considered two-phase system. Furthermore the existence of the precursor layer has additional influence on the breakthrough of the phases.     

A method of separating blended images in space debris observation

Due to the relative movement between space debris and background stars, the blending of objects and stars is ineluctable through observation. It brings down position accuracy of objects and even makes the tracking break down in worse conditions. In view of the difference of geometry between stars and objects in space debris observation, a technique for separating blended objects based on mathematical morphology is presented. It’s sufficiently flexible to be applied in image processing, and the blending images can be separated effectively with a high degree of centroid precision.

     

A new formulation of regularized meshless method applied to interior and exterior anisotropic potential problems

This paper proposes a new formulation of regularized meshless method (RMM), which differs from the traditional RMM in that the traditional formulation generates the diagonal elements of influence matrix via null-field integral equations, while our new one directly employs the boundary integral equations at the domain point to evaluate the diagonal elements. We test the present RMM formulation to two-dimensional anisotropic potential problems in finite and infinite domains in comparison with the traditional RMM. Numerical results show that the present RMM sharply outperforms the traditional RMM in the solution of interior problems, while the latter is clearly superior for exterior problems. A rigorous theoretical analysis of circular domain case also corroborates such numerical experiment observations and is provided in the appendix of this paper.