An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field

We study the limiting behavior of a singularly perturbed Schr?dinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane (x, y) and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr?dinger equations in the plane (x, y), coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator.     

Microwave-assisted synthesis and characterization of Bi-substituted yttrium garnet nanoparticles

Bi-substituted yttrium iron garnet (Bi-YIG, Bi_1.8Y_1.2Fe₅O₁₂) nanoparticles were prepared by microwave-assisted co-precipitation as well as conventional co-precipitation using ammonia aqueous solution as precipitant. The nanoparticles were characterized by thermal gravity-differential thermal analysis, X-ray powder diffraction, transmission electron microscopy, dynamic light scattering and vibrating sample magnetometer, respectively. The Faraday rotation of Bi-YIG modified PMMA slices was also investigated. Results demonstrate that the Bi-YIG nanoparticles prepared by microwave-assisted co-precipitation show smaller particle size and higher Faraday rotation than those prepared by conventional co-precipitation.     

On the nontrivial non-travelling wave profiles of nonlinear evolution and wave equations

The overall aim of the present paper is to find and analyze the new non-travelling wave solutions of the nonlinear evolution and wave equations. With the aid of symbolic computation and based on the generalized extended tanh-function method, we propose the newly extended tanh-function expansion algorithm and get many new non-travelling wave solutions of the (2 + 1)-dimensional Broer–Kaup–Kupershmidt equations. The solutions which we obtain are more abundant than the solutions which the generalized extended tanh-function method gets. At the same time, the solutions contain arbitrary functions which may be helpful to explain some complex phenomena. We also give some figures to describe the property of these solutions. In additions, the method can also be successfully applied to other nonlinear evolution and wave equations.     

Room temperature gaseous hydrogen storage properties of Mg-based metallic glasses with ultrahigh Mg contents

Mg–Ce–Ni metallic glasses with record high Mg content larger than 90 at.% were fabricated. Remarkably, the metallic glasses can reversibly absorb and desorb about 0.2–0.4 wt.%-H at room temperature without activation, and the hydrogenation capacity of the glassy Mg-based alloy is twice larger than that of the corresponding crystalline alloy. It is found that hydrogenation capacity shows close connection with the glassy structure of the alloys, and the higher Mg content amorphous structure can store more hydrogen. The work might present a way for gaseous hydrogen storage by metallic glasses media.     

Eulerian numbers: A spline perspective

In this paper, the spline interpretations of Eulerian numbers and refined Eulerian numbers are presented. Many classical results about Eulerian numbers can follow from the properties of B-splines directly, and some new results about the refined Eulerian numbers and descent polynomials are also derived. Specifically, the explicit and recurrence formulas for the refined Eulerian numbers and descent polynomials are obtained. This paper also provides a new approach to study Eulerian numbers.     

CHEMICAL STRUCTURE DEPENDENCE OF THE INTERNAL ENERGY CONTRIBUTION IN RUBBER ELASTICITY

Conformational elasticity theory recently developed has been used to explore the internal energy contribution tothe elastic force f_e/f as a function of strain for poly(cis-1,4-isoprene) and poly(trans-1, 4-isoprene). Calculated f_e/f values arein good agreement with those obtained experimentally. Results show that behavior of f_e/f is mainly contributed by chemicalstructure, or intramolecular interaction, supporting the experimental observations, and that the internal energy contribution isstrain dependent.     

Application of enthalpy method for moving boundary problem in laser surface melting

A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization. The enthalpy method was applied to solve this two-phase axisymmetrical melting problem. Computational results of temperature fields were obtained, which provide useful information to practical laser treatment processing. The validity of enthalpy method in solving such problems is pressented. Supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences     

SYNTHESIS AND CHARACTERIZATION OF NOVEL REACTIVE POLYORGANOSILOXANE CONTAINING NITRO GROUPS*

 A novel reactive polyorganosiloxane containing nitro groups was first prepared by acid-catalyzed equilibration polymerization. The monomer, 3-(4-nitrophenoxy)propylmethyldichlorosilane (NPPMS), was synthesized by hydrosilylation reaction with dicyclopentadienylplatinum(II) chloride (Cp₂PtC1₂) catalyst in high yield. The synthesized polynitroorganosiloxane, which has potential application as a precursor for synthesizing advanced functional polymers, was characterized by FTIR, ¹H-NMR, ¹³C-NMR, ²⁹Si-NMR, vapor pressure osmometry (VPO) and gel permeation chromatography (GPC).     

Formation of binary alloy cluster ions from group-14 elements and cobalt and comparison with solid-state alloys.

By using laser ablation on mixtures of transition metal cobalt and group-14 elements, binary alloy cluster anions were produced while no binary alloy cluster cations were detected, and the homocluster cations of group-14 elements appeared at very low abundance. The differences between clustering abilities of germanium, tin and lead with cobalt are described, and the chemical bonds in the binary alloy cluster anions appear to indicate a transition from covalent to metal bonds. The cluster anion [CoPb10](-) appears in very high abundance (magic number), and an endohedral structure is proposed for this cluster. The cluster anion [CoPb12](-), also representing a magic number, probably has an icosahedral structure. Compared with solid-state Co/Ge binary alloys, the compositions of most binary alloy cluster anions are germanium-rich, in which the covalent bonds are predominant.