Addendum to “Switching effect and the metal–insulator transition in electric field” by A.L. Pergament et al. [J. Phys. Chem. Solids 71 (2010) 874]

In the paper mentioned above we reported on the switching mechanism in vanadium dioxide which was shown to be based on the electronically-induced Mott insulator-to-metal transition occurring in conditions of the non-equilibrium carrier density excess in the applied electric field, and the proposed model involved the dependence of the carrier density n on electric field (the Poole–Frenkel effect), as well as the dependence of the critical electric field on n. The data on the n(T) dependence were obtained on the assumption of a temperature-independent carrier mobility μ, and the problem of n reduction at lower temperatures was not fully understood. In this Letter we revisit this problem in the light of some recent data on the μ(T) dependence for VO₂. It is shown that the adjusted values of n, taking into account this μ(T), correspond to the Mott critical density within an order of magnitude.     

Cauchy-type integral formula and Plemelj formula of hypermonogenic functions on unbounded domains

In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries.     

关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

The depth spectrums of constacyclic codes over finite chain rings

In light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n,p)=1$(n,p)=1$.     

Method of infinite systems of equations for solving an elliptic problem in a semistrip

Many problems of mechanics and physics are posed in unbounded (or infinite) domains. For solving these problems one typically limits them to bounded domains and finds ways to set appropriate conditions on artificial boundaries or use quasi-uniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite systems of equations. In this paper we develop this approach for an elliptic problem in an infinite semistrip. Using the idea of Polozhii in the method of summary representations we transform the infinite system of three-point vector equations to infinite systems of three-point scalar equations and obtain the approximate solution with a given accuracy. Numerical experiments for several examples show the effectiveness of the proposed method.     

Schrödinger eigenbasis on a class of superconducting surfaces: Ansatz,analysis, FEM approximations and computations

In this work we focus on the efficient representation and computation of the eigenvalues and eigenfunctions of the surface Schrödinger operator ${(i\mathrm{\nabla }+{\mathbf{A}}_0)}^2$ that governs a class of nonlinear Ginzburg–Landau (GL) superconductivity models on rotationally symmetric Riemannian 2-manifolds S. We identify and analyze a complete orthonormal system in $L^2(S;\mathbb{C})$ of eigenmodes having a variable-separated form. For the unknown functions in this ansatz, our analysis facilitates the identification of approximate spectral problems whose eigenvalues lie arbitrarily near corresponding eigenvalues of the Schrödinger operator. We then develop and implement an arbitrary order finite element method for the efficient numerical approximation of the eigenvalue problem. We also demonstrate our analysis, algorithm and its convergence rate using parallel computations performed on a variety of choices of smooth and non-smooth surfaces S.     

Quaternary (liquid + liquid) equilibrium data for the extraction of toluene from alkanes using the ionic liquid [EMim][MSO4]

(Liquid + liquid) equilibrium (LLE) studies for the extraction of aromatics from alkanes present in the petroleum fractions are important to develop theoretical/semiempirical (liquid + liquid) equilibrium models, which are used in the design of extraction processes. In this work, the ionic liquid 1-ethyl-3-methylimidazolium methylsulfate, [EMim][MSO₄], was evaluated as potential solvent for the separation of toluene from heptane and cyclohexane. The LLE data for the quaternary system {heptane (1) + cyclohexane (2) + toluene (3) + [EMim][MSO₄] (4)} were experimentally determined at T = 298.15 K and atmospheric pressure. Moreover, the LLE data for the ternary systems {heptane or cyclohexane (1) + toluene (2) + [EMim][MSO₄] (3)} were also determined. Solute distribution ratios and selectivities were calculated and analysed in order to evaluate the capability of the ionic liquid to accomplish the separation target. A comparison between the solute distribution ratios and selectivities for the quaternary and the ternary systems was also made. Finally, the experimental tie-line data were correlated with the NRTL model.     

Explicit finite difference simulations for accelerating cross diffusion flow over a perpendicular shield with parabolic motion

The heat transfer phenomenon subject to thermos-diffusion effects convey important applications in the heating processes, extrusion systems, chemical processes and various engineering systems. The objective of current work is to observe the contribution of Soret and Dufour effects in oscillating shield for cross diffusion flow. The perpendicular shield with oscillating motion induced the flow. The magnitude of oscillations is assumed to be small so that laminar flow due to oscillating shield has been resulted. The motivations for addressing the thermos-diffusion phenomenon due to oscillating of shield are due to applications in oscillatory pumps, moving surface, metal detectors, power systems etc. The dimensionless problem is obtained via introducing the appropriate set of variables. The numerical outcomes are suggested by using the most interesting explicit finite difference scheme. The physical illustration for flow parameters is presented. Moreover, the aspect of physical quantities involving the flow are graphically reported.     

Longitudinally Grafting of Graphene with Iron Phthalocyanine-based Porous Organic Polymer to Boost Oxygen Electroreduction

Iron phthalocyanine-based polymers (PFePc) are attractive noble-metal-free candidates for catalyzing oxygen reduction reaction (ORR). However, the low site-exposure degree and poor electrical conductivity of bulk PFePc restricted their practical applications. Herein, laminar PFePc nanosheets covalently and longitudinally linked to graphene (3D-G-PFePc) was prepared. Such structural engineering qualifies 3D-G-PFePc with high site utilization and rapid mass transfer. Thence, 3D-G-PFePc demonstrates efficient ORR performance with a high specific activity of 69.31 μA cm⁻², a high mass activity of 81.88 A g⁻¹, and a high turnover frequency of 0.93 e s⁻¹ site⁻¹ at 0.90 V vs. reversible hydrogen electrode in O₂-saturated 0.1 M KOH, outperforming the lamellar PFePc wrapped graphene counterpart. Systematic electrochemical analyses integrating variable-frequency square wave voltammetry and in situ scanning electrochemical microscopy further underline the rapid kinetics of 3D-G-PFePc towards ORR.     

Hierarchical chlorine-doped rutile TiO2 spherical clusters of nanorods: Large-scale synthesis and high photocatalytic activity

In this study, we report the synthesis of hierarchical chlorine-doped rutile TiO₂ spherical clusters of nanorods photocatalyst on a large scale via a soft interface approach. This catalyst showed much higher photocatalytic activity than the famous commercial titania (Degussa P25) under visible light (λ>420 nm). The resulting sample was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution TEM (HRTEM), nitrogen adsorption, X-ray photoelectron spectroscopy (XPS), UV-vis diffuse reflectance spectroscopy, ¹H solid magic-angle spinning nuclear magnetic resonance (MAS-NMR) and photoluminescence spectroscopy. On the basis of characterization results, we found that the doping of chlorine resulted in red shift of absorption and higher surface acidity as well as crystal defects in the photocatalyst, which were the reasons for high photocatalytic activity of chlorine-doped TiO₂ under visible light (λ>420 nm). These hierarchical chlorine-doped rutile TiO₂ spherical clusters of nanorods are very attractive in the fields of environmental pollutants removal and solar cell because of their easy separation and high activity.