The Wigner Function as Distribution Function

Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the dynamical variables have their values defined even when they cannot be measured.     

First-principles investigation of electronic and optical properties in wurtzite Zn<Subscript>1-x</Subscript>Mg<Subscript>x</Subscript>O

A first-principles study has been performed to evaluate the electronic and optical properties of wurtzite Zn_1-xMg_xO. Substitutional doping is considered with Mg concentrations of x = 0, 0.0625, 0.125, 0.1875 and 0.25, respectively. Mg incorporation can induce band gap widening due to the decrease of Zn 4s states. The imaginary part of the dielectric function shows that the optical transition from band edge emission decreases slightly with increasing Mg contents. The optical band gap also increases from 3.2 to 3.7 eV with increasing Mg contents from 0.0625 to 0.25. The calculated results suggest that relatively high Mg concentration is necessary for effective band gap engineering of wurtzite Zn_1-xMg_xO.     

Nano-sized local magnetic field induced by circular motion of ions and molecules in a nanotorus under gigahertz rotating electric fields

Recently, we reported molecular dynamics simulations of stable cyclotron motions of ions and water molecules in a carbon nanotorus, induced by different rotating electric fields (EFs). This study is devoted to the calculation and characterisation of the magnetic field (MF) induced by these cyclotron motions. Results show that carbon nanotorus containing ions or water molecules acts as an EF-to-MF transducer. Components of the instantaneous induced MF show large-scale oscillations superimposed by strong fluctuations arising respectively from overall circular motion and random collisions of moving species. Analysis of the space-dependencies of the induced MF components shows that the induced MF is maximum at the centre of the nanotorus. The MF induced by cyclotron motion of ions follows the orders B(Ca²⁺)?>?B(Na⁺)?≈?B(K⁺) at E?=?1.0?V/nm and B(E?=?1.0?V/nm)?>?B(E?=?0.5?V/nm)?>?B(E?=?0.1?V/nm). The time-averaged induced MF of the cyclotron motion of 81 water molecules is almost 10² times stronger than that of ions. The induced MF strength is decreased with increasing distance from nanotorus and decays effectively at about 17.3–18.1 and 15.9–18.2?nm along the z-axis of the nanotorus for ions and water molecules, respectively. The magnitude of the MF induced by cyclotron motions of water molecules and ions, respectively, decreases and increases in the nanotorus with freed carbon atoms.     

On a conjecture of Lynch

Abstract

We comment on a conjecture of Lynch on annihilators of local cohomology.

Communicated by Lawrence Ein     

On the (N+1)-dimensional local fractional reduced differential transform method and its applications

In this paper, we generalize the (N+1)-dimensional local fractional reduced differential transform method (LFRDTM) within the local fractional derivative sense. First, we show some new properties, lemmas, theorems and corollariesfor the (N+1)-dimensional LFRDTM. Second, these new properties, lemmas and theorems can be proved immediately after. Thirdly, we used two examples to state that this approach is efficient and simple to find numerical solutions to higher dimensional local fractional partial differential equations. Finally, we can be seen that this work can be looked as an extension of the prior work.     

Finite element computations of viscoelastic two-phase flows using local projection stabilization

A three-field local projection stabilized (LPS) finite element method is developed for computations of a three-dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier-Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. Interface-resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one-level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape.     

The connected partition lattice of a graph and the reconstruction conjecture

Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question.     

Novel local smoothness indicators for improving the third‐order WENO scheme

The local smoothness indicators play an important role in the performance of a weighted essentially nonoscillatory (WENO) scheme. Due to having only 2 points available on each substencil, the local smoothness indicators calculated by conventional methods make the third‐order WENO scheme too dissipative. In this paper, we propose a different method to calculate the indicators by using all the 3 points on the global stencil of the third‐order WENO scheme. The numerical results demonstrate that the WENO scheme with the new indicators has less dissipation and better resolution than the conventional third‐order WENO scheme of Jiang and Shu for both smooth and discontinuous solutions.     

元素周期表中元素单晶基于局域密度理论的正电子寿命计算

在局域密度近似理论（LDA）的基础上用中性原子叠加模型和有限插分方法（SNA-FD）计算了元素周期表中各种元素单晶的正电子体寿命和单空位寿命.分析了不同结构的单晶中自由正电子的分布信息和湮没信息.元素单晶的正电子寿命计算值与文献中的实验测量值相符合,表明LDA基础上的SNA-FD方法可以作为单晶中正电子湮没理论计算的有效研究手段. 关键词： 局域密度近似理论 正电子寿命