Symmetry calculation for molecules and transition states

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three‐dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label‐stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. © 2014 Wiley Periodicals, Inc.     

硅烯中受电场调控的体能隙和朗道能级

近年来, 硅烯(单层硅)由于其独特的结构和电子性质以及在量子霍尔效应等领域的潜在应用而成为理论和实验研究的一个热点. 借助于四带次近邻紧束缚模型, 详细计算和研究了硅烯中受电场调制的体能隙和电子能级. 结果表明: 硅烯原胞中的两个子格处于不同的平面上, 可以通过外电场区分和控制这两个子格, 这将破坏在纯石墨烯中无法被破坏的K-K'对称性, 并消除由这一对称性导致的电子能级的二重简并; 外加电场还会引起硅烯中次近邻格点之间的Rashba自旋轨道耦合, 这一作用会在不同狄拉克点有选择地消除电子能级在部分电场点的简并, 相邻能级从交叉状态变为反交叉状态; 电子能级中除一些孤立的交叉点外, 每个能级都具有确定的自旋取向, 石墨烯中电子能级的四重简并在硅烯中被完全消除, 从而导致填充因子ν=0, ±1, ±2, ±3,…的量子霍尔平台.     

Hohenberg–Kohn theorems in the presence of magnetic field

In this article, we examine Hohenberg–Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg–Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation (Vignale and Rasolt, Phys. Rev. Lett. 1987, 59, 2360), which uses the paramagnetic current density, we address the issue of degenerate ground states and prove that the ensemble‐representable particle and paramagnetic current density determine the degenerate ground states. For the formulation that uses the total current density, we note that the proof suggested by Diener (Diener, J. Phys.: Condens. Matter. 1991, 3, 9417) is unfortunately not correct. Furthermore, we give a proof that the magnetic field and the ensemble‐representable particle density determine the scalar and vector potentials up to a gauge transformation. This generalizes the result of Grayce and Harris (Grayce and Harris, Phys. Rev. A 1994, 50, 3089) to the case of degenerate ground states. We moreover prove the existence of a positive wavefunction that is the ground state of infinitely many different Hamiltonians. © 2014 Wiley Periodicals, Inc.     

蝙蝠听觉神经系统如何在复杂环境中识别昆虫

生物声纳的高灵敏度和高可靠性一直是仿生设计所追求的目标, 然而至今仍没有一个令人信服的物理模型能很好得解释生物声纳优越性能的原因, 其主要是缺乏对动物听觉系统神经信息编码的认识. 本文从蝙蝠听觉神经系统的生理结构出发, 用圆映射和符号动力学方法讨论了蝙蝠听觉神经系统在复杂环境中处理多普勒信号的一种可能性方案, 并通过计算机仿真证明了其合理性. 针对蝙蝠神经系统的不稳定性, 用符号动力学的方法分析神经系统信息处理的机理具有良好的鲁棒性和高灵敏度. 这种新的信号处理方法的研究, 为生物声纳信号的处理过程的进一步认识提供了一种新的解释.     

A deterministic method study of the impact of the Pauli principle in double-gate MOSFETs

The Pauli principle is included in a multisubband deterministic solver for two-dimensional devices without approximations.The nonlinear Boltzmann equations are treated properly without compromising on accuracy,convergence,or CPU time.The simulation results indicate the significant impact of the Pauli principle on the transport properties of the quasi-2D electron gas,especially for the on state.     

DEGENERATE OPTIMAL BASIS GRAPHS IN LINEAR PROGRAMMING

§ 1　IntroductionA graph-theoretic approach for investigating basis transformations in a linear pro-gramming has been historically developed.Let V be the setof all bases with respectto thecolumn vectors of a matrix A.Two bases are called adjacentifthey can be transformed intoeach other by a pivot operation.Denote by E the set of edges each of which is incidentwith a pair of adjacentbases.Then G=(V,E) is called the basisgraph of matrix A(or ofthe corresponding LP) .Tucker[1 ] first called…     

Thermodynamic conditions for a symmetric form of superfluid's equations

Summary Going on with a research started in a previous paper, we examine carefully Putterman's system of superfluid hydrodynamic equations, assuming as viewpoint the theory of quasi-linear hyperbolic symmetric systems with constraints. We prove that such a system is always hyperbolic. It can be put in a symmetric form, provided suitable thermodynamic conditions, ensuring the convexity of the entropy function, hold.

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Riassunto Si approfondisce l'esame, iniziato in un precedente lavoro, del sistema di equazioni idrodinamiche del superfluido di Putterman dal punto di vista della teoria dei sistemi quasi lineari iperbolici simmetrici e con vincoli. Si dimostra che tale sistema è sempre iperbolico e può essere posto in forma simmetrica quando siano soddisfatte opportune condizioni termodinamiche che assicurano la convessità della funzione entropia.

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Резюме Углубляется начатое в одной из предыдущих работ исследование системы гидродинамических уравнений супержидкости Паттермана с точки зрения теории систем квазилинейных гиперболических симметрических и со связями. Доказывается, что такая система является всегда гиперболической и может быть приведена к симметрической форме, когда выполнены соответствующие термодинамические условия, обеспечивающие вьшуклость функции энергии.