氨分子逐级键解离能降低的解释

采用理论计算方法解释了氨逐级解离能降低的现象。计算结果表明,随着N与H原子结合数目的减少,键解离能降低、键长增长;随着N与H原子结合数目的增多,N的2s电子跃迁到N的2p轨道上的几率增大,减小了屏蔽作用;更多电子从H的1s轨道迁移到N的2p轨道,增大了N和H之间的静电作用;单电子或孤对电子与N-H键夹角的增大减小了排斥作用。这3个因素造成NH3的逐级键解离能有降低的趋势。     

Efficient Gaussian sample specific network marker discovery and drug enrichment analysis validation

Identifying stable gene markers at an individual level can help to understand the genetic mechanisms of each individual patient and accomplish personalized medicine. In this paper, we propose an efficient framework to identify sample-specific markers. Gene expression data first is transformed to a corresponding likelihood matrix to alleviate inherent noise besides adding population information to each sample. Then those significantly differential genes or gene pairs are further mapped to a STRING network for analysis by assuming that the likelihood of each gene or gene pairs in the control group follows a Gaussian distribution. The proposed method is applied to three benchmark datasets including lung adenocarcinoma, kidney renal clear cell carcinoma, and uterine corpus endometrial carcinoma. It is found that disease gene markers identified by the proposed methods outperform the previous sample-specific network (SSN) method in both subtyping and survival analysis. Furthermore, we exploit the application of the subtype markers in following drug selection. The difference of the enriched drug set may reflect some underlying mechanisms of the subtypes and shed light on selecting appropriate drugs for each cancer subtype.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

Relativistic correlating basis sets for 57La and 89Ac

Developed and reported are compact yet efficient correlating basis sets for the ₅₇La and ₈₉Ac atoms, missing in the literature. Good performance of these correlating sets is exemplified in molecular applications to diatomic oxides and fluorides. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation

This paper introduces a wavepacket-transform-based Gaussian beam method for solving the Schrödinger equation. We focus on addressing two computational issues of the Gaussian beam method: how to generate a Gaussian beam representation for general initial conditions and how to perform long time propagation for any finite period of time. To address the first question, we introduce fast Gaussian wavepacket transforms and develop on top of them an efficient initialization algorithm for general initial conditions. Based on this new initialization algorithm, we address the second question by reinitializing the beam representation when the beams become too wide. Numerical examples in one, two, and three dimensions demonstrate the efficiency and accuracy of the proposed algorithms. The methodology can be readily generalized to deal with other semi-classical quantum mechanical problems.     

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation

We propose the backward phase flow method to implement the Fourier–Bros–Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.     

Asymptotic Expansions for the Distribution of the Maximum of Gaussian Random Fields

Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of ^N . They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level inside S and on the border S. Depending on the geometry of the border we give up to N+1 terms of the expansion sometimes with exponentially small remainder. Application to waves maximum is shown.     

Exact Gaussian expansions of Slater-type atomic orbitals

Three exact Slater-type function (STO) integral transforms are presented. The STO-NG basis set can then be developed using either only 1s Gaussian functions, the same Gaussian exponents for each shell, or using the first Gaussian of each symmetry. The use of any of these three alternatives depends only on appropriate numerical integration techniques.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

Design of Transmission Line for Submillimeter Wave Gyrotron Using Dielectric-Lined Waveguide

The excitation and transmission losses of a dielectric-lined waveguide have been calculated with real, experimentally measured output beams of a submillimeter wave gyrotron. It is shown that for not-so-long transmission lines the coupling losses far exceed the transmission losses in the waveguide.