示性函数在初等概率论中的应用

示性函数在实分析等课程中很基本且应用广泛,但在初等概率论教材里应用不多.本文举例说明示性函数可以帮助学生理解初等概率论中一些基本概念、结论并精简其中一些计算.     

Properties of RhP predicted by first-principles

Using density functional theory combined with a global crystal structure search with the particle swarm optimization method, we propose three stable three-dimensional (3D) metallic RhP structures, namely, the Cmcm (RhP-I), P6/mmm (RhP-II), and P6₃mc (RhP-III) phases. All these structures are found to be dynamically stable through vibrational normal mode calculations, indicating that they could be successfully synthesized in experiments. We show that the RhP-I phase has a relatively high thermodynamic stability and high mechanical strength in comparison with the others. The RhP-II and RhP-III phases have porous structures which could accommodate small atoms or molecules. However their thermodynamics are poor, especially the RhP-III phase. The RhP-II structure is stable at 500 K, but the RhP-III fails to survive even at the freezing point of water. Importantly, all these materials have one dimensional conducting channels corresponding to ultrahigh Fermi velocities. Moreover, the porous hexagonal RhP-II and III structures exhibit excellent ability to trap lithium, hydrogen, oxygen, and boron atoms. The RhP-II structure could be especially useful for directly dissociating the hydrogen molecule into two atoms without an energy barrier. In the present study, we identify three new metallic structures to the family of RhP structures, and anticipate their potential for technological applications.     

Electrical switching effect in a photochromic molecule between two graphene electrodes

We propose a single-molecule electrical switches consisting of a photochromic dimethyldihydropyrene/cyclophanediene molecule sandwiched between two graphene electrodes and investigate the electronic transport by using density-functional theory and nonequilibrium Green's function methods. The “open” and “closed” isomers of the photochromic molecule are shown to have electrical switching behavior and negative differential resistance effect. Moreover, it is also found that the switching ratio between two different conductive states depends on the ambient temperature, and the device behaves as a stable electrical switch around room temperature, which is in agreement with a recent experimental study of another photochromic molecule diarylethene reported by Jia et al. (2016) [17].     

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.     

叶黄素简介

叶黄素属类胡萝卜素,近年研究发现其具有保护视觉、抗氧化、抗癌等作用。本文从叶黄素的结构、性质、来源、生理功效、研究现状及应用前景等方面进行了介绍。     

Molecular Weight Distribution Control for Polymerization Processes Based on the Moment-Generating Function

The molecular weight distribution is an important factor that affects the properties of polymers. A control algorithm based on the moment-generating function was proposed to regulate the molecular weight distribution for polymerization processes in this work. The B-spline model was used to approximate the molecular weight distribution, and the weight state space equation of the system was identified by the subspace state space system identification method based on the paired date of B-spline weights and control inputs. Then, a new performance criterion mainly consisting of the moment-generating function was constructed to obtain the optimal control input. The effectiveness of the proposed control method was tested in a styrene polymerization process. The molecular weight distribution of the styrene polymers can be approximated by the B-spline model effectively, and it can also be regulated towards the desired one under the proposed control method.     

Investigations of nuclear dynamics of LaI<Subscript>3</Subscript> molecule. I. Potential functions of normal vibrations in harmonic and anharmonic approximations

The potential energy surface of the LaI₃ molecule is scanned along the normal coordinate by a B3LYP/SDD, SDD method. It is shown that a nonplanar ν₂(A ₂″) vibrational potential function is most anharmonic. The effect of anharmonicity on the root mean square amplitudes of vibrations and the vibrational molecule spectrum is stated.     

取代1-氯蒽醌中分子内卤键的电子密度拓扑分析

运用量子化学密度泛函B3LYP方法,在6-311＋＋G（d,p）基组水平上对邻位和间位取代1-氯葸醌的分子内卤键进行了研究．用电子定域函数和“分子中的原子,,理论对分子内卤键的性质进行了电子密度拓扑分析．通过对计算得到的密度矩阵进行σ-π兀分离,得到了π-键的键径和分子图,并讨论了。电荷密度和兀电荷密度对卤键的影响．结果表明,键鞍点和环鞍点处的电子密度拓扑性质均可作为衡量分子内卤键强度的量度．键鞍点和环鞍点处的电荷密度P越大,键鞍点与环鞍点的距离越大,卤键强度越大．除σ电荷密度外,π电荷密度对分子内卤键的性质也有明显影响．     

甲醇制烯烃催化剂失活模型

在固定床反应器中,研究了甲醇制烯烃反应中当SAPO-34分子筛处于失活期时催化剂活性的变化情况,主要考察催化剂活性随反应温度、空速和运行时间的变化,通过对实验数据的分析拟合,得到了催化剂活性与失活时间、反应温度、空速的经验关联式(失活模型),对失活模型的检验表明,该模型与实验数据较为吻合,表明了该式的准确性。 通过对失活模型的分析,获得了当失活速率达到最大时的失活时间与反应时间、空速的关联式,失活过程应服从不均匀表面失活机理,并且当催化剂处于失活区时,失活时间对活性的影响要大于空速和温度。     

The changes in free energies and entropies from analytical radial distribution functions

The changes in Helmholtz free energies and entropies in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs) of Lennard–Jones (L-J) fluid. This method provides a simpler and a more expeditious way for the calculation of free energy and entropy in L-J dense fluids through statistical mechanics. Previously, integral equations or perturbation theories were used for this purpose. Such approach not only tests the power of analytical distribution functions in predicting the changes in Helmholtz free energies and entropies, but also specifies better expressions in determining these properties. The results are compared with experimental data and an accurate analytic equation of state for the L-J fluid. It is shown if an expression properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate the changes in Helmholtz free energies and entropies from analytical distribution functions.