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January 15,2016
Volume 9,Issue 1
Pages -
Subject Area:Applied Mathematics,Acoustics,Chemical Separation Engineering,Chemical System Engineering

Title: A multiresolution finite element method based on a new plane element

Authors: XIA Yiming
PP: 93-100
Abstract: Based on a node shape function for the plane stress element, the basic node shape function is constructed by extending the node shape function to other three quadrants around the coordinate zero point and a mutually nesting displacement subspace sequence is constituted out of scaling and shifting of the basic node shape function on the element domain, which brings about a simple, clear and rigorous mathematical basis for the multiresolution analysis (MRA). After that, the multiresolution plane stress element and method is formulated through applying the minimum potential energy principle. Hence, the MRA concept is established and the resolution level (RL) for the element is introduced. Hence, the proposed element is a meshless one and possesses the following features: 1) the node number the element contains can be modulated by adjusting the RL, thus improving the element analysis clarity. The overall analysis of a structure can be executed through splicing elements, hence the analysis clarity being actually determined by the RL, not by the mesh. 2) The element stiffness matrix, node equivalent loading vector can be automatically acquired for the proposed while those being obtained by artificially reassembling for the traditional after the node layout is reset. 3) The boundary conditions can be conveniently handled by the proposed just as those by the traditional. As a result, traditional 4-node plane stress element and method is essentially a mono-resolution one and also a special case of the proposed element and method.
Keywords: applied mathematics; plane element; basic node shape function; scaling and shifting; mutually nesting displacement subspace sequence; rational multiresolution analysis

Title: A pseudo-range singe point positioning algorithm for the Beidou navigation system based on total least squares

Authors: MA Tianming, ZENG Fanhui
PP: 88-92
Abstract: Ordinary least squares is adopted commonly in Beidou pseudo-range single point positioning at present, however, the deviation of constant term is considered and the deviation of coefficient matrix is not considered in ordinary least squares algorithm, total least squares in pseudo-range single point positioning is presented. Single point positioning program of Beidou by using C++ is presented, which is proved by the measured Beidou data. Comparing with that, total least squares algorithm is more accurate in positioning and has wider application.
Keywords: applied mathematics; Beidou; pseudo-range single point positioning; total least squares

Title: Game analysis of the integrity protection and destruction of users' data in the cloud storage

Authors: CHEN Jie, HOU Jicheng
PP: 81-87
Abstract: We used evolutionary game theory to analyze the integrity protection and destruction of users’ data in the cloud storage. According to the benefit matrix, we established an evolutionary game model about the integrity protection and destruction of users’ data in the cloud storage. Then, we used the replicator dynamic equation to analyze the evolutionary stable strategy of the users and the cloud storage service providers. The results show that it is of value for the integrity of users’ data in cloud storage to reduce investment of users to detect their data and increase loss of vandalism data integrity of cloud service providers.
Keywords: operational research; game theory; cloud storage; data integrity; replicator dynamics; evolutionary stable strategy

Title: A new variant of particle swarm optimization method: the GLbest-PSO

Authors: CHEN Xiangtuo, WANG Huiwen, SUN Yueyuan
PP: 75-80
Abstract: Global particles swarm optimization (PSO), noted as Gbest-PSO, has a faster convergence, but it causes easily the premature and local convergence. However, the local PSO algorithm, noted as Lbest-PSO, makes the research in space more refined but weakens the effect of the optimal particles. In this paper, trying to neutralize the gathering effects of Gbest-PSO and Lbest-PSO, we have proposed a GLbest model in order to have an optimization algorithm, which is able to obtain both a fast convergence and a refined search in space. GLbest-PSO and some other variants are tested on a common used set of optimization functions and their capacities are compared in the end. The results show that the convergence speed and convergence effect of the propsosed algorithm are improved, which proved to be an effective method.
Keywords: optimization; particles swarm optimization; global-local; topology neighborhood

Title: Study on calculation methods of the limit of function of two variables

Authors: ZHANG Fuchen
PP: 71-74
Abstract: The limit of the function of two variables is an important content in the course of calculus calculation. Also, the limit of the function of two variables plays a very important role in the continuity of functions. For beginners, it is difficult to obtain the limit of function of two variables. This paper mainly aims at calculation problem of the limit of the function of two variables, summarizes several commonly used methods and techniques. For example, definition method, substitution method, equivalent infinitesimal replacement method, on both sides of the clip criterion method, scaling, circles and infinitely small quantity of the product is infinitesimal method, using polar coordinate transformation method, etc. These methods are not alone in the practical use, sometimes several methods need to be combined with each other. This is helpful for satisfying students curiosity and desire for knowledge, making the students study in a vivid and humorous classroom context, enriching their knowledge, improving their innovation ability, and stimulating students enthusiasm and interest greatly in learning.
Keywords: mathematical analysis; function of two variables; limits; calculation method

Title: Hyers-Ulam stability of fractional differential equations

Authors: ZHENG Anli, FENG Yuqiang, WANG Weimin
PP: 63-70
Abstract: This paper studies the Hyers-Ulam stability of fractional differential equations. The fractional differential equation with Caputo’s derivative is solved by applying Laplace transform, and then its Hyers-Ulam stability is discussed. As for nonlinear condition, due to that the corresponding solution can not be directly found, the expression of the analytical solutions is given by Volterra equations. The conclusion of Hyers-Ulam stability is drawn via fractional Gronwall inequality and scaling of inequality to give the corresponding K values.
Keywords: ordinary differential equation; fractional differential equation; Hyers-Ulam stability; fractional Gronwall inequality; Laplace transform

Title: Existence and uniqueness of solutions for fractional order differential difference equations

Authors: SUN Yufeng, WANG Zhaoshun, ZENG Guangzhao, QU Wei
PP: 55-62
Abstract: From a class of fractional order differential difference equation boundary value problem of approximate solution, the application Picard’s iteration method is used to prove the form of the boundary problems satisfied by the iterative sequence of the solutions and the necessary and sufficient conditions proving the existence and uniqueness of the solution are discussed. Without considering approximate solution and non Lipschitz class factors, the conditions for the existence of the general solutions of the boundary value problem are discussed. Finally, a numerical example shows the existence of this kind of solution for boundary value problem and the error estimation of the iterative sequence.
Keywords: ordinary differential equation; fractional order; iterative algorithm; approximate solution; estimation of error

Title: Error analysis of sound power of noise sources by cross-spectral sound intensity method

Authors: JI Mingxiang, LU Yimin
PP: 49-54
Abstract: In this paper, taking the case of point source and coherent source, using the method of numerical simulation, aimed at finite difference of two microphone cross-spectral sound intensity, we analyzed the error of sound power of noise sources in the method of discrete point sound intensity by comparing the sound intensity theoretical value to the measured value and carried on verification testing of point source in a semi anechoic-chamber. The results show that when there are enough numbers of measuring points, sound power of sound source can be calculated by numerical simulation precisely. In order to obtain the same measurement accuracy, the coherent sound source field needs more measurement points than the point sound source field. In the envelope surface of hexahedron, take 1 dB error for reference, the accuracy of sound power is greater than that of sound intensity.
Keywords: acoustics; cross-spectral sound intensity; numerical simulation; sound power; error

Title: Molecular dynamics simulations of the deuterium bubbles evolution in tungsten

Authors: LIU Shengguang, WANG Yanfang, SUN Jizhong, WANG Dezhen
PP: 44-48
Abstract: Molecular dynamics simulations are carried out to investigate the evolution of deuterium bubbles in tungsten exposed to the irradiation of high deuterium flux. It is found that tungsten bulk becomes disordered in bubble region. The simulation displays the development of a dome-shaped structure at the tungsten surface and the formation of grain boundaries. It is also found that the number of deuterium molecules increases as the bubble grows, and the number of molecules in bubbles under relaxation is much larger than the number in bubbles under cumulative bombardment. In company with the blister bursting, tungsten atoms are ejected into the free space and obvious crack forms subsequently. The crack may be potential sources of tungsten flakes if they are under further bombardment.
Keywords: plasma physics; bubbles; molecular dynamics; tungsten; hydrogen isotope

Title: Fabrication of bismuth stannate modified ZnO microspheres for enhanced photocatalytic activity

Authors: XING Yonglei, QUE Wenxiu
PP: 39-43
Abstract: ZnO microspheres synthesized by using a hydrolysis method were modified with different contents of Bi2Sn2O7 (BSO) which was prepared by a hydrothermal method. Transmission electron microscope (TEM), ultraviolet visible (UV-Vis) and photoluminescence (PL) were employed to study morphological, optical and photocatalytic properties of the BSO-ZnO heterostructures. Effects of BSO contents on photocatalytic activities of the as-prepared samples were also investigated, and the highest photocatalytic efficiency was observed for the 12.5BSO-ZnO sample. Enhanced photocatalytic efficiency was ascribed to enhanced separation of the photogenerated electrons and holes, due to the presence of the BSO-ZnO heterojunction.
Keywords: optics; Bi2Sn2O7; ZnO; heterojunction; Rhodamine B; photocatalytic activity

Title: First-principles study on the effects of surface oxygen vacancy concentration on the properties of ZnO

Authors: HUANG Ping, SHANG Bo, LI Lingjie, LEI Jinglei
PP: 32-38
Abstract: The effects of different surface oxygen vacancy concentration in the structural stability, the electronic structure and optical properties of ZnO(10-10) surface system were studied using density functional theory (DFT) methods. The results showed that the structural stability of the systems with oxygen vacancy concentration of 4.17% was better than that 2.08% system. When the surface with oxygen vacancies, the Fermi level moved to the high energy level, a defect energy level occured in the band gap, and the Fermi level and defect energy levels had some overlap. In addition, the greater the concentration of oxygen vacancies, the defect energy levels accounted for the wide energy range and delocalized more obviously, which was conducive to the movement of electrons. Moreover, the oxygen vacancies led to a reduced band gap. As a result, the photocatalytic efficiency of the system had been improved. For the absorption spectrum, with the concentration of oxygen vacancies increasing, the absorption coefficient in ultraviolet and visible light region increased, which means that the utilization of solar energy improved. In this paper, calculations were promising for the evidence of the experimental research of ZnO with oxygen vacancies.
Keywords: physical chemistry; ZnO; density functional theory; vacancy formation energy; electronic structure; optical properties

Title: Synthesis and characterization of phosphoramide piperazine analogues of paeonol

Authors: BI Wenzhu, CHEN Xiaolan, FU Wenkai, XIA Xiaoyi, ZHAO Yufen
PP: 26-31
Abstract: Based on the phosphorylated reaction, through an efficient general synthetic approach that provide facile, rapid and cheap access to a wide range of novel phosphoramide derivatives of paeonol, eight analogues of paeonol are synthesized in high yields (71%-86%) and elucidated by infrared spectroscopy (IR), high resolution mass spectrum (HR-MS) and nuclear magnetic resonance (NMR).
Keywords: organic chemistry; paeonol; phosphoramide piperazine; synthesis and characterization

Title: Study on the dynamics of extracting rutin from Sophara japonica by ultrasonic extraction

Authors: YANG Kai, CONG Jingxiang, HU Yaoyun, DENG Xianghua
PP: 21-25
Abstract: Rutin was used as the target, the dynamic processes of extracting rutin were studied by using ultrasonic extraction, and then the corresponding dynamics models were established. The changing of rutin concentrations with ultrasonic extraction time, extraction temperature, and the ratio of liquid and solid was investigated. Through a large number of experimental data, the second-order kinetic models of ultrasonic extracting rutin were established under different condition processes, such as at 20, 30, 35, 40, 50℃ and the ratio of liquid and solid were 10, 20, 30, 40, 50 g/mL, respectively. The optimum ultrasonic extraction conditions was as follows, extract time 30 min, extract temperature 40℃, liquid to solid ratio 10 g/mL. Validity of the models was verified by experiments. The experimental results can provide theoretical guidance for the effective extraction of rutin.
Keywords: chemical separation engineering; ultrasonic extraction; rutin; dynamics

Title: Design and optimization of the industrial process of butyl acetate production

Authors: WANG Xiaohong, TIAN Peng, TIAN Guangzhen
PP: 9-20
Abstract: The design and economic optimization of butyl acetate production were presented using Aspen Plus process simulation software. After butanol and methyl acetate reacted in continuous stirred tank reactor, the production of butyl acetate and methanol could be obtained in downstream through pressure-swing distillation. Then a global optimization method using total annual cost (TAC) as the objective function was developed, a sequential iterative search was used to calculate the optimum pressure-swing distillation technological parameters and economic cases with the no heat integration, the partial heat integrated and the fully heat integrated. The capital cost was gradually increased as the energy cost decreased with the growth of theoretical stages. The lowest TAC can be gained in differential groups of theoretical stages and feed stage. The results showed that the capital and energy cost in the partial heat integrated and the fully heat integrated processes become lower while the partial heat integrated got the lowest energy cost and full heat integrated got the lowest capital cost. The parameters of the optimal heat integrated process could be efficient not only in industrial heat integrated network and dynamic simulation, but also in practical industrial production.
Keywords: chemical system engineering; butyl acetate; optimal design; total annual cost; heat integrated

Title: Research progress on the polypyrrole/graphene composites

Authors: WANG Zhenqiang, MO Haodao, HUANG Xianxian, LIU Liangqin, LAO Jiaping, YANG Chao
PP: 1-8
Abstract: With the development of the conducting polymers, the composite nanomaterials have become the focus of the study at home and abroad due to the excellent capability including light, electricity and heat, et al. Graphene (GNS) has the outstanding performance by the special single layer structure among these materials. In recent years, the researches of nanocomposite about conducting polymer and GNS have made great progress and achievement. However, the study has come across a series of problems about the preparation and functionalizational applications. In this paper, it summarizes the main methods of the synthesis of polypryrrole (PPy)/GNS and the applications of the supercapacitors and sensors, et al. It also makes the expectation of the future development.
Keywords: polymer engineering; polypyrrole; review; graphene; supercapacitor

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