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Size distributions and magic number characteristics of cluster configurations formed during solidification processes of liquid metal Al

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Science China(Technological Sciences) 2006年第2期49卷 172-187页

作者： LIU Rangsu1, LIU Fengxiang1, DONG Kejun1, ZHENG Caixing1, LIU Hairong2. PENG Ping2.& LI Jiyong3 1. department of physics,{2., changsha 410082. China 2. department of Material Science and Engineering,{2., changsha 410082. China 3. department of Chemistry,{2., changsha 410082. China 1. department of physics Hunan University Changsha 410082 China 2. department of Material Science and Engineering Hunan University Changsha 410082 China 3. department of Chemistry Hunan University Changsha 410082 China

A molecular dynamics simulation study has been performed for a large systemconsisting of 100000 liquid metal Al atoms to investigate the formation and magic numbercharacteristics of the cluster configurations formed during the rapid solidification processes. Thecluster-type index method (CTIM) has been adopted to describe various types of clusterconfigurations. The results indicate that the icosahedral clusters (12.0 12.0) and theircombinations play the most important role in the rnicrostructure transitions during solidificationprocesses; for the cluster configurations of different levels formed by various combinations withdiffering numbers of basic clusters, their size distributions possess obvious magic number sequencewhich is in turn as 13(13), 19(2.), 2.-2.(2.), 32.33(32., 39-40, 43-44, 48..., (those in bracket arethe corresponding value in liquid state); the magic numbers correspond to the peak value positionsof the cluster numbers for corresponding level formed with various combinations by 1, 2. 3, 4, 5, 6,7, ...basic clusters, respectively. This magic number sequence is in good agreement with theexperimental results obtained by Harris et al. At the same time, this simulation study also gives ascientific and reasonable explanation to these experimental results.

关键词： liquid metal, solidification processes, cluster configuration, magic numbers, computer simulation.

A new orthogonality relationship for orthotropic thin plate theory and its variational principle

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Science China(physics,Mechanics & Astronomy) 2005年第3期48卷 371-380页

作者： LUO Jianhui 1 , LONG Yuqiu 2.& LIU Guangdong 1 1. College of Civil Engineering, hunan university, changsha {2. China 2. department of Civil Engineering, Tsinghua university, Beijing 100084, China 1. College of Civil Engineering Hunan University 410082 Changsha China 2. department of Civil Engineering Tsinghua University 100084 Beijing China

The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relationships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.

关键词： theory of elasticity, thin plate theory, dual vectors, orthogonality relationship, orthotropic, variational principle.

Effect of static magnetic field on activity of immobilized α-amylase

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Chinese Science Bulletin 1997年第2期42卷 127-130页

作者： YAN Liushui, ZHU Yuanbao, HE-Shuang’e and CAO Zhixiang1 department of Chemical Engineering, Nanchang Institute of Aeronautical Technology, Nanchang 330034, China 2. department of Chemistry and Chemical Engineering,{2., changsha 410082. China department of Chemical Engineering Nanchang Institute of Aenwututical Techndogy Nanchang China department of Chemistry and Chemical Engineering Hunan University Changsha China

BIOLOGICAL effect of magnetic field is one of the three major subjects of contemporary biomagnetism, and is also the basis of applied biomagnetism. In order to explore magnetic biological effects, the influence of various sorts of magnetic field on many living systems as well as their different constructural levels has been extensively studied. However, only a few studies with in vitro enzyme have been reported, and few researches concerning the influence of magnetic field on immobilized enzyme reactions have been published. This note describes

关键词： static magnetic field immobilized α-amylase enzyme activity oscillatory behaviour.

Formation and evolution mechanisms of large-clusters during rapid solidification process of liquid metal Al

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Science China(physics,Mechanics & Astronomy) 2005年第1期48卷 101-112页

作者： LIU Rangsu, DONG Kejun, LIU Fengxiang, ZHENG Caixing, LIU Hairong & LI Jiyong department of applied {2., hunan university, changsha 410082. China College of Materials Science and Engineering, hunan university, changsha 410082. China College of Chemistry and Chemical Engineering, hunan university, changsha 410082. China 1. department of applied {2. Human University 410082 Changsha China 2. College of Materials Science and Engineering Hunan University 410082 Changsha China 3. College of Chemistry and Chemical Engineering Hunan University 410082 Changsha China

A molecular dynamics simulation study has been performed for the formation and evolution characteristics of nano-clusters in a large-scale system consisting of 400000 atoms of liquid metal Al. The center-atom method combined with pair-bond analysis technique and cluster-type index method (CTIM) has been applied here to describe the structural configurations of various basic clusters. It is demonstrated that both the 1551 bond-type and the icosahedral cluster (12.0 12.0) constructed by 1551 bond-types are dominant among all the bond-types and cluster-types, respectively, in the system and play a critical role in the microstructure transitions of liquid metal Al. The nano-clusters (containing up to 150 atoms) are formed by the combination of some middle and small clusters with distinctly different sizes, through mutual competition by unceasing annex and evolution in a seesaw manner (in turn of obtaining and losing),which do not occur as the multi-shell structures accumulated with an atom as the center and the surrounding atoms are arranged according to a certain rule. This is the essential distinction of nano-cluster in liquid metal from those obtained by gaseous deposition, ionic spray methods, and so on. Though the nano-clusters differ from each other in shape and size, all of them possess protruding corners that could become the starting points of various dendrite structures in the solidification processes of liquid metals.

关键词： liquid metal, solidification process, large-cluster configuration, evolution mechanism, computer simulation.

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2.and CHEN Nanxian1(1. department of physics, Tsinghua {2., Beijing 100084, China 2. department of physics, Peking {2., Beijing 100871, China) department of physics Tsinghua University Beijing 100084 China department of physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

Analytical study of stationary soliton excitations in diamond-structure chain with quartic anharmonicity

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原子与分子物理学报 2001年第2期18卷 143-149页

作者： XIA Qing lin 1, ZHOU Guang hui 2. YAN Jia ren 2. (1.department of applied {2. and Heat Engineering, Central South university, hunan changsha 410083 2.department of {2., hunan Normal university, hunan changsha 410081) 中南大学湖南长沙 410083 湖南师范大学湖南长沙 410081

This work analytically study soliton excitations in an one dimensional chain with the same mass but two alternating force constants between the nearest neighbors by means of multiple scales method plus quasi discrete approximation. This model simulates a row of atoms in the 〈111〉 direction of a diamond structure type of crystals. The explicit expressions of the stationary soliton solutions are obtained at some special wave vectors of the carrier wave ( q =±π/ a for acoustic mode and q=0 , ±π/ a for optical mode). The configuration of the atomic displacements of this model is different from that of diatomic chain with quartic anharmonicity.

关键词： Stationary soliton excitation Diamond structure Multiple scales method Quasi discrete approximation

Asymptotic stability for nonautonomous delay differential equations

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Chinese Science Bulletin 1997年第20期42卷 1676-1679页

作者： YU Jianshedepartment of applied Mathematics,{2., changsha 410082. China department of applied Mathematics Hunan University Changsha China

MANY dynamic population models can be transformed to the form of delay differential equationx（t） + λx（t） + f（t,x（t-τ1）,….,x（t-τm））=0,t≥0,（1）where the biologically meaningful equilibrium of the original equation is transformed into thezero equilibriurn of （1）. Throughout this note, we assume that λ>0,τi>0（i=1,…,m ）,

关键词： delay equation stability asymptotic stability.

Extended Fan's Algebraic Method and Its Application to KdV and Variant Boussinesq Equations

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Communications in Theoretical physics 2007年第7期48卷 1-6页

作者： YANG Xian-Lin TANG Jia-Shi College of Mechanics and Aerospace,hunan university,{2. 410082.China2.department of Computer Science,hunan Radio and Television university,{2. 410004,China College of Mechanics and Aerospace Hunan University department of Computer Science Hunan Radio and Television University

An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential *** key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>*** efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq *** results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.

关键词： algebraic method KdV equation variant boussinesq equations polynomial complete discrimination system

The proof of FFD(L)≤11/9OPT(L) +7/9

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Chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： LI Rongheng, YUE Minyi1. department of Mathematics, hunan Normal {2., changsha 410081, China 2. Institute of applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China department of Mathematics Hunan Normal University Changsha 410081 China Institute of applied Mathematics Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2.…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capaci... 详细信息

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2./sub>,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.