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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 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

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.

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 department of physics Hunan University

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.

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.

BROYDEN'S METHOD FOR SOLVING VARIATIONAL INEQUALITIES WITH GLOBAL AND SUPERLINEAR CONVERGENCE

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Journal of Computational Mathematics 2000年第3期18卷 289-304页

作者： Yu-fei Yang Dong-hui Li (department of applied Mathematics, Hnnan {2., changsha 410082. china) 湖南大学湖南长沙 410082

In this paper, we establish a quasi-Newton method for solving the KKT system arising from variational inequalities. The subproblems of the proposed method are lower-dimensional mixed linear complementarity problems. A suitable line search is introduced. We show that under suitable conditions, the proposed method converges globally and superlinearly.

关键词： Variational inequality quasi-Newton method global convergence,superlinear convergence

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 410082. china 2. {2. of Civil Engineering, Tsinghua university, Beijing 100084, china College of Civil Engineering Hunan University Changsha China department of Civil Engineering Tsinghua University 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.

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

Stability Caused by Impulses for Delay Difierential Equations

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Acta Mathematica Sinica,English Series 1997年第2期13卷 193-198页

作者： Yu Jianshe (department of applied Mathematics,{2. university,changsha 410082.china)

In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential equation caused by impulses.

关键词： Delay differential equation Stability Impulse

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, hunan university, 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.

REFINED CONNECTIVITY PROPERTIES OF ABELIAN CAYLEY GRAPHS

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Chinese Annals of Mathematics,Series B 1998年第4期19卷 409-414页

作者： LI QIAOLIANG (department of applied Mathematics, Shanghai Jiaotong {2., Shanghai 2.0030, chinaPresend in department of Mathematics, hunan Normal {2., changsha 410082. china.)LI QIAO (department of applied Mathematics, Shanghai Jiaotong Univ department of applied Mathematics Shanghai Jiaotong University Shanghai 200030 China department of Mathematics Hunan Normal University Changsha 410082 China

Restricted edge connectivity of a graph G is defined to be the minimum size |U| of a set U of edges such that G-U is disconnected and G-U contains no trivial component K1. The high order edge connectivity Ni, i1, is the number of edge outsets of size i. TO determine all Ni, i 1, for a general graph is NP-hard. In this paper, the authors evaluated the restricted edge connectivity and the high order edge connectivity Ni, 1 i -1, for any connected Abelian Cayley graphs explicitly.

关键词： Abelian Cayley graph Restricted edge connectivity High order edge connectivity