Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Charge transport in a polypeptide chain

Charge transport is one important example of signal transduction in a protein which is responsible for action at a distance, and is a fundamental process in biochemical action. A model is presented in which electronic effects interact with motional processes to combine into a bifunctional model. This model is investigated with new detailed molecular dynamics calculations and successfully explains such action at a distance. Received 1st February 2002 / Received in final form 26 May 2002 Published online 13 September 2002     

工作气压对电子束沉积ZrO2薄膜折射率和聚集密度的影响

采用电子束蒸发的方法，用石英晶体振荡法监控薄膜的蒸发速率，在不同工作气压下制备了ZrO2薄膜样品.在相调制型椭圆偏振光谱仪和分光光度计上对样品的光谱特性进行了测试.根据波长漂移的理论，计算出薄膜的聚集密度.结果表明，随着工作气压的降低，薄膜的聚集密度和折射率都随之增大.     

The Kissing Triangles: The Aesthetics of Mathematical Discovery

Papert's (1978) appeal to reconsider the power and possibilities of the aesthetic in mathematics learning is often ignored in mathematics education research. This paper begins with the premise, put forth by Dewey (1934), that the aesthetic structures many dimensions of inquiry and experience. In the same way that using particular paintings, musical compositions, or even everyday experiences has been instrumental to attempts by philosophers to understand the aesthetic dimensions of meaning and experience in artistic domains, I propose that analysing a particular encounter with mathematics may help reveal the nature and role of the often nebulous responses of elegance, beauty, and `fit' to which mathematicians lay claim in their mathematical activity. To achieve this, I draw on and adapt the defining features of the aesthetic character of experience set forth by the aesthetician Beardsley (1982). This, in turn, sheds light on the role thataesthetics can play in mathematical inquiry and experience, and provides initial categories and conjectures that can be used to investigate the potential roles of aesthetics in mathematics learning contexts.This revised version was published online in September 2005 with corrections to the Cover Date.     

Large set of P3‐decompositions

Let G=(V(G),E(G)) be a graph. A (n,G, λ)‐GD is a partition of the edges of λK_n into subgraphs (G‐blocks), each of which is isomorphic to G. The (n,G,λ)‐GD is named as graph design for G or G‐decomposition. The large set of (n,G,λ)‐GD is denoted by (n,G,λ)‐LGD. In this work, we obtain the existence spectrum of (n,P₃,λ)‐LGD. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 151–159, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10008     

Resistance of nondiffracting vortex beam against amplitude and phase perturbations

The revival of the nondiffracting vortex beam after its interaction with the 2D on axis obstacle is examined. We show that the phase topology and the spatial distribution of the orbital angular momentum of the beam transmitted through the obstacle regenerate to the initial form during further free propagation. We verify that the healing effect appears even if the interaction is accompanied by the exchange of the orbital angular momentum.     

电子束产生大尺度等离子体过程的数值模拟研究

建立了一个四组分一维混合模型，对电子束注入大气产生大尺度等离子体的过程进行了数值模拟.结果表明了能量为140keV、流强为50mA/cm²的注入电子束，可以产生线度为0.5m，密度为10¹²cm^-3量级的大气环境下等离子体.电子束所伴随的空间电荷效应由于等离子体的产生会很快消失，不影响后续的等离子体产生过程.电子束注入流强主要影响产生等离子体的密度，而电子束能量则同时影响其空间线度和密度. 关键词： 电子束 碰撞 电离     

强流脉冲离子束辐照靶及其喷发的数值研究

利用拟合实测的TEMP Ⅱ型加速器磁绝缘二极管(MID)电压波形及其焦点附近束流密度曲线，建立了Gaussian分布模型，据此计算了与靶作用的离子的能量及数量，采用Monte Carlo(MC)方法计算了沉积在靶内的能量.并以此作为热源，与流体动力学(HD)模型相结合，对不同的靶状态采用相应的状态方程，模拟计算了靶内压力演化情况; 同时对烧蚀产生的等离子体采用理想气体状态方程, 结合HD方程组, 模拟计算了喷发过程中压力的空间演化过程. 关键词： 强流脉冲离子束 Gaussian模型 HD方程 数值研究