Spectral Domain Analysis of Coaxial Cavities

Coaxial cavities are used in high power gyrotrons as the beam-wave interaction structure. Much research has been devoted to their mode selective properties. A coaxial cavity lacks a sharp boundary at its open end, so it has some physical features that can only be observed using a spectral model, such as frequency-dependent field profiles and mode overlapping effects. These properties are important since cold tests are usually conducted in the frequency domain. This study applies the incident/reflected wave boundary condition to the wave equation of a weakly irregular coaxial waveguide. The resistivity of the wall is considered in the analysis. Calculations reveal that the fixed-position spectrum yields an uncertain resonant frequency and quality factor. Although the maximum-field spectrum can uniquely determine the properties of the coaxial cavity, the resonant frequency obtained using the maximum-field spectral model is inconsistent with that obtained using the temporal model. The field-energy spectrum explains the low Q nature of the coaxial cavity. Moreover, resonant frequencies evaluated using the field-energy spectrum agree precisely with those evaluated using the temporal model.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

偶数个多原子Greenberger-Horne-Zerlinger态的制备

提出了一种制备偶数个多原子Greenberger-Horne-Zerlinger态的方案,它是基于原子-腔场相互作用.首先n个分离的腔初始时处于真空态,通过双光子转移,把n个腔制备成数态|2>和真空态|o>的缠结态.随后,与腔场发生共振相互作用的2n个等同的原子被分别送入n个腔,通过相互作用后,2n个原子处于GHZ态,而n个腔仍然处于真空态.     

Mindlin层合圆柱壳理论的Hamiltonian结构与辛解析解

通过引进状态变量及其对偶变量。建立Ｍｉｎｄｌｉｎ层合圆柱壳的Ｈａｍｉｌｔｏｎ正则方程．在辛几何数学框架下，采用共轭辛正交归一关系给出各种复杂边界条件下的精确解．     

多势垒结构中的共振能量和量子能级的差异分析

利用Ｃｈｅｂｙｓｈｅｖ多项式和传输矩阵方法解析推导出多量子阱（ＭＱＷ）系统的束缚电子级公式，并定量分析了多势垒结构中的共振能量和相应ＭＱＷ系统量子能级的差异。     

New Aspects of Cyclodextrin Chemistry Induced by Outside Type Complex Formation; Asymmetric Reduction of Indol-3-Pyruvic Acid with NaBH4 in Aqueous Solution

Asymmetric reduction of indol-3-pyruvic acid (IPA) with NaBH₄ in aqueous solution in the presence of various cyclodextrins (α-, β-, γ-, mono-6-amino-6-deoxy-β- and di-6^ABamino-6^AB-deoxy-β-cyclodextrin) was investigated. From the NMR and circular dichroism spectral studies, the conformation of the CyD–substrate complexes is suggested; the part of carboxylic group stay in the cavity of α-CyD, whole of IPA in β-CyD, two molecules in a γ-CyD cavity, and IPA(s) is/are on the rim of the cavity of mono-6-amino-6-deoxy-β- and di-6^ABamino-6^AB-deoxy-β-CyD (AβCyD, DAβCyD) with electrostatic interaction between amino group and carboxylic group. This conformational difference provides in the difference in the optical selectivity of reduction.     

Extremal k *-Cycle Resonant Hexagonal Chains

Denote by ^* _n the set of all k ^*-cycle resonant hexagonal chains with n hexagons. For any B _n ^* _n , let m(B _n ) and i(B _n ) be the numbers of matchings (=the Hosoya index) and the number of independent sets (=the Merrifield–Simmons index) of B _n , respectively. In this paper, we give a characterization of the k ^*-cycle resonant hexagonal chains, and show that for any B _n ^* _n , m(H _n )m(B _n ) and i(H _n )i(B _n ), where H _n is the helicene chain. Moreover, equalities hold only if B _n =H _n .     

Enthalpic determinations of aliphatic ester-solvent systems with correlations

Calorimetric measurements were carried out on ester-solvent systems where the esters were H(CH₂)_xCOO(CH₂)_yH, with x and y varying from 1 to 5, and the solvents were n-hexane and 1,2-dichloroethane. Calculation of the enthalpies of cavity formation enabled the enthalpies of interaction to be determined. Both enthalpies correlated with number of carbon atoms N, equal to x+y in the esters, giving for 1,2-dichloroethane