Noetherian PI Hopf algebras are Gorenstein

We prove that every noetherian affine PI Hopf algebra has finite injective dimension, which answers a question of Brown (1998).

     

Preparation and characterization of a poled nanocrystal and polymer composite PbTiO3/PEKc film for electro-optic applications

Composite thin films of PbTiO₃ nanocrystals and high-transparency PEKc polymer for applications in electro-optical devices were prepared using the spin coating technique. The size of the PbTiO₃ nanocrystals was estimated to be 30–40 nm using a transmission electron microscope. The transmission technique, a simple method for measuring the electro-optic coefficients of poled composite polymer films was developed. The electro-optic coefficient γ₃₃ of poled PbTiO₃/PEKc composite polymer films was measured to be 18.34 pm  V^-1 at 633 nm under room temperature. The index at 633 nm and the dielectric constant at 100 kHz under room temperature were determined to be 1.65248 and 7.32, respectively. The figure of merit F₂=n⁷γ²/ε was estimated to be 1546, showing very good electro-optical properties. Received: 5 February 2002 / Accepted: 12 March 2002 / Published online: 19 July 2002 RID="*" ID="*"Corresponding author. Fax: +852/2788-7791, E-mail: eeytc@cityu.edu.hk     

Studies of ion energy and yield from argon clusters heated by intense femtosecond laser pulses

Using time-of-flight spectrometry, the interaction of intense femtosecond laser pulses with argon clusters has been studied by measuring the energy and yield of emitted ions. With two different supersonic nozzles, the dependence of average ion energy on cluster size in a large range of has been measured. The experimental results indicate that when the cluster size , the average ion energy Coulomb explosion is the dominant expansion mechanism. Beyond this size, the average ion energy gets saturated gradually, the clusters exhibit a mixed Coulomb-hydrodynamic expansion behavior. We also find that with the increasing gas backing pressure, there is a maximum ion yield, the ion yield decreases as the gas backing pressure is further increased.     

Quantum entanglement and chaos in kicked two-component Bose-Einstein condensates

We study two-component Bose-Einstein condensates that behave collectively as a spin system obeying the dynamics of a quantum kicked top. Depending on the nonlinear interaction between atoms in the classical limit, the kicked top exhibits both regular and chaotic dynamical behavior. The quantum entanglement is physically meaningful if the system is viewed as a bipartite system, where the subsystem is any one of the two modes. The dynamics of the entanglement between the two modes in this classical chaotic system has been investigated. The chaos leads to rapid rise and saturation of the quantum entanglement. Furthermore, the saturated values of the entanglement fall short of its maximum. The mean entanglement has been used to clearly display the close relation between quantum entanglement and underlying chaos.     

Design of interdigital transducers for crack detection in plates

Interdigital transducers (IDT) for non-destructive evaluation (NDE) of cracks in plates are designed based on an analytical model established previously. Key considerations include mode selectivity, excitation strength, collimation of wave and cost. The advantage of mode selectivity of IDT over PZT patch is presented both analytically and experimentally. Effects of parameters, namely finger spacing, width, length, number of fingers, and the size of IDT, on the excitation strength and mode selectivity are considered. This led to the design of a mobile double-sided IDT as an efficient device where excitation strength is strong and focused. The device was fabricated in-house using commercially available piezoelectric ceramics and used to develop a procedure for accurate identification of the direction and extent of cracks in plates. Three aluminum plates, one with a linear deep crack, another with a piecewise linear shallower crack and the third with a curved crack, were used to illustrate the accuracy and efficiency of both the proposed device and procedure for effective NDE.     

All-solid-state continuous-wave frequency doubling Nd:LuVO4/LBO laser with 2.17 W output power at 543 nm

Efficient and compact green-yellow laser output at 543 nm is generated by intracavity frequency doubling of a CW diode-pumped Nd:LuVO₄ laser at 1086 nm under the condition of suppressing the higher gain transition near 1064 nm. With 16 W of diode pump power and the frequency-doubling crystal LBO, as high as 2.17 W of CW output power at 543 nm is achieved, corresponding to an optical-to-optical conversion efficiency of 13.6% and the output power stability over 8 hours is better than 2.86%. To the best of our knowledge, this is the highest watt-level laser at 543 nm generated by intracavity frequency doubling of a diode pumped Nd:LuVO₄ laser at 1086 nm.     

Mössbauer Spectroscopic Study on Vertical Distribution of Iron Species in Sediments from Qinghai Lake,China

In this study, ⁵⁷Fe Mössbauer spectroscopy has been applied to sediments collected from Qinghai Lake in Qinghai Province, China, to investigate the vertical distribution of iron species. Their Mössbauer spectra consisted of four doublets ascribable to one paramagnetic high-spin Fe³⁺, two paramagnetic high-spin Fe²⁺ with different quadrupole splittings, and one diamagnetic low-spin Fe²⁺ that corresponds to pyrite (FeS₂). The distribution of pyrite suggested climatic changes during the past nine thousand years. It was demonstrated that the iron speciation in the salt lake sediments by Mössbauer spectroscopy can be used to reconstruct the past environment.

     

Formation of hydrogenated amorphous carbon films from polymer pyrolysis

Free-standing and supported hydrogenated amorphous carbon films (a:C–H) were prepared upon pyrolysis of the polymer formed by ethanolamine (EA) and citric acid (CA), under an ambient atmosphere at 300 °C. EA facilitates the formation of the macroscopic films, while CA is essential for obtaining the a:C–H microstructure, which comprises a mixture of sp² and sp³ carbon. Received: 29 May 2001 / Accepted: 17 August 2001 / Published online: 20 December 2001     

单链表在离子发动机光学系统粒子模拟中的应用

 目前离子发动机光学系统数值模拟大多采用PIC方法,由于该方法需要跟踪单个粒子的运动,因此需要存储每个粒子的位置信息与运动信息。传统的粒子模拟程序中,保存粒子信息大多采用数组的方式,但是采用这种方式存在弊端,例如对粒子总数变化的自适应不好。基于此开发了一种使用链式存储结构的粒子模拟程序,该程序使用带头节点的单向链表存储粒子信息。使用基于链式存储结构的PIC方法对离子发动机光学系统进行了粒子模拟,验证了链式粒子信息存储方法在粒子模拟中的可用性。模拟表明：（1）在粒子模拟中采用链式存储结构存储粒子信息,无需预先指定最大粒子总数,程序可自适应粒子总数的变化,因此无需进行试算,节省了计算时间;（2）在粒子模拟中采用链式存储结构,由于不存在内存资源的浪费,因而可显著提高程序的存储效率与计算效率。