Polar electro-optic switching in droplets of an achiral nematic liquid crystal

A polar electro-optic response is observed in droplets of an achiral nematic liquid crystal in coexistence with the isotropic phase. Between crossed polarizers each pancake-shaped droplet shows extinction brushes in the form of a centred cross aligned with the polarizer axes. An applied electric field E induces a rotation of the crosses about the field direction, with about half the droplets switching clockwise and the other half anticlockwise. The sense of rotation in each droplet changes when E is reversed. We propose that a twisted bipolar director structure is stabilized in the droplets by a relatively large splay elastic constant and tangential boundary conditions. The molecules twist along the diameter of the droplets, perpendicular to the applied field, which results in a linear rotation of the director by the inverse flexoelectric effect. Since the molecules are achiral, the handedness of the twist, and hence the sense of the switching, in any droplet is arbitrary.     

行波光电二极管级联阵列输出功率合成研究

针对未来光载无线通信所需的高功率、大带宽的光电探测器,提出了一种行波光电二极管级联阵列功率合成电路.先将行波光电二极管级联,再按照阵列式结构将多组级联的光电二极管组合起来,实现射频功率合成,以获得高功率、大带宽的射频信号.采用EDA工具,对该光电转换射频功率合成电路进行仿真模拟.仿真结果表明,该功率合成电路可以有效地将各光电二极管的射频输出信号进行功率合成,功率合成后的信号带宽显著增加,仿真结果与理论分析完全一致.此外,电路分析表明,增加该功率合成电路中的高阻微带线的特性阻抗可以有效提高其输出射频信号的带宽.     

Summation of electrostatic interactions in quasi-two-dimensional simulations

An error in our previous paper (Clark, A. T., Madden, T. J. and Warren, P. B., 1996 Molec. Phys., 87, 1063) is corrected. This brings the results into agreement with the recent work of Grønbech-Jensen et al. (Grønbech-Jensen, N., Hummer, G. and Beardmore, K. M., Molec. Phys., 1997, 92, 941).     

Singular Matched Eigenfunction Expansions for Stokes Flow around a Corner

A singular matched eigenfunction expansion method is describedfor solving Stokes flow around a corner. The flow region isdecomposed into a number of simpler rectangular subregions;this enables the stream function to be represented by meansof an expansion of Papkovich-Fadle eigenfunctions in each ofthese subregions. The coefficients in these expansions are obtainedby matching them across common interfaces in a weak sense. Theresulting solution is used in a post-processing technique todetermine the coefficients in the known locally convergent expansionof the stream function at reentrant and salient corners. A smallnumber of terms in this expansion is necessary to produce accurateapproximations.     

Fourier Series Solutions to Poisson's Equation in Rectangularly Decomposable Regions

Fourier senes solutions to Poisson problems defined in rectangularlydecomposable regions are found by matching solutions in a weaksense across the interfaces dividing subregions. The matchingprocess produces an infinite system of algebraic equations forthe unknown expansion coefficients. Complex analysis is usedto investigate theoretically the conditioning of the coefficientmatrix for both the C⁰ and C¹ matching problems. The formeris shown to be not well-defined whereas the latter is extremelywell-conditioned. Furthermore, the analysis of the coefficientmatrix for the weak C¹ problem suggests a rapidly convergentiterative method for solving the truncated algebraic systemfor the expansion coefficients. Accurate approximations areobtained after a handful of iterations and with few degreesof freedom.     

A Consistent System of Curved Electron Arrows

Many students of organic chemistry find it difficult to properly use electron arrows. Traditional arrows do not end at one type of location. Whereas the vast majority end at an atom, an arrow that indicates formation of a bond points to a bond instead. Rethinking electron arrows leads to the following four rules, which form a consistent system:1. An electron arrow always begins at an electron pair, either bonding or nonbonding. One arrow begins at the nucleophilic electron pair, if any.2. An electron pair always remains attached to an atom, normally indicated by its arrow.3. An electron arrow always ends at an atom, not at a bond. One arrow ends at the electrophilic atom, if an.4. In a series of arrows for one mechanistic step, a succeeding arrow begins by the atom where the preceding arrow ends.This system of electron arrows is superior because the rules can be more generally applied, the arrows reflect the nucleophilicity of electron pairs, the arrows carry more meaning, the arrows in a series flow more directly from one to the next, and the arrows clearly prescribe products.     

THE EFFECT OF FLOW PULSATIONS ON CORIOLIS MASS FLOW METERS

It has been reported that the accuracy of Coriolis mass flow meters can be adversely affected by the presence of pulsations (at particular frequencies) in the flow. A full analysis of the transient performance of a commercial Coriolis meter is only possible using finite element techniques. However, this is a transient, nonlinear problem in which the space and time variables are not (strictly) separable and the finite element techniques for tackling such problems make it desirable to have an analytical solution for a simplified meter, against which the finite element solution can be compared. This paper reports such a solution. The solution will also provide guidance for experiments. Existing analytical solutions for the performance of Coriolis meters in steady flow (a complex eigenvalue problem) are not easily extended to the transient flow case. The paper thus begins with the presentation of an alternative solution for steady flow through a simple, straight tube, Coriolis meter and it is notable that this solution gives a simple analytical expression for the experimentally observed small change in the resonant frequency of the meter, with flow rate, as well as an analytical expression for the meter sensitivity. The analysis is extended to the transient case, using classical, forced vibration, modal decomposition techniques. The solution shows that, unlike the steady flow case where the detector signals contain components at the drive frequency and the second mode frequency (Coriolis frequency), for pulsatile flow the detector signals will in general contain components involving at least four frequencies. It is demonstrated that the meter error depends on the algorithm used to estimate the phase difference from the detector signals. The particular flow pulsation frequencies which could possibly lead to large meter errors are identified.     

Local spin II

Equations are discussed for computing, from ah initio wavefunctions, average values of quantities like S_A. S_B which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators onto local regions of space. They result in local spin operators S_A which obey the definition of angular momentum operators and commute with each other. These averages are evaluated for UHF and CI wavefunctions for a few examples of closed and open shell molecules. The calculations are compared with the assumptions made in the Noodleman method for evaluating the parameters in the Heisenberg Hamiltonian and with various definitions of bond order.