Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

多孔活性自燃金属的光谱辐射特性研究

多孔活性金属材料因为内部存在大量的孔隙，大大地增加了与空气的接触面积，使得其在空气中的燃烧较为猛烈，燃烧温度迅速上升。其燃烧过程属于固体燃烧的范畴，较为复杂。以镁为例，通过建立燃烧模型，来研究多孔活性金属的光谱辐射特性。首先，建立氧气总消耗量与活性金属剩余质量的关系，研究氧气在活性金属孔隙内的扩散浓度关系，通过求解活性金属热平衡方程得到活性金属燃烧过程中温度与时间的关系式，进而得到活性金属的峰值光谱辐射强度表达式；然后，将模型计算的仿真结果与红外热像仪测得的实验结果对比，结果表明，模型的计算结果与实验结果相一致，误差在了10%以内；最后，通过建立的燃烧模型来研究活性金属燃烧规律以及其光谱辐射特性，解决了高空、高速下的活性金属光谱辐射强度难以实验获得的问题，大大减小了实验成本与时间。分别对比不同时间活性金属箔片在1～3，3～5以及8～12 μm波段下的辐射强度，得出活性金属燃烧时的辐射强度主要集中在3～5 μm波段的结论。研究结果表明：自燃金属最大燃烧温度随高度的增加逐渐下降，随气流速度的增加先增加后减小，在速度为30 m·s-1时，温度达到最大；自燃金属的光谱辐射强度在2～6 μm波段达到最大。该模型也可以用来研究其他活性金属的燃烧特性。     

Torsion balances with fibres of zero length

Torsion balances have good immunity to tilt and low rotational stiffness. However precise control of the position of the suspended torsion ‘bob’ is difficult in the presence of ground vibrations and tilt and this is a limiting factor in applications where Casimir forces or putative non-Newtonian short-range forces are being measured. We describe how the desirable characteristics of torsion balances can be reproduced in a rigid body that is suspended using applied forces rather than a torsion fibre. The suspension system can then provide a more precise control of the degrees of freedom of the suspended body. We apply these ideas to a superconducting levitated torsion balance, developed by the authors, and a generic electrostatic suspension. We present results of preliminary experiments that provide support for our analyses.     

一种基于0.18-μm CMOS工艺的新型超宽频带毫米波混频器设计与分析

本文提出了一种超宽频带毫米波混频器电路.混频器采用分布式拓扑结构和中频功率合成技术,具有宽带宽和高转换增益.该混频器采用TSMC 0.18-μm CMOS工艺设计并制造,芯片总面积为1.67mm².测试结果表明:混频器工作频率从8GHz到40GHz,中频频率为2.5GHz时的转换增益为-0.2dB至4dB,其本振到中频端口和射频到中频端口间的隔离度均大于50dB.整个电路的直流功耗小于32mW.     

基于肖特基二极管改进模型的W波段宽带八次谐波混频器

在对肖特基二极管电磁模型和电路模型精确建模的基础上,设计并制作了W波段宽带八次谐波混频器.通过对肖特基二极管物理结构的分析,建立了其精确的三维电磁仿真模型和直到180 GHz的改进的宽带等效电路模型.针对W波段八次谐波混频器混频产物能量分布特点和工作带宽要求,设计了宽带射频和本振匹配网络,使混频器的工作带宽能覆盖整个W波段.测试结果显示,射频信号在75~110 GHz频率范围内,W波段八次谐波混频器最大变频损耗28 d B,最小变频损耗18 d B.     

太赫兹信号发生与接收技术

论文重点论述了固态太赫兹信号发生和接收技术,太赫兹信号发生采用倍频级联的方案,重点解决了倍频器的 压缩点、驱动功率和倍频效率等三个方面的问题,实现了频率覆盖500GHz 的大功率信号发生。信号接收采用了分谐波 混频的方案,通过构建二极管模型,利用超薄微带电路,实现了混频电路的一体化设计,完成了宽带、低变频损耗的分 谐波混频器,频率覆盖至500GHz。     

脉冲调制信号的相位噪声恶化仿真

为了量化分析连续波信号经过脉冲调制后相位噪声的恶化程度,利用SystemVue 软件搭建了脉冲调制对连续波相位噪声恶化的仿真模型。仿真结果表明:脉冲调制后的相位噪声在连续波基础上恶化,近端频偏处的相位噪声由于基底较高,对脉冲调制混叠效应引入的相噪恶化不敏感,远端频偏恶化程度较大。相位噪声的具体恶化程度与频偏位置、脉冲周期、脉冲宽度及基底热噪声等因素有关。     

Implementation of depth-dependent soil concentrations in multimedia mass balance models

In standard multimedia mass balance models, the soil compartment is modeled as a box with uniform concentrations, which often does not correspond with actual field situations. Therefore, the theoretically expected decrease of soil concentrations with depth was implemented in the multimedia model SimpleBox 3.0. The effects of this implementation on the model outcomes were explored for nine compounds in four environmental compartments. For compounds with a low penetration depth, the new model predicts substantially higher or lower concentrations in the vegetation compartment than the old model. For those compounds, predicted concentrations in surface water and air were higher in the new model, but the deviations from the old model were smaller than in the vegetation compartment. For compounds with a large penetration depth, the model adaptations show little effect. No field study was carried out to validate the results of the model calculations, but we did collect measured data on concentrations in vertical soil profiles from literature. According to those data, we concluded that the implementation of depth dependent soil concentrations might be a useful extension for steady state multimedia mass balance models. More field study has to be carried out to validate the model outcomes.     

Rheological Study of Interactions between Anionic Guar and Oppositely Charged Surfactant

We have studied the interactions between anionic carboxymethyl guar (CMG) and oppositely charged surfactant: dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB), cetyltrimethylammonium bromide (CTAB), and gemini surfactants (16-4-16), using rheological measurements. In the present study, two competing forces, electrostatic interaction and hydrophobic interaction, have been identified as important factors. Various types of structure formed on the anionic CMG chains are qualitatively discussed in comparison. For example, C₁₂TAB and gemini surfactant tend to form polymer-bound aggregates, whereas the C₁₆TAB tend to form the polymer-associated architecture. Furthermore, possible mechanisms based on the experimental results to elucidate these interesting phenomena have been proposed and discussed.     

基于思维模型建构的高三化学复习教学*—— 以“平衡原理的应用”为例

以高三复习课“平衡原理的应用”为例,通过真实情境的剖析让学生感知模型,引导学生分析归纳提炼模型,并进行针对练习运用模型,变式训练体会模型,让学生在实践中以模型思维为突破,深入领悟建构模型的实质,有序解决复杂化学问题,提升科学思维能力,发展化学学科核心素养。