Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates

We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.     

Evolving a three-world framework for solving algebraic equations in the light of what a student has met before

In this paper we consider data from a study in which students shift from linear to quadratic equations in ways that do not conform to established theoretical frameworks. In solving linear equations, the students did not exhibit the ‘didactic cut’ of Filloy and Rojano (1989) or the subtleties arising from conceiving an equation as a balance (Vlassis, 2002). Instead they used ‘procedural embodiments’, shifting terms around with added ‘rules’ to obtain the correct answer (Lima & Tall, 2008). Faced with quadratic equations, the students learn to apply the formula with little success. The interpretation of this data requires earlier theories to be seen within a more comprehensive framework that places them in an evolving context. We use the developing framework of three worlds of mathematics (Tall, 2004, Tall, 2013), based fundamentally on human perceptions and actions and their consequences, at each stage taking into account the experiences that students have ‘met-before’ (Lima and Tall, 2008, McGowen and Tall, 2010). These experiences may be supportive in new contexts, encouraging pleasurable generalization, or problematic, causing confusion and even mathematical anxiety. We consider how this framework explains and predicts the observed data, how it evolves from earlier theories, and how it gives insights that have both theoretical and practical consequences.     

氧化石墨超声时间对三维还原氧化石墨烯结构及超级电容性能的影响

将氧化石墨凝胶超声不同时间制备氧化石墨烯(GO)溶胶,再以GO溶胶为前驱体采用一步水热法制备了三维还原氧化石墨烯(3DRGO),采用X射线衍射(XRD)、拉曼光谱、原子力显微镜(AFM)、扫描电子显微镜(SEM)和电化学测试等研究了不同超声时间对3DRGO的形貌、结构及超级电容性能的影响.结果表明,当超声时间不超过120 min时,经水热反应后还原氧化石墨烯均能形成稳定的三维结构,但随着超声时间的延长,三维结构尺寸不断减小,强度增加,样品的内部结构也由片状逐渐向多孔网状转化;当超声时间超过120 min时,还原氧化石墨烯虽具有网状结构,但在宏观上不利于形成稳定的三维结构.电化学测试结果表明,经不同超声时间所制备的还原氧化石墨烯均表现出较好的超级电容性能,其中超声时间为120 min时制备的3DRGO具有更均匀的多孔网状结构,表现出了最佳的超级电容性能,在1 A/g电流密度下其比电容可达328 F/g,即使在20 A/g的大电流密度条件下,其比电容仍可高达240 F/g.     

Development of a triple channel detection probe for hydrogen peroxide

The rapid and reliable measurement of hydrogen peroxide (H₂O₂) is imperative for many areas of technology, including pharmaceutical, clinical, food industry and environmental applications. In this work, a novel multifunctional complex, [Ru(bpy)₂(luminol-bpy)](PF₆)₂ (bpy: 2,20'-bipyridine), was designed and synthesized by incorporating a Ru(II) complex with a luminal group. In the presence of horseradish peroxidase (HRP), reaction of [Ru(bpy)₂(luminol-bpy)]²⁺ with H₂O₂ can be monitored by three sensing channels including photoluminescence (PL), chemiluminiscence (CL) and eletrochemiluminiscence (ECL). The quantitative assays for H₂O₂ in aqueous solutions using [Ru(bpy)₂(Luminalbpy)]( PF₆)₂ as a probe were established with PL, ECL and CL signal output modes, respectively.     

三维运动接触问题的广义Галин定理

本文给出了求解一类相当普遍的三维运动接触问题的分析解法,并且把仅仅对静态接触问题成立的 定理推广到动力学情形,作了严格证明。作为例子,对接触区为椭圆的情形给出了积分形式的解,并且作了数值计算,由这些结果可以看出运动压体速度的效应。     

三峡库区万州段高切坡破坏模式和防护措施研究

高切坡是三峡库区新的地质灾害形式。通过对重庆库区万州区47个高切坡的调查和试验分析表明,万州高切坡主要表现为崩塌破坏、表层风化破坏、差异风化破坏、和土体滑塌破坏4种形式。影响破坏模式的因素主要是构成高切坡的组成物质及其性质、水文气象条件、高切坡的形态和治理时间等。针对不同的破坏类型提出相应的防治措施,以指导设计与施工。     

三峡库区滑坡的时空分布特征与成因探讨

三峡库区地质灾害频繁发生,地质历史上大型滑坡广泛发育。近年库区滑坡灾害有逐年增加趋势。这些滑坡形成的堆积体成因复杂,不能单纯从传统的外动力或内动力作用来解释,给库区灾害的防治工程带来了很大困难。三峡库区大型古滑坡主要沿长江干流和支流的深切河谷两岸分布,与河流发育演化史密切相关。15万年以来,长江三峡地区经历了新构造期以来抬升速率最快的一次构造幕,山原期夷平面上升了100m,河流强烈下切,形成高陡岸坡,卸荷效应显著;同时,该时期三峡地区的气候受到青藏高原环境变化的影响,在间冰期可能存在相似的暖湿古气候环境,降水极为丰富。三峡库区的大型古滑坡在新构造快速抬升时期广泛发育,并且与暖湿多雨期相对应,表明库区滑坡的发育演化是新构造运动和气候变化内外动力耦合作用的结果。     

基于Surfer平台的FLAC3D 复杂三维地质建模研究

复杂三维地质体模型的建立一直是FLAC^3D软件前处理过程中的一个难题。因此,提出以Surfer软件为过渡平台,通过对地表及岩层分界面三维地质信息的提取、转换,并将Surfer输出的数据经由FLAC^3D软件内嵌的Fish语言编制的程序的二次转换,生成FLAC^3D软件可以直接读取的模型数据文件,从而实现了该软件前处理过程中复杂三维地质模型的快速、准确建立。同时结合工程实际,检验了该方法的可行性和仿真效果,结果表明,建模过程简捷、实用,可操作性强,是FLAC^3D软件前处理的一种新方法。     

A novel nanoscale fin field effect transistor by amended channel: Investigation and fundamental physics

The present paper proposes a new Fin Field Effect Transistor (FinFET) with an amended Channel (AC). The fin region consists of two sections; the lower part which has a rounded shape and the upper part of fin as conventional FinFETs, is cubic. The AC-FinFET devices are proven to have a lower threshold voltage roll-off, reduced DIBL, better subthreshold slope characteristics, and a better gate capacitance in comparison with the C-FinFET. Moreover, the simulation result with three-dimensional and two-carrier device simulator demonstrates an improved output characteristic of the proposed structure due to reduction of self-heating effect. Due to the rounded shape of the lower fin region and decreasing corner effects there, the heat can flow easily, and the device temperature will decrease. Also the gate control over the channel increases due to the narrow upper part of the fin. The paper, thus, attempts to show the advantages of higher performance AC-FinFET device over the conventional one, and its effect on the operation of nanoscale devices.     

A domain decomposition method for three species modeling of multi-electrode negative corona discharge – With applications to electrostatic precipitators

The negative corona discharge problem for multi-electrode geometries is modeled by a three species model. The equations are solved using domain decomposition, by recognizing that multiple species are only present in a small part of the domain, and hence only need to be incorporated locally in the model.The method is applied to an industrially relevant three wire electrostatic precipitator geometry. The calculated current density is in good agreement with experimental data. To further illustrate applications of the three species solution, it is used for coupled particle, fluid, and electrostatic simulations to analyze particle collection properties.