A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

峨山褐煤的分子结构和分子模拟

作为重要的化石能源，褐煤资源潜力巨大、分布广泛但综合利用率低。研究褐煤的分子结构模型，有助于预测褐煤在热解、液化和气化过程中的化学反应机理及反应路径，进而提高褐煤的综合应用水平。以云南峨山褐煤为研究对象，利用傅里叶变换红外光谱、13C核磁共振波谱及X射线光电子能谱等分析测试方法，获取了峨山褐煤的含碳、含氧及含氮结构参数。在此基础上，借助Gaussian 09计算平台，采用量子化学建模的方法构建并优化了峨山褐煤的分子结构模型。研究结果表明：峨山褐煤的芳碳率为39.20%，芳香碳结构主要为苯和萘，且芳香桥头碳与周边碳的比值χ_b为0.07；脂碳率为49.51%，脂肪碳结构主要为亚甲基，季碳和氧接脂碳；氧原子主要存在于羟基、醚氧、羰基和羧基结构中；含氮结构则以吡啶为主。基于元素分析、13C 核磁共振波谱分析，又经过热重实验消除褐煤中残余水分的影响后，计算出峨山褐煤的分子式为C₁₅₃H₁₃₇O₃₅N₂。依据分子式及分析结果计算出峨山褐煤的结构单元含量并构建出其初始结构模型，采用半经验法PM 3基组及密度泛函理论M06-2X/3-21G基组对初始分子构型进行优化。优化后的分子模型具有明显的三维立体特征，芳香环之间较为分散且在空间中排列不规则，芳香簇主要通过亚甲基、醚氧基、羰基、酯基和脂肪环连接，含氧官能团主要分布在分子边缘，脂肪族侧链较多。对优化后的分子模型进行振动频率计算进而获得了分子模型的模拟红外光谱，其与实验红外谱图吻合度良好，证明了峨山褐煤分子结构模型的准确性、合理性。分子结构模型的构建有利于直观地了解峨山褐煤的分子结构特征，从而有助于从微观分子角度研究峨山褐煤的宏观性质。同时，峨山褐煤分子结构模型可为其在热解、液化和气化等领域研究中提供理论指导。     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

小直径棒材超声横波检测仿真分析

采用超声水浸聚焦斜入射方式进行小棒材表面、近表缺陷检测时,声波在水/棒和棒/缺陷界面会发生反射、折射、散射、衍射及波形转换等一系列物理变换。此时缺陷可检性对声波入射条件十分敏感,常出现由于检测条件设置不当而导致缺陷漏检、误检的情况。为解决这一问题,本文针对小棒材超声斜入射检测中的主要参数——入射角和水距,开展声场及缺陷声响应仿真,研究检测参数对不同部位缺陷检测能力的影响,并对仿真结果进行试验验证。通过研究得到了检测水距、入射角度对缺陷检测能力的影响,并得到最优检测条件。试验验证结果表明研究制定的检测方案可有效检测出表面、近表面裂纹缺陷。     

基于NICE-OHMS技术进行大气压气样直接检测的理论分析

噪声免疫腔增强光外差分子光谱技术(NICE-OHMS)是目前世界上最灵敏的激光吸收光谱技术,其在低压环境中具有极高的探测灵敏度。然而当测量样品处于大气压时,NICE-OHMS系统的探测灵敏度会大幅下降。主要原因之一是大气压下获取最大NICE-OHMS信号幅度的条件与低气压下不同。通过对大气压NICE-OHMS理论进行分析,分析了影响信号幅度的参数,并通过数值模拟来寻找最佳的实验条件。本文着重讨论影响信号的主要参数包括光学腔腔长L,调制系数β,探测相位θ。其中,由于在NICE-OHMS中使用DeVoe-Brewer技术将调制频率ν_m锁定到Fabry-Parot(FP)腔的自由光谱区(FSR)。因此FP腔的腔长决定了ν_m,同时还作用于信号幅度S■。模拟结果显示,当腔长增大时,由于ν_m随之减小,载波和边带的光谱成分相互重叠部分增大,因此线型函数的幅度逐渐减小。而吸收信号幅度随着腔长的增加而逐渐增加,色散信号幅度先增大后减小,并且在腔长等于8 cm时达到最大值。调制系数β会影响频率调制后激光载波和边带的幅度大小,并且影响信号线型。随着腔长的增加,最大信号幅度对应的β值也随之增加。在相同腔长下,色散信号的最佳β值小于吸收信号,更容易使用电光调制器实现。最后分析了参数的可实现性,分析了不同种类激光器的频率调谐能力,压电陶瓷的扫描宽度等。以乙炔气体为例,大气压下NICE-OHMS的谱线半宽达到~3 GHz,而光谱覆盖范围大于10 GHz。分布反馈式半导体激光器(DFB)与外腔二极管激光器(ECDL)的频率调谐范围可以达到30 GHz以上,但是由于激光线宽宽,得到的PDH锁定性能欠佳。回音壁模式激光器(WGM)和掺饵光纤激光器(EDFL)线宽为百Hz量级,是目前高灵敏NICE-OHMS系统中常用的光源。但是WGM目前可以实现了5 GHz的激光频率调谐范围,而EDFL的外部电压可控制的调谐范围仅为3 GHz。使用精细度为55000的腔进行模拟,调制系数β=1,腔长大于8 cm时,可使用WGM激光器实现,腔长大于25 cm时,可以使用EDFL激光器实现。而对于在设计光学腔中常用的伸缩长度为25μm的PZT,随着腔长的增加,对应的腔模频移范围逐渐减小,在腔长为典型的40 cm时,扫描范围大于12 GHz。     

真空条件下LiCl溶液蒸发量随浓度变化规律研究

除湿溶液再生是除湿空调系统的核心过程,为了提高除湿溶液再生效率,以蒸发量作为评价标准,在不同的真空度下对不同浓度LiCl溶液进行再生。对不同再生条件下,溶液的再生情况进行数学模拟及实验研究,并将模拟结果与实验结果进行对比分析,结果表明,实验结果同模拟结果具有相同的变化趋势。在6 kPa和8 kPa的压强下,LiCl溶液的蒸发量随浓度的增大先上升后下降,而在1 kPa的压强下,LiCl溶液的蒸发量随浓度的增大呈现出先下降再升高接着又下降的趋势。     

基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。     

Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semiempirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.