Equilibrium of ion-exchange polymeric membrane with aqueous salt solution and its thermodynamic modeling

A thermodynamic model is proposed to describe distribution of the components between a liquid solution and a swollen membrane undergoing structural transformations. Free energy contributions related to formation of solution-filled micro-cavities in the membrane interior are estimated. Formation of the cavities of different shape is accounted for by using the Helfrich expressions for the bending energy of a curved interface. Three adjustable parameters of the model are related to the hydrophobic polymer matrix of the membrane, while the electrostatic contribution is estimated explicitly. Structural changes in the membrane are described as a transition from spherical to cylindrical cavities. Predominance of cavities having definite shape (spheres, cylinders) results in a specific shift of the Donnan equilibrium, which thus, becomes dependent on the structure of the membrane on the mesoscale. The results of model calculations are compared with the experimental data on the distribution of ions (H⁺, Li⁺, Cs⁺, K⁺, Na⁺, Ca²⁺, Mg²⁺) between the aqueous solution and the membrane. Different types of predicted thermodynamic behavior of the membrane in the liquid solution, including the hysteresis of ion-exchange equilibrium curves, are discussed. The model takes into account the effect of micro-inhomogeneties and helps to establish a link between molecular characteristics of the perfluoropolymer membrane and its macroscopic behavior in the liquid solution.     

Uncertainty functions, a compact way of summarising or specifying the behaviour of analytical systems

Analytical chemists can advantageously use an uncertainty function to describe the performance of an analytical system in terms of the standard uncertainty or standard deviation as a function of the concentration of the analyte. This “characteristic function” is useful for estimating uncertainty at a new concentration. A similar function can be used to prescribe the uncertainty that is regarded as fit for purpose for a particular application. This “fitness function” is useful in setting standards of accuracy in proficiency tests and similar exercises without revealing the concentration of the analyte. In combination, these two functions provide a rational basis for method selection.     

Path-following barrier and penalty methods for linearly constrained problems

In the present paper some barrier and penalty methods (e.g. logarithmic barriers, SUMT, exponential penalties), which define a continuously differentiable primal and dual path, applied to linearly constrained convex problems are studied, in particular, the radius of convergence of Newton’s method depending on the barrier and penalty para-meter is estimated, Unlike using self-concordance properties the convergence bounds are derived by direct estimations of the solutions of the Newton equations. The obtained results establish parameter selection rules which guarantee the overall convergence of the considered barrier and penalty techniques with only a finite number of Newton steps at each parameter level. Moreover, the obtained estimates support scaling method which uses approximate dual multipliers as available in barrier and penalty methods     

Modeling of the Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer working in orbit

Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer (TSMFTIS) is a new kind of imaging spectrometer and is applicable in remote sensing. Compared with Temporally Modulated Imaging Interferometer and Spatially Modulated Imaging Interferometer, it employs immovable parts and abandons slit. Based on the analysis of its physical theory, optical principle, data gathering and processing, the mathematical model of the TSMFTIS working in orbit is proposed in this paper. The model is comprised of different function blocks, such as fore-optics, interferometer and so on. For simulation, a big remote sensing image is utilized as ground scene, and a conversion which is similar to color mode conversion from RGB to Lab is made to produce artificial spectra of various ground objects. At last, a validation experiment is performed with real-world spectra of four pieces of colorful cloths by using a commercially available spectrometer.     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.     

Experimental caustics analysis in fracture mechanics of anisotropic materials

The originally developed reflection method of caustics is presented for application to cracks in mechanically anisotropic materials such as fiber-reinforced composites. The derived solutions for the combination of crack-opening modes I and II show that the size of the dark spot depends on the load intensity, whereas its shape depends strongly on the mechanical properties of the material, the orientation of the crack tip and the mixed-mode mixture. The evaluation of optical effects is possible using the diameter-measuring method or the advanced multipoint overdeterministic data reduction method. To find the exact position of caustics, the experimental images are analyzed by the simple boundary value method and a more sophisticated differential method, which is accomplished by shifting the real image onto the gradient image. The standard experimental testing procedure is performed for cracks oriented 0 deg, 45 deg and 90 deg to the material axes in carbon-fiber-reinforced polymer composites.     

一种时间分辨激光诱导击穿光谱的测量方法

激光诱导击穿光谱(LIBS)是一种动态光谱。时间分辨LIBS光谱测量是研究激光诱导等离子体演化和谱线自吸收的重要技术。结合激光诱导击穿光谱测量的时序特性,提出一种利用常规性能光谱探测设备获得微秒级时间分辨LIBS光谱的测量方法。通过控制毫秒级光谱探测设备的积分延迟时间,获得不同延时下的LIBS光谱信号,对所得光谱进行处理得到相应特征谱线拟合强度,将所测的特征谱线强度按照一定的时间间隔进行差分,得到差值即为差分间隔时间内特征谱线的积分强度。采用差分时间间隔应大于系统最差时序精度,同时优选无重叠干扰和背底连续的谱线信号进行分析。以等离子体产生后持续时间为横坐标,计算所得谱线差值强度为纵坐标,即可获得特征谱线的强度演化曲线。通过实验验证,使用积分时间为毫秒量级光谱仪和时序精度为0.021微秒控制系统,该方法可以实现微秒量级时间分辨LIBS光谱测量,可用于表征LIBS光谱特征谱线演化过程,降低了LIBS光谱时间分辨测量系统成本。     

改进力法计算的研究

针对传统力法的缺点, 利用VBA进行了Excel电子表格的编制, 对传统力法 进行了改进. 在保持传统力法的基本原理和计算过程的基础上, 解决了力法计算繁琐的问题, 提高了计算速度和学习效率, 增强了结构力学课程与实际的联系, 对工科课程的教学具有一 定的指导意义.     

A simulation-based analysis of the effect of a reflecting surface on aeroacoustic time-reversal source characterization and comparison with beamforming

This paper presents a simulation-based analysis of the effect of a reflecting surface on aeroacoustic Time-Reversal (TR) source localization/characterization and compares the results of TR with those obtained using cross-spectral Conventional Beamforming (CB). The TR technique is shown to require the use of at least two line arrays of microphones to accurately characterize the nature of aeroacoustic sources. This work, however, shows that in the presence of a rigid surface, only one line array of microphones is sufficient to accurately localize and characterize idealized aeroacoustic sources. Forward simulations were carried out using the 2-D Linearized Euler Equations on a rectangular domain with a rigid bottom boundary (modeling a 2-D semi-infinite space) for the test-cases of stationary idealized tonal aeroacoustic (monopole, dipole and lateral quadrupole) sources located in a fully-developed mean shear flow field wherein the acoustic pressure time–history was stored at the computational boundaries. A set of TR simulations are implemented that show for each test-case that only the top line array is required to accurately characterize the idealized aeroacoustic sources in the presence of a reflecting bottom boundary, thereby suggesting the redundancy of acoustic pressure measurement at the rigid surface. The test-case of convecting (moving) idealized aeroacoustic source was also considered and the TR simulation using only the top line array in the presence of reflecting bottom boundary was able to accurately retrieve the source trajectory and simultaneously characterize its nature. This numerical experiment demonstrates in principle that when a rigid surface is mounted on the floor of an Anechoic Wind Tunnel, the use of only one (top) line array of microphones should be sufficient to characterize the nature and location of experimental flow-induced noise source. Acoustic source maps were also obtained using the CB method based on the Method of Images (to model the reflecting surface) and incorporation of the Ray-Tracing algorithm necessary to account for the effect of mean flow. The CB results were found to be highly comparable to those obtained using TR for the test-cases of non-convecting sources; thereby demonstrating the conceptual equivalence of the Method of Images and directly implementing the rigid-wall condition during TR for source localization/characterization.