Light Scattering by Small Particles: an Ellipsoidal Model That Uses a Quasistatic Approach

Optics and Spectroscopy - To describe light scattering by small nonspherical particles, we have constructed an ellipsoidal model using a quasistatic approximation. The semiaxes of the model...     

The Condition of Applicability for the Extended Boundary Conditions Method for Small Multilayer Particles

We have examined an analog to the extended boundary conditions method (EBCM) with the standard spherical basis, which is popular in light scattering theory, with respect to its applicability to the solution of an electrostatic problem that arises for multilayer scatterers the sizes of which are smaller compared to the wavelength of the incident radiation. It has been found that, in the case of two or more layers, to determine the polarizability and other optical characteristics of particles in the far-field zone, the parameters of the surfaces of layers should obey the condition max{σ₁^(j)} < min{σ₂^(j)}. In this case, appearing infinite systems of linear equations for expansion coefficients of unknown fields have a unique solution, which can be found by the reduction method. For nonspheroidal particles, this condition is related to the convergence radii of expansions of regular and irregular fields outside and inside of the particle, including its shells—R₁^(j) = σ₁^(j) and R₂^(j) = σ₂^(j). In other words, a spherical shell should exist in which expansions of all regular and irregular fields converge simultaneously. This condition is a natural generalization of the result for homogeneous particles, for which such a condition is imposed only on expansions of the “scattered” and internal fields—R₁ < R₂. For spheroidal multilayer particles, which should be singled out into a separate class, the EBCM applicability condition is written as max{σ₁⁽¹⁾, σ₁⁽²⁾, …, σ₁^(J?1), σ₁^(J)} < min{σ₂⁽¹⁾, σ₂⁽²⁾, …, σ₂^(J?1)} and parameters σ₂^(j) of the surfaces of shells are not related to corresponding convergence radii R₂^j of irregular fields. Numerical calculations for two-layer spheroids and pseudospheroids have confirmed completely theoretical inferences. Apart from the EBCM algorithm, an approximate formula has been proposed for the calculation of the polarizability of two-layer particles, in which the polarizability of a two-layer particle is interpreted as a linear combination of the polarizabilities of homogeneous particles that consist of the materials of the shell and core proportionally to their volumes. The range of applicability of this formula is wider than that for the EBCM, and the calculation error is smaller than 1%.     

Light Scattering by Small Multilayer Particles: A Generalized Separation of Variables Method

A Rayleigh approximation is constructed for light scattering by small multilayer axisymmetric particles, in which their polarizability is determined by the generalized separation of variables method (SVM). In this method, scalar potentials, the gradients of which yield the electric-field strengths, are represented as expansions in spherical harmonics of the Laplace equation. Unknown coefficients of expansions are determined from the boundary conditions, which are reduced to infinite systems of linear algebraic equations (ISLAEs), since the separation of variables is incomplete. The T matrix of the electrostatic problem, principal element T₁₁ of which is proportional to the particle polarizability, is determined. The necessary condition for the ISLAEs solvability for the SVM coincides with the condition of the correct application of the extended boundary conditions method (EBCM). However, numerical calculations in which finite-dimensional (i.e., reduced) systems are solved, yield different results in ranges of variation of parameters that are close to the boundary of the range of applicability. An analysis of the numerical calculations of the scattering and absorption cross sections for two-layer confocal spheroids, an exact solution for which can be obtained using spheroidal harmonics, shows that the SVM is preferable to the EBCM. It turned out that the proposed method yields workable results in a wider range of variation of parameters. Even outside the range of applicability, in which it should be regarded as a certain approximate solution, its use in a number of cases is quite acceptable. Additional calculations for three-layer nonconfocal spheroids, as well as for three-layer similar pseudospheroids and Pascal’s snails, which can be obtained from spheroids as a result of the inversion with respect to the coordinate origin and one of the foci, respectively, confirm these inferences. We note that, for certain values of the parameters, the shapes of the latter particles are nonconvex.     

An Internet-Oriented Multilayer Network Model Characterization and Robustness Analysis Method

The Internet creates multidimensional and complex relationships in terms of the composition, application and mapping of social users. Most of the previous related research has focused on the single-layer topology of physical device networks but ignored the study of service access relationships and the social structure of users on the Internet. Here, we propose a composite framework to understand how the interaction between the physical devices network, business application network, and user role network affects the robustness of the entire Internet. In this paper, a multilayer network consisting of a physical device layer, business application layer and user role layer is constructed by collecting experimental network data. We characterize the disturbance process of the entire multilayer network when a physical entity device fails by designing nodal disturbance to investigate the interactions that exist between the different network layers. Meanwhile, we analyze the characteristics of the Internet-oriented multilayer network structure and propose a heuristic multilayer network topology generation algorithm based on the initial routing topology and networking pattern, which simulates the evolution process of multilayer network topology. To further analyze the robustness of this multilayer network model, we combined a total of six target node ranking indicators including random strategy, degree centrality, betweenness centrality, closeness centrality, clustering coefficient and network constraint coefficient, performed node deletion simulations in the experimental network, and analyzed the impact of component types and interactions on the robustness of the overall multilayer network based on the maximum component change in the network. These results provide new insights into the operational processes of the Internet from a multi-domain data fusion perspective, reflecting that the coupling relationships that exist between the different interaction layers are closely linked to the robustness of multilayer networks.     

微通道内椭球颗粒惯性聚焦行为数值研究

基于浸没边界-格子Boltzmann方法,对方形截面微通道内椭球颗粒的惯性迁移与旋转动力学行为进行数值研究,发现微通道内椭球颗粒的惯性迁移存在两种主要的运动状态：①翻转状态,即椭球颗粒前进过程中长轴始终在中心对称平面内;②滚动状态,即椭球颗粒前进过程中长轴始终垂直于中心对称平面.研究表明：在低Re数（Re=10）下颗粒以两种状态随流体迁移至平衡位置;在较大Re数（50≤Re≤200）下最终均以翻转状态随流体迁移,随Re数增加,平衡位置先逼近壁面后远离壁面.通过对不同运动状态下椭球颗粒周围的微观流场进行分析,提示该微观流动在颗粒惯性聚焦行为特征中有重要影响,并从流体和颗粒的惯性角度对颗粒不同运动状态的转换机理给出解释.     

光学薄膜的分层界面散射模型

提出了一种计算光学介质膜系表面总积分散射(TIS)的理论模型。该模型认为,介质膜系粗糙的膜层界面和表面为微观结构不均匀的微薄过渡区;过渡区可用折射率为不同常量的层数足够多的均匀子层来代替,同时这些均匀子层的折射率变化满足指数函数的分布规律。利用矩阵法对积分散射的表达式进行了推导。对于电子束蒸发方法在K9玻璃上沉积的ZrO2单层膜,分层界面散射模型对积分散射的理论计算值要比非相关表面散射模型的计算值更加符合总积分散射仪的实验测量结果。     

Structural Reliability Analysis by Using Non-Probabilistic Multi-Cluster Ellipsoidal Model

Uncertainties are normally unavoidable in engineering practice, which should be taken into account in the structural design and optimization so as to reduce the relevant risks. Yet, the probabilistic models of the uncertainties are often unavailable in the problems due to the lack of samples, and the precision of the conventional non-probabilistic models are not satisfactory when the samples are of multi-cluster distribution. In view of this, an improved method by using a non-probabilistic multi-cluster ellipsoidal model (multi-CEM) for the critical structural reliability analysis is proposed in this paper, which describes the samples in a more accurate and compact way and helps to acquire more satisfactory reliability analysis results. Firstly, a Gaussian mixture model (GMM) is built for the multi-cluster samples with performing expectation maximization (EM) algorithm, based on which the multi-CEM can be constructed. In the structural reliability analysis, two cases, respectively, considering whether the components of the multi-CEM are intersected or not are researched in detail. The non-probabilistic reliability (NPR) indexes for each component of the multi-CEM are computed using the Hasofer–Lind–Rackwitz–Fiessler (HL-RF) algorithm, and then the multidimensional volume ratios of the safe domain to the whole uncertainty domain are computed based on these indexes, indicating the structural NPR. In the end, two numerical examples and a practical application are conducted and analyzed to testify the effectiveness of the method.     

Size Measurement of Small Magnetic Particles

Many different methods for size measurement are known and since they differ in their physical principles, different results are also obtained. In the recent past, there were rapid developments in new measurement techniques and one can now quickly and routinely determine particle sizes in the very fine range. Smaller particle sizes, on the other hand, tend to increase the probability of agglomeration. The measurement of the particle sizes for magnetic materials is not well understood and this paper reports results regarding the size determination of very fine magnetic materials. Because of their dipole moment, these particles tend to agglomerate even more, which in turn causes certain difficulties during the measurements. Wet and dry laser measurement systems were compared and also magnetic materials with different permeabilities in order to establish the influence of individual factors on the measurement process and on the accuracy of the results obtained.     

Large Molecules as Models for Small Particles in Aqueous Geochemistry Research

Many questions that geochemists now pose about mineral surfaces concern the properties of individual molecular functional groups. These questions can be answered directly with large aqueous molecules where the positions of atoms can be determined with accuracy and related to the reactive properties. It is time to abandon this approach with colloidal solid suspensions and employ aqueous molecular clusters. The reactive properties of individual oxygens can be determined separately using these aqueous clusters in spectroscopic studies. These molecules are sufficiently large (1–5 nm) that they overlap in size with the smallest colloids, yet the bond lengths and atom positions can be determined unequivocally from X-ray structural studies. In this paper we present research on a 2-nm cluster that provides a particular useful example. These molecules, unlike surface structures that are inferred from bulk structures, allow direct comparison of experimental data with molecular simulations.     

An Exactly Soluble Model for Hopping Particles Moving with Correlations Between States due to Exchange Sites

The motion of hopping particles on an infinite chain is investigated. The model is characterized by the correlations between states due to exchange sites. The analytic solutions for this syttem are discussedin general case. For some special cases, exact results are obtained with the help of explicit calculations of propagators and mean square displacement deviation. Both probability propagators for the creation and annihilation of two particles or for the deformation and formation of Frenkel excitons are indicated.     

一种近似计算金属多层膜界面过渡层厚度的方法

在用小角射线衍射研究离子束溅射法制备的多层膜基本结构时,提出了一个可以计算界面过渡层厚度公式。由实验曲线和文中提出公式得到过渡层厚度,并与用实验曲线和理论曲线进行拟合所得值进行了对比,结果表明这两种方法得到的过渡层厚度基本一致。     

The Phase-Doppler Method Applied to Very Small Particles

Using a computer model based on Lorenz-Mie and generalized Lorenz-Mie theory, various optical confiugurations of a phase-Doppler system were analysed with regard to their suitability for diameter measurements in the sub-micron range. The major concern in this size range is multi-valuedness of the phase-diameter characteristic, the relatively small signal-to-noise ratio obtained with the very low scattered intensity and the small value of the phase difference to be measured. It is shown numerically and by experiment that for particles in a free stream the multi-valuedness and the shot noise need not prohibit measurements in the sub-micron size range. The major source of phase error results from light scattered form objects or material other than the particle inside the measuring volume. Using an optical set-up with nearly counter-propagating incident beams and a large angle between the detectors, measurements were obtained for particle diameters down to 200 nm, and it is estimated that with some improvements in receiver optics measurement down to 100 nm will be possible.     

Ellipsoidal bag model for heavy quark system

The ellipsoidal bag model is used to describe heavy quark systems such asQ ,Q g andQ ² . Instead of two step model, these states are described by an uniform picture. The potential derived from the ellipsoidal bag forQ is almost equivalent to the Cornell potential. For aQ ² system with large quark pair separation, an improvement of 70 MeV is obtained comparing with the spherical bag.     

Nanoscale Iron Particles for Environmental Remediation: An Overview

Nanoscale iron particles represent a new generation of environmental remediation technologies that could provide cost-effective solutions to some of the most challenging environmental cleanup problems. Nanoscale iron particles have large surface areas and high surface reactivity. Equally important, they provide enormous flexibility for in situ applications. Research has shown that nanoscale iron particles are very effective for the transformation and detoxification of a wide variety of common environmental contaminants, such as chlorinated organic solvents, organochlorine pesticides, and PCBs. Modified iron nanoparticles, such as catalyzed and supported nanoparticles have been synthesized to further enhance the speed and efficiency of remediation. In this paper, recent developments in both laboratory and pilot studies are assessed, including: (1) synthesis of nanoscale iron particles (10–100nm, >99.5% Fe) from common precursors such as Fe(II) and Fe(III); (2) reactivity of the nanoparticles towards contaminants in soil and water over extended periods of time (e.g., weeks); (3) field tests validating the injection of nanoparticles into aquifer, and (4) in situ reactions of the nanoparticles in the subsurface.     

Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles

We study a model of mass-bearing coagulating-fragmenting planar Brownian particles. Coagulation occurs when two particles are within a distance of order ε. Our model is macroscopically described by an inhomogeneous Smoluchowski’s equation in the low ε limit provided that the initial number of particles N is of order |log ε|. When a detailed balance condition is satisfied, we establish a central limit theorem by showing that in the low ε limit, the particle density fluctuation fields obey an Ornstein-Uhlenbeck stochastic differential equation.     

针剂中异物的光电检测方法研究

针剂在实际生产过程中容易混入异物颗粒,异物颗粒影响人体健康,因此针剂在出厂前必须进行异物检测.本文提出了一种基于光阻法的针剂异物的检测方法,介绍了检测原理及其信号处理方法,单瓶静态实验表明,该方法与人工检测方法比较,符合率为96.30%.针对检测区域和测试时间过小所造成的漏检可能,提出了双光路检测方法,并通过实验论证了其可行性.     

Ellipsoidal space-times,sources for the Kerr metric

The paper develops a systematic derivation of the Kerr metric and its possible sources in a clear geometric manner. It starts with a concise account of previous attempts at constructing an interior Kerr solution. Then a treatment of stationary-axisymmetric spacetimes, specially fitted to the needs of the following analysis, is presented. A new notion of an ellipsoidal space-time is introduced: it is a space-time in which local rest 3-spaces of some observers split naturally into congruences of concentric and coaxial ellipsoids. It is shown that these 3-spaces are natural spaces to consider the ellipsoidal figures of equilibrium. The investigation is carried out in detail for axially symmetric oblate confocal ellipsoids, but possible generalizations are indicated. The Kerr metric is found to be an ellipsoidal space-time of this special kind. Some remarks concerning an (unfound) explicit interior Kerr solution conclude the paper.     

Light Scattering by Small Multilayer Nonconfocal Spheroids Using Suitable Spheroidal Basis Sets

Optics and Spectroscopy - We construct a Rayleigh approximation for multilayer particles the layer boundaries of which are nonconfocal spheroids. The geometry of the problem is taken into account...