载机平台光电转塔目标定位的仿真算法

目标定位是光电转塔典型功能和任务之一，对其定位精度的考量也是转塔作战技术指标之一，针对该问题，从理论和仿真角度进行了分析。分析目标定位中用到的坐标系及其相互转换关系，给出光电转塔视轴反演、有源目标定位、无源目标定位的算法流程，通过仿真实验加以验证，考虑了定位过程中可能的随机误差来源，并分析是否采用均值滤波及其对定位结果的影响，最后通过Monte-Carlo分析计算了定位精度。分析结果表明:1）有源定位比无源定位的精度高，在仿真假设条件下，精度约提高1倍；2）均值滤波后，定位精度有较大提升（约提高15倍）；3）18 km距离时典型无源定位精度在80%置信度条件下约为39.4 m；4）统计直方图反映出80%置信度CEP半径及最大误差距离随载机位置、姿态、转塔视轴等（体现在目标载机距离上）不同参数的变化结果。     

Comparative study of optical analysis methods for thin films

Three popular optical analysis methods (the transfer-matrix method, the Tinkham formula, and Beer's law) have been used for analyzing the optical spectra of thin films. While the transfer-matrix method is an accurate method, the Tinkham formula and Beer's law are approximate methods. Here we investigated the three methods using measured transmittance spectra of insulating transition-metal dichalcogenide (TMD) thin films on a quartz substrate. Three different semiconducting 2H-TMD systems (MoS₂, MoSe₂, and MoTe₂) were measured and analyzed. The optical conductivities obtained from the measured transmittance spectra using the transfer-matrix method and Tinkham formula and the absorption coefficients obtained using the transfer-matrix method and Beer's law were compared. The comparisons show some discrepancies. The reasons for the discrepancies between the results obtained via the two different methods were examined and the application limitations of the Tinkham formula and Beer's law were discussed.     

Mixed eigenvalues of discrete p-Laplacian

This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation： the difference form, the single summation form, and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity （which was known years ago）, as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at presented at the end of Section 2 to infinity is also studied. Two examples are illustrate the value of the investigation.     

Force-field parametrization based on radial and energy distribution functions

We propose a novel force-field-parametrization procedure that fits the parameters of potential functions in a manner that the pair distribution function (DF) of molecules derived from candidate parameters can reproduce the given target DF. Conventionally, approaches to minimize the difference between the candidate and target DFs employ radial DFs (RDF). RDF itself has been reported to be insufficient for uniquely identifying the parameters of a molecule. To overcome the weakness, we introduce energy DF (EDF) as a target DF, which describes the distribution of the pairwise energy of molecules. We found that the EDF responds more sensitively to a small perturbation in the pairwise potential parameters and provides better fitting accuracy compared to that of RDF. These findings provide valuable insights into a wide range of coarse graining methods, which determine parameters using information obtained from a higher-level calculation than that of the developed force field. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

Euler–MacLaurin formulas via differential operators

Recently there has been a renewed interest in asymptotic Euler–MacLaurin formulas, because of their applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth functions on intervals, polygons, and three-dimensional polytopes, where the coefficients in the asymptotic expansion are sums of differential operators involving only derivatives of the function in directions normal to the faces of the polytope. Our formulas apply to wedges of any dimension.     

Construction of Helical Structures with Multiple Fused Anthracenes: Structures and Properties of Long Expanded Helicenes

Polycyclic aromatic compounds consisting of four or five fused anthracene units were synthesized by PtCl₂-catalyzed cycloisomerization as novel long expanded helicenes. These compounds have helical structures with significant stacking of the terminal anthracene moieties at 0.33 nm interlayer distance. In the UV-vis and fluorescence spectra, the absorption and emission bands were red-shifted as the number of fused anthracene units was increased. The characteristic broad and long-lived emission bands of the long analogues are explained by the excimer-like stabilization of the excited state. These photophysical data as well as their cyclic voltammetric data are discussed on the basis of the π-conjugation and interlayer π⋅⋅⋅π interactions in the molecular structures and the molecular orbitals. The barrier and mechanism of helical inversion are also reported.