Sommerfeld-type integrals for discrete diffraction problems

Three problems for a discrete analog of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: (1) the problem with a point source on an entire plane; (2) the problem of diffraction by a Dirichlet half-line; (3) the problem of diffraction by a Dirichlet right angle. It is shown that the total field can be represented as an integral of an algebraic function over a contour drawn on some manifold. The latter is a torus. As a result, explicit solutions are obtained in terms of recursive relations (for the Green’s function), algebraic functions (for the half-line problem), or elliptic functions (for the right angle problem).     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One

By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n$. We obtain that the upper bound is $7[(n-3)/2]+5$ when $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$.     

黏弹性接触界面端附近的奇异应力场

研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性.      

含非完整界面的功能梯度压电材料Ⅲ型裂纹问题

本文研究了含非完整界面的功能梯度压电复合材料的Ⅲ型裂纹问题．此裂纹垂直于非完整界面,采用弹簧型力电耦合界面模型模拟非完整界面．界面两侧材料的性质,如弹性模量、压电常数和介电常数均假定呈指数函数形式且沿着裂纹方向变化．运用积分变换法将裂纹面条件转换为奇异积分方程,并使用Gauss-Chebyshev方法对其进行数值求解．根据算例结果讨论了一些退化问题并分析了裂纹尖端强度因子与材料的非均匀系数和非完整界面参数的关系．     

Learning Visible Thermal Person Re-Identification via Spatial Dependence and Dual-Constraint Loss

Visible thermal person re-identification (VT Re-ID) is the task of matching pedestrian images collected by thermal and visible light cameras. The two main challenges presented by VT Re-ID are the intra-class variation between pedestrian images and the cross-modality difference between visible and thermal images. Existing works have principally focused on local representation through cross-modality feature distribution, but ignore the internal connection of the local features of pedestrian body parts. Therefore, this paper proposes a dual-path attention network model to establish the spatial dependency relationship between the local features of the pedestrian feature map and to effectively enhance the feature extraction. Meanwhile, we propose cross-modality dual-constraint loss, which adds the center and boundary constraints for each class distribution in the embedding space to promote compactness within the class and enhance the separability between classes. Our experimental results show that our proposed approach has advantages over the state-of-the-art methods on the two public datasets SYSU-MM01 and RegDB. The result for the SYSU-MM01 is Rank-1/mAP 57.74%/54.35%, and the result for the RegDB is Rank-1/mAP 76.07%/69.43%.     

Numerical and Experimental Investigation of the Conjugate Heat Transfer for a High-Pressure Pneumatic Control Valve Assembly

This paper uses heat transfer experiments and computational fluid dynamics (CFD) simulations to investigate the conjugate heat transfer (CHT) in a high-pressure pneumatic control valve assembly. A heat transfer test rig was constructed, and time–temperature histories of five test points placed on the valve assembly’s outer surface were recorded for study validation. The Unsteady Reynolds-Averaged Navier–Stokes (URANS) CFD methods with the standard k-ε turbulence closure equations were adopted in the numerical computations. Polyhedral grids were used; time step and mesh convergence studies were conducted. Simulated and measured temperatures profile comparisons revealed a good agreement. The CHT results obtained from CFD showed huge velocity fields downstream of the valve throat and the vent hole. The airflow through the valve was icy, mainly in the supersonic flow areas. Low temperatures below 273.15 K were recorded on the internal and external walls of the valve assembly. The consistency of the measured data with the numerical results demonstrates the effectiveness of polyhedral grids in exploring the CHT using CFD methods. The local entropy production rate analysis revealed that irreversibility is mainly due to viscous dissipation. The current CHT investigation provides a potential basis for thermostress analysis and optimization.     

Evolution of Er^3＋ Distribution in the Oxyfluoride Glass Ceramics with Heating

The distribution characteristics of Er3+ ions doped in the oxyfluoride glass ceramics containing LaF3 nanocrystals heat-treated at 650 ℃ for different durations were investigated. The results of the integral absorption cross-section analysis demonstrated that the partition fraction of Er3+ in LaF3 nanocrystals increases with prolonging of heating time. The anomalous phenomena of Er3+ emissions in the up-and the down-conversion fluorescence spectra are well explained based on the calculated results.     

整数环上一类三阶矩阵方程有解的充要条件

给出了整数环上一类三阶矩阵方程有解的充要条件.