基于保角映射的格林函数法及其应用

将格林函数法与保角映射相结合,求解复杂形状边界的二维静电场边值问题,得出电场分布规律,并通过MATLAB数据处理软件的数值计算功能进行数值模拟,绘制出其电场线与等势线(面)分布图,验证了所得结论的正确性.此方法拓展了格林函数法的应用范围,为求解边界形状复杂的二维静电场的边值问题提供了一种新的思路和途径.     

有限元-边界法在光电目标散射计算中的应用

为了解决三维目标电磁散射计算中准确性与有效性的矛盾,建立了有限元-边界法的计算模型,对三维腔体目标的电磁散射计算方法进行了研究。首先,分析了针对三维电磁腔体目标的电磁散射计算边界积分方法,引入了矢量格林函数,利用麦克斯韦方程得到电磁场形式与三维腔体形式的关系,建立了三维开口腔体边界模型;然后,结合光电目标曲面建模方法及高阶基函数的方法,建立了三维光电目标的有限元泛函,完成了有限元-边界法在三维腔体目标电磁散射计算中的应用;最后,进行了实例验证。分析显示,当三维腔体内部为空或为各向异性物质时,角度吻合非常理想,与传统模式匹配法所得结果的吻合度达90%以上。结果表明,采用本方法对三维腔体目标进行电磁散射计算,准确度、效率均有所提高。     

用傅里叶变换求静电场格林函数

通过实例，说明了当求解区域边界在某此方向上伸向无限远时，如何使用傅里叶变换求解静电场格林函数。     

浅海波导中目标散射的边界元方法

提出了一种计算三维散射体在声速剖面随深度变化、距离无关浅海波导中散射声场的数值方法波导边界元方法。当散射体不十分靠近波导界面因而边界多次散射可以忽略时,在边界元计算中可以用自由场格林函数近似波导格林函数。应用镜像法和球波函数加法定理推导了理想波导中球体散射声场的解析解,用来验证波导边界元方法的计算精度,证明该数值方法是准确的。对浅海波导中水下潜器散射声场数值模拟的结果表明,浅海波导海面、海底界面反射、声速剖面等对目标散射声场的幅值和方向性都有很大的影响。      

纳米器件的非零点能Casimir排斥力

结合边界元方法,利用离散点表面电流及表面磁流的格林函数得到任意三维几何体及任意材料纳米器件互相作用离散点之间的Casimir力.给出浸泡在液体中纳米器件的"非零点能"Casimir效应,分析Casimir排斥力产生的条件,为实际纳米器件之间Casimir效应分析提供新的数值方法.     

关于一道狄利克雷边界条件下电势计算题的思考

利用格林函数法计算了在狄利克雷边界(第一类边界)条件下,边界为无穷大平面、边界电势在由x=±1和y=±1的4个点形成的正方形区域内为1、其他地方为零的上半空间的电势精确解.利用函数图像辅助方法阐明如何得到狄利克雷边界条件下电势在z→0的近似解,分别用精确解和近似解讨论了在z→0时的边界电势,两者给出了相同的结果.求解过...     

三维曲面腔顶盖驱动流的MRT-LBM研究

采用多松弛时间格子玻尔兹曼方法(MRT-LBM)的D3Q15模型分别对长方体腔、圆柱腔、半圆柱腔、旋转双曲面腔、旋转椭球面腔、半球腔以及两种组合腔体的三维顶盖驱动腔流进行数值模拟, 比较分析各腔体内流线分布、流速等值线分布和涡心的发展, 对于典型腔体模拟不同雷诺数下的流动情况。结果表明: 在同一雷诺数下, 曲面边界不仅能消除从边界产生的次涡, 还会导致腔内主涡的分离, 增大中心纵剖面纵向回流速度; “上长方体+下半圆柱”腔内流函数分布与边界贴合度最高。当雷诺数不断增大时, 半圆柱腔内主涡逐渐分离成两个同向涡, “上圆柱+下半球”腔内始终保持着圆柱腔与半球腔内的基本流动特征; 而长方体腔内主涡涡心保持在同一高度, 次涡逐渐增强, “上长方体+下半圆柱”腔内流动愈加规则, 主涡逐渐下沉, 流速等值线分布逐渐趋于中心小、四周大。     

土壤模型对地表电位影响及合理选取土壤模型方法研究

首次利用物理意义明确的模拟镜像法推导出三维复合分层土壤模型格林函数, 基于特定土壤模型, 分析了不同土壤配置下土壤模型对地表电位的影响. 结果表明, 在一定条件下土壤模型变化仅改变地表电位绝对值, 基本不改变地表电位差, 从理论上阐明了土壤参数变化对地表电位影响的物理机理. 针对如何选取合适土壤模型来准确计算流过变压器中性点的直流量难题, 提出了合理选取土壤模型的判据及其阈值, 避免了土壤模型选取的随意性和盲目性, 为准确评估流过变压器中性点直流量和直流接地极附近变电站选址提供理论依据. 关键词： 格林函数 模拟镜像法 直流偏磁 土壤模型     

三维润滑问题的数值分析

本文求解了轴承的三维润滑问题。使用格林函数方法,将基本方程化为求解区边界上的积分方程。采用空间曲边三角形单元离散边界,并用六结点等参数无数值求解积分方程,确定了速度场,压力场和边界上的应力。算例与解析解比较表明有较高的精度。其它一些典型问题的计算也给出满意的结果,表明本文方法对数值分析这类问题的有效性。     

三维显微图像复原及点扩散函数的研究

三维显微图像去卷积计算量巨大,运算时间长。评价和分析了三维点扩散函数、散焦像、光学切片以及不同三维点扩散函数去卷积的复原图像,进一步证明了散焦光信息对焦面像的干扰,主要来自于焦面像两侧附近的散焦像。提出了折中选择三维PSF的空间大小,可以获得良好的复原效果,并且减少运行时间。提出了频谱图均值的新概念,作为评价图像清晰及模糊程度的标准,并运用于散焦像、光学切片以及复原结果图的评价。     

Quantum conformal fluctuations near the classical space-time singularity

This paper investigates the behavior of conformal fluctuations of space-time geometry that are admissible under the quantized version of Einstein's general relativity. The approach to quantum gravity is via path integrals. It is shown that considerable simplification results when only the conformal degrees of freedom are considered under this scheme, so much so that it is possible to write down a formal kernel in the most general case where the space-time contains arbitrary distributions of particles with no other interaction except gravity. The behavior of this kernel near the classical space-time singularity then shows that quantum fluctuations inevitably diverge near the singularity. It is shown further that the root cause of this divergence lies in the fact that the Green's function for the conformally invariant scalar wave equation diverges at the singularity. The limitations on the validity of classical general relativity near the space-time singularity are discussed and it is argued that the notion of singularity itself needs to be radically modified once the quantum effects are taken into account.On leave of absence from the Tata Institute of Fundamental Research, Bombay, India     

Dyadic Green‘s function for an unbounded gyroelectric chiral medium in cylindrical coordinates

The dyadic Green‘s function for an unbounded gyroelectric chiral medium is formulated in the Fourier domain in cylindrical coordinates.After a triple Fourier integral of the dyadic Green‘s function has been obtained,the integral is reduced by performing the integration over the transverse Fourier variable.     

Scalar Green's functions in an Euclidean space with a conical-type line singularity

In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux.Supported by a grant from CNPq (Brazilian government agency FA)     

The dyadic Green's function for the cylindrical chirostrip antenna

Using the eigenfunction expansion of dyadic Green's function in unbounded chiral medium, and the method of scattering superposition, the expressions of dyadic Green's function for the one and two—layer cylindrical chirostrip antennas are derived, when the field sources are placed in any layer of cylindrical chirostrip antenna. Also, using the method of saddle point integration, the asymptotic expression of dyadic Green's function for the wraparound chirostrip antenna is obtained. The results can be directly used to analyse the radiation characteristics of cylindrical chirostrip dipolc antenna, et al.     

Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordström black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case M ²>Q ². This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Schwarzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit Q→0. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.     

用圈量子引力解除Schwarichild-de Sitter黑洞的时空奇点

通过引入圈量子引力中holonomy基本变量的类比变量和采用相应的量子化方法,对Schwarichild-de Sitter黑洞中心附近的引力场进行量子化.分析和计算了黑洞中心附近的1r和曲率标量的谱分布,得到了它们均存在有限上界的结果.通过求解经典时空奇点r=0附近的量子哈密顿约束方程,给出了黑洞波函数在黑洞中心附近的时间演化行为,得到了该波函数可以通过经典奇点进行量子演化的结果.     

Analytical derivation of the impulse response for the bounded 2-D diffusion channel

This letter focuses on the derivation of the hitting probabilities of diffusing particles absorbed by an agent in a bounded environment. In particular, we analogously consider the impulse response of a molecular communication channel in a 2-D and 3-D environment. In 2-D, the channel involves a point transmitter that releases molecules to a circular absorbing receiver that absorbs incoming molecules in an environment surrounded by a circular reflecting boundary. Considering this setup, the joint distribution of the molecules on the circular absorbing receiver with respect to time and angle is derived. Using this distribution, the channel characteristics are examined. Then, we extend this channel model to 3-D using a cylindrical receiver and investigate the channel properties. We also propose how to obtain an analytic estimate for the unbounded 2-D channel from our derived solutions, as no analytic derivation for this channel is present in the literature. Throughout the letter, we perform particle-based simulations to compare the analytic results and lay evidence for our findings.     

Resonance cones in cylindrically anisotropic metamaterials: a Green's function analysis

A Green's function analysis for cylindrically anisotropic media is presented that can be used in the design of various metamaterial devices. The resonance cones, which describe the direction of power flow, result from the Green's function singularity when the permittivity tensor elements have opposite signs. Shadow and accessible regions for the source are also identified.     

小波方法分析小流量喷气影响两级低速轴流压气机失速特性的动态效果研究

本文用连续小波变换和二维图像处理方法对三个不同角度的喷气试验数据进行了分析．通过对比分析，连续小波变换发现失速前转速频率成分的能量在两级动叶前的信号中出现波动现象，而这种波动的强度与喷射角有关；二维小波图像分析发现，压力场中相对于叶片通道而言的大尺度奇异性均在失速前呈波动性增强，这种波动以接近转子转速沿压气机周向旋转，喷射角度对失速前的奇异性及其波动程度有明显影响．一维小波方法和二维方法的结果相互对应，但二维方法更加具有优势．