基于平滑因子和勒让德多项式展开的月坑地形模型

提出引入平滑因子的月坑模型,使其接近月坑真实的碗状模型,以利于吉布斯现象的抑制.考虑月坑旋转体模型的对称性,仅对模型剖面进行建模,使用勒让德多项式进行展开,可有效地简化运算.结果表明：平滑因子的引入使得月坑理论模型的边界更加平滑,有效地避免了吉布斯现象中杂波的产生.对勒让德展开系数求解的两类方法REC和ASY进行比较分析,发现基于渐近公式的ASY算法更加稳定,特别是超高阶展开系数的求解.研究可为月坑区域有效弹性厚度的估计提供参考.     

从振动波形研究贝塞尔函数和勒让德函数的渐近关系

通过圆平面和球面上对称振动的分析,比较了零阶贝塞尔函数和勒让德函数曲线,发现两者形状有明显的相似性.在进行振幅变换后,两者曲线几乎重合.从数学和物理角度解释了圆平面和球面上振动波形相似的原因,导出了零阶贝塞尔函数和勒让德函数的渐近关系,并得到了贝塞尔函数零点的一个估计公式.     

混沌通信系统中非线性信道的自适应神经Legendre正交多项式均衡

针对混沌通信系统中非线性信道干扰问题，基于混沌信号重构理论和Legendre正交多项式结构，提出了一种自适应神经Legendre正交多项式信道均衡器，并给出相应的归一化最小均方算法. 仿真研究表明：所提出的自适应神经Legendre正交多项式信道均衡器能有效地消除线性和非线性信道干扰，均衡器输出信号能反映出混沌信号的特性，具有良好的抗干扰性能.该均衡器的结构简单，权系数参数较少，收敛稳定性较好. 关键词： Legendre 正交多项式 信道均衡 混沌吸引子 神经网络     

Experimental analysis of shape deformation of evaporating droplet using Legendre polynomials

Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup.     

Effects of charged sand on electromagnetic wave propagation and its scattering field

Based on the Rayleigh’s scattering theory, the effects of sandstorms on the propagation of electromagnetic wave with different visibilities are presented by solving the scattering field of charged sand particles. Because of the electric charges on the sand surface, the theoretical attenuation will be large enough to match the measured value under certain conditions. And the results show that the effect of sand with electric charges all over its surface on electromagnetic wave attenuation is the same as that of sand without charge, which proves that electric charges distribute on partial surface of the sand in fact.     

麦克斯韦积分方程的一种数值解法

直接从麦克斯韦积分方程出发,采用FIT算法,模拟电磁场的分布情况。     

推广的Tschebyshev多项式及其在解强耦合波导方程中的应用

推广了Tschebyshev多项式，对推广的Tschebyshev多项式的性质作了分析；并应用于求解（ N+1）×（N+1）强耦合环形波导耦合器方程，得出解析解. 具体计算了5×5环形定向耦合器 的解，并对弱耦合与强耦合的关系进行了详细分析. 关键词： 推广的Tschebyshev多项式 强耦合波导耦合器     

旋转带电体和电磁场的角动量守恒定律及能量守恒定律

对均匀带电薄球壳匀加带旋转问题,由电磁场的角动量定恒守律和能量守恒定律两种方法分别得出了外力矩力其功率的正确正确结果。     

Currents in a Quantum Nanoring Controlled by Non-Classical Electromagnetic Field

Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb interaction between fermions influences entanglement of quantum ring and the driving field. In particular it is shown that in an absence of decoherence and under certain conditions fermion–fermion interaction is necessary for a ring–field entanglement to occur.     

均匀带电圆环的电场强度

求出了均匀带电圆环的电场强度,给出了它在3种坐标系里的表达式.     

也谈均匀带电细圆环的电场分布

用Mathematica研究均匀带电细圆环的电场的空间分布,准确地绘制出电场强度量值的分布图和电场方向的分布图,并纠正了最近文献中一幅场强量值分布图的失误.