高功率激光驱动器中小尺度自聚焦和噪声模型

 建立了一套线性的近似分析方法，研究高功率激光驱动器中强激光传输的小尺度自聚焦效应和相位噪声对光束传输和光束质量的影响，给出了系统噪声强度、B积分值与光束近场调制对比度之间的定量关系。研究表明,为保证输出光束质量，即近场调制对比度小于给定值，系统内的噪声强度必须符合一定的谱分布。     

Continuum percolation of the four-bonding-site associating fluids

Wertheim’s integral equation theory for associating fluids is reformulated for the study of the connectedness properties of associating hard spheres with four bonding sites. The association interaction is described as a square-well saturable attraction between these sites. The connectedness version of the Ornstein-Zernike (OZ) integral equation is supplemented by the PY-like closure relation and solved analytically within an ideal network approximation in which the network is represented as resulting from the crossing of ideal polymer chains. The pair connectedness functions and the mean cluster size are calculated and discussed. The condition for the percolation transition and the analytical form of the percolation threshold are derived. The connection of the percolation with the gas-liquid phase transition is discussed.     

Veiled assonance between geodesics on ellipsoid and billiard in its focal ellipse

We introduce new special ellipsoidal confocal coordinates in ⁿ (n ≥ 3) and apply them to the geodesic problem on a triaxial ellipsoid in ³ as well as the billiard problem in its focal ellipse.

Using such appropriate coordinates we show that these different dynamical systems have the same common analytic first integral. This fact is not evident because there exists a geometrical spatial gap between the geodesic and billiard flows under consideration, and this separating gap just “veils” the resemblance of the two systems.

In short, a geodesic on the ellipsoid and a billiard trajectory inside its focal ellipse are in a “veiled assonance”—under the same initial data they will be tangent to the same confocal hyperboloid. But this assonance is rather incomplete: the dynamical systems in question differ by their intrinsic action angle-variables, thereby the different dynamics arise on the same phase space (i.e. the same phase curves in the same phase space bear quite different rotation numbers).

Some results of this work have been published before in Russian (Tabanov, 1993) and presented to the International Geometrical Colloquium (Moscow, May 10–14, 1993) and the International Symposium on Classical and Quantum Billiards (Ascona, Switzerland, July 25–30, 1994).     

实验室晶体积分衍射效率标定方法研究

基于X射线衍射仪运行的稳定性和角度的精密控制能力,以平面季戊四醇(PET)晶体为样品,对晶体的积分衍射效率标定方法进行了实验研究。实验的光源是Cu靶X射线管,通过适当选取镍滤片和精细控制管电压,极大地抑制了Kβ线谱和韧致辐射,实现了Kα线能量单色化。正比计数器前端的狭缝是0.05mm,采用0.001°的步进角度对源强和Kα线衍射峰分别进行扫描。数据处理后得出在Cu的Kα线能点(8047.823eV)处,该平面PET晶体的积分衍射效率是(1.759±0.002)×10-4 rad。实验结果表明该方法可以在实验室条件下快速、方便地完成平面晶体积分衍射效率的标定。     

相空间路径积分中的Feynman规则和广义Ward恒等式

基于Green函数的相空间生成泛函,导出了广义正则Ward恒等式.指出无须作出相空间生成泛函中对正则动量的路径积分,即可求得树图近似下的Feynman规则.对场的拉氏量添加一个四维散度项后,场的传播子发生了改变.     

一些高振荡积分、高振荡积分方程的高性能计算

电磁、声波散射问题的研究涉及一类数学物理问题, 此类问题具有深刻的理论价值和重要的应用背景, 亟待解决. 高振荡微分、积分方程是刻画这些问题的重要的数学模型, 其数值计算存在许多挑战性研究课题. 本文从积分方程解法角度出发, 综述了求解这类高振荡问题的一些最新进展, 特别是针对广义Fourier 变换、Bessel 变换的高效算法、高振荡核Volterra 积分方程的数值解法作了详细介绍. 这些数值方法共有特点是振荡频率越高算法精度愈高, 且可望为电磁计算的研究提供一些新的高效算法.     

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1$\alpha =1$), the Helmholtz equation (α→0$\alpha \to 0$) and the wave equation (α=2$\alpha =2$) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.     

Affine holomorphic quantization

We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation, allowing to implement manifest locality without the necessity for metric or causal background structures. The quantization combines the holomorphic version of geometric quantization for state spaces with the Feynman path integral quantization for amplitudes. We also develop an adapted notion of coherent states, discuss vacuum states, and consider observables and their Berezin–Toeplitz quantization. Moreover, we derive a factorization identity for the amplitude in the special case of a linear field theory modified by a source-like term and comment on its use as a generating functional for a generalized S$S$-matrix.     

层叠Blumlein线多开关导通时间分散性

高介电常数陶瓷储能脉冲形成线需要用到多开关触发的层叠Blumlein线结构。从形成线波过程理论出发,分析了多开关导通时间分散性对层叠Blumlein线及其输出波形的影响。主要包括两方面影响:其一是造成输出方波脉冲的前沿和后沿均出现阶梯形畸变;其二是使得各延迟导通的平行平板Blumlein线承受过电压,容易引起陶瓷储能介质的电击穿。在不单独考虑开关电感的理想情况下,利用PSpice电路程序模拟了开关导通时间分散性对四级层叠Blumlein线的影响,模拟结果与波过程理论分析一致。为减弱这些影响,提出了可行的解决方案。     

非完整约束奇异广义力学系统的Poincaré-Cartan积分

对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系 统，基于广义Apell-Четаев约束条件，并考虑到系统的内在约束，导出了该非完整 约 束奇异广义力学系统的广义Poincaré-Cartan积分不变量. 并证明了该不变量与非完整约束 奇异广义力学系统的广义正则方程等价.