微小光学的研究现状

叙述了微小光学的新进展，对微小光学基本原理给出了简单概括，并对发展动态进行了评论，在微小光学理方面，讨论了“阵列光学”理论，研究了光学阵列的物与共轭象间的关系；在微小光学器件方面，讨论了变折射率透镜，平面微透镜列阵，衍射光学元件和三维集成光学系统；在应用方面，讨论了和并行光通信，光计算有关的一些新应用。     

有关“交流电桥”实验的讨论

本文讨论了“交流电桥”实验中收敛性的问题，并通过对电容桥电路的分析，讨论了抗干扰问题．     

横向位移双曝光散斑图维纳谱的信息分布

讨论了横向位移双曝光散斑图维纳谱的信息分布，并由此导出杨氏纹图的一般表达式。讨论了条纹可见度与应变，面内转动，照明光束直径与条纹图图空间坐标的关系，指出了在条纹可见度影响下最大可见条纹数目。还讨论了散斑衬比与衍射晕的关系。     

量子力学中算符规则的唯一性讨论

本文介绍了一般经典力学量相应算符的确定方法，讨论了算符规则确定的唯一性，并讨论了和其他规则的联系．     

有关光栅衍射教学的几点看法

结合干涉与衍射的关系，讨论了在光栅衍射的教学中的一种教法，并讨论了光栅的概念性问题。     

抛物型反射面镜对光波场的转换

讨论了抛物型反射面镜对光波场的转换，指出了获得严格傅里叶变的条件，并讨论了反射镜内的成像特征，以及聚焦误差所产生的影响。     

偏振光中的算符及表示

本文在偏振光的态矢量表示基础上，进一步讨论了偏振算符和相移算符，讨论了本征值方程和投影方程．提出了用本征态矢构成偏振算符和相移算符的方法．最后讨论了经过偏振器后的光强问题．     

离子束技术在金属中氦行为研究中的应用

结合我们近期的研究工作，本文介绍和讨论了离子束技术在金属中氦行为研究中的应用，还介绍和讨论了氦在金属中的基本特性，如氦的捕获、迁移和氦泡结构等．     

中子星与奇异星

主要评述了奇异星物理的发展概况和研究前景，讨论了与此有关的奇异特问题，阐述了奇异星在存在性和动力学问题，并讨论了如何区分奇异星和中子星的观测效应。     

惠斯通电桥问题的一题多解

本文讨论了惠斯通电桥问题的一题多解，这种讨论有益于拓宽学生的思路，启迪思维，贯穿所学过的知识与方法，能培养学生分析问题和解题的能力。     

The structural, electronic, and magnetic properties of Fe-Ir, Co-Ir and Ni-Ir linear and zigzag nanowires: First-principles calculations

The magnetic and electronic properties of both linear and zigzag bimetallic chains of Fe-Ir, Co-Ir and Ni-Ir have been calculated based on density functional theory and using the generalized gradient approximation. It is found that all considered zigzag chains form a twisted two-legged ladder, look like a corner-sharing triangle ribbon, and have a lower total energy than the corresponding linear chains. All the Fe-Ir, Co-Ir and Ni-Ir linear and zigzag chains have stable or metastable ferromagnetic (FM) states. The bond lengths in bimetallic Fe-Ir, Co-Ir and Ni-Ir at ferromagnetic state are larger than those in the corresponding structures at nonmagnetic state. Interestingly, the Ni-Ir zigzag nanowire has two energy minimum states, both ferromagnetic and nonmagnetic (NM), indicating a possible stable condition for mechanically controllable break-junction experiments.     

Understanding finite size effects in quasi-long-range orders for exactly solvable chain models

In this paper, we investigate how much of the numerical artefacts introduced by finite system size and choice of boundary conditions can be removed by finite size scaling, for strongly correlated systems with quasi-long-range order. Starting from the exact ground-state wave functions of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion on finite periodic chains and finite open chains, we compute the two-point, density-density, and pair-pair correlation functions, and fit these to various asymptotic power laws. Comparing the finite-periodic-chain and finite-open-chain correlations with their infinite-chain counterparts, we find reasonable agreement among them for the power-law amplitudes and exponents, but poor agreement for the phase shifts. More importantly, for chain lengths on the order of 100, we find our finite-open-chain calculation overestimates some infinite-chain exponents (as did a recent density-matrix renormalization-group (DMRG) calculation on finite smooth chains), whereas our finite-periodic-chain calculation underestimates these exponents. We attribute this systematic difference to the different choice of boundary conditions. Eventually, both finite-chain exponents approach the infinite-chain limit: by a chain length of 1000 for periodic chains, and >2000 for open chains. There is, however, a misleading apparent finite size scaling convergence at shorter chain lengths, for both our finite-chain exponents, as well as the finite-smooth-chain exponents. Implications of this observation are discussed.     

Resonance Chains and Geometric Limits on Schottky Surfaces

Resonance chains have been observed in many different physical and mathematical scattering problems. Recently, numerical studies linked the phenomenon of resonances chains to an approximate clustering of the length spectrum on integer multiples of a base length. A canonical example of such a scattering system is provided by 3-funneled hyperbolic surfaces where the lengths of the three geodesics around the funnels have rational ratios. In this article we present a mathematically rigorous study of the resonance chains for these systems. We prove the analyticity of the generalized zeta function, which provides the central mathematical tool for understanding the resonance chains. Furthermore, we prove for a fixed ratio between the funnel lengths and in the limit of large lengths that after a suitable rescaling, the resonances in a bounded domain align equidistantly along certain lines. The position of these lines is given by the zeros of an explicit polynomial that only depends on the ratio of the funnel lengths.     

Synthesis of Fe3O4 hollow microsphere chains and their magnetic properties

Fe₃O₄ hollow microsphere chains with lengths of 8–11 μm have been solvothermally synthesized in the mixed solution of glycerol and water with 1 M NaOH. The hollow microspheres have diameters in the range 0.7–1 μm, and the thickness of the shells is 150–300 nm. The shell of the hollow microspheres is constructed by octahedrons of 100–170 nm. However, when the concentration of NaOH is adjusted to 3 M, the octahedron chains with lengths of 30–50 μm can be obtained. The magnetic saturation values of hollow microsphere chains and octahedron chains are 88.1 and 102.4 emu/g at room temperature, respectively.     

Dependence of the Distribution of Atomic Chain Lengths on a Vicinal Surface on External Parameters

The growth of one-dimensional atomic chains along the vicinal surface has been studied by the kinetic Monte Carlo method. It has been shown that their growth is determined exclusively by kinetic parameters such as the temperature, flux of deposited atoms, and degree of coating rather than by the binding energy and quantum effects. Conditions under which chains with “magic lengths” appear have been determined.     

Heat exchange at laminar flow in rectangular channels

Numerical modeling of heat exchange at a laminar stationary and pulsatile flow in rectangular channels with different aspect ratios of side lengths γ has been carried out by a finite difference method for two boundary conditions: a constant wall temperature and a constant heat flux density on the wall. For the boundary condition of the first kind, the similarity of distributions of the heat flux density and shear stress on the walls over the channel perimeter has been established. The reasons for a nonmonotonous dependence of the initial thermal interval length on γ are discussed. For the boundary condition of the second kind, the difference of the Nusselt number averaged over the perimeter at γ → 0 from its value for a flow in a flat channel has been explained. An increase in the Nusselt number averaged over the perimeter and the period of oscillations has been revealed for a pulsatile flow in the quasi-stationary regime at large amplitudes of the oscillations of the velocity averaged over the cross section.     

Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes

In this paper, the accuracy of the Frensley inflow boundary condition of the Wigner equation is analyzed in computing the I–V characteristics of a resonant tunneling diode (RTD). It is found that the Frensley inflow boundary condition for incoming electrons holds only exactly infinite away from the active device region and its accuracy depends on the length of contacts included in the simulation. For this study, the non-equilibrium Green’s function (NEGF) with a Dirichlet to Neumann mapping boundary condition is used for comparison. The I–V characteristics of the RTD are found to agree between self-consistent NEGF and Wigner methods at low bias potentials with sufficiently large GaAs contact lengths. Finally, the relation between the negative differential conductance (NDC) of the RTD and the sizes of contact and buffer in the RTD is investigated using both methods.     

Some approximations in the linear dynamic equations of thin cylinders

Theoretical analysis is performed on the linear dynamic equations of thin cylindrical shells to find the error committed by making the Donnell assumption and the neglect of in-plane inertia. At first, the effect of these approximations is studied on a shell with classical simply supported boundary condition. The same approximations are then investigated for other boundary conditions from a consistent approximate solution of the eigenvalue problem. The Donnell assumption is valed at frequencies high compared with the ring frequencies, for finite length thin shells. The error in the eigenfrequencies from omitting tangential inertia is appreciable for modes with large circumferential and axial wave lengths, independent of shell thickness and boundary conditions.     

平面光波导器件时域有限差分束传输法分析中边界和初始条件的处理

从慢变包络（SVEA）时域光传输方程出发,对比了综合道格拉斯（GD）和传统的中心差分（CN）两种离散化格式,指出GD法比CN法精度有了很大提高.重点讨论了GD法的TD-BPM边界处理问题,给出了吸收边界和透明边界离散的显式和隐式表达式,分析并确定了交替方向隐式法（ADIM）的边界处理方式;同时,对激励源加入的连接边界进行了仔细讨论.结果表明对于隐式GD-TD-BPM法边界处理应采用隐式,中间激励更能反映光波导反射场的情况.     

Ordering and the relaxation properties of macromolecules in ferroelectric polymer films

The orientational order and dynamic properties of macromolecules have been studied in two- and three-dimensional systems of polymer chains that are orientationally ordered on the level of elastically strained kinetic units (Gaussian subchains) with anisotropic local intra- and interchain interactions of the dipole type. The values of the order parameter as a function of the film thickness for the corresponding type of boundary conditions imposed on the ends of the film have been calculated, and a comparison with the phenomenological theory and experimental data on polarization distribution in ferroelectric films based on vinylidene fluoride has been performed. Equations of motion have been obtained for transverse and longitudinal mean projections of kinetic units and relaxation time spectra for large-scale motions of chains in the state with a planar order. The long-range order in three-dimensional layers leads to anisotropy of mean-square sizes and, therefore, to relaxation properties of chains in their orientational motions (with respect to the direction of ordering).