用于并行激光直写的连续深浮雕衍射透镜阵列研究

研究了一种用于并行激光直写的连续深浮雕衍射透镜阵列方法.该方法采用连续浮雕衍射透镜阵列替换传统并行激光直写中的物镜阵列,在兼顾系统分辨力基础上,克服了波带片等衍射透镜阵列衍射效率低的缺点;同时因采用深浮雕结构优化环带宽度,可降低阵列的制作难度.针对并行激光直写系统阵列F/#小的特点,在建立连续深浮雕衍射透镜阵列非旁轴近似聚焦模型基础上,设计、制作和测试了波长为441.6 nm,F/#为7.5的连续深浮雕衍射透镜阵阵列.测试结果表明:该阵列的衍射效率优于70%,远高于波带片阵列的40%.     

Nonlinear Waves in Two-Dimensional （2D） Square Lattice Frenkel-Kontorova （FK） System

A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.     

Complex Wave Solutions for （2＋1）-Dimensional Modified Dispersive Water Wave System

The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the （2＋1）-dimensional modified dispersive water-wave （MDWW） system are obtained. Based on a derived periodic solitary wave solution and a rational solution, we study a type of phenomenon of complex wave.     

Theoretical Strength of Face-Centred-Cubic Single Crystal Copper Based on a Continuum Model

The constitutive relation of single crystal copper based on atomistic potential is implemented to capture the nonlinear inter-atomic interactions. Uniaxial loading tests of single crystal copper with inter-atomic potential finite-element model are carried out to determine the corresponding ideal strength using the modified Born stability criteria. Dependence of the ideal strength on the crystallographic orientation is studied, and tension- compression asymmetry in ideal strength is also investigated. The results suggest that asymmetry for yielding strength of nano-materials may result from anisotropic character of crystal instability. Moreover, the results also reveal that the critical resolved shear stress in the direction of slip is not an accurate criterion for the ideal strength since it could not capture the dependence on the loading conditions and hydrostatic stress components for the ideal strength.     

HOMOTOPY CONTINUATION ALGORITHM FOR STRUCTURAL DAMAGE IDENTIFICATION

I. INTRODUCTIONStructural damages due to the loss of sti?ness such as crack, localization bulking have remarkablein?uences on the physical properties of structure such as deformation, stress, frequency and modelshape. So the change of these properties can be used to identify the damage location and degree ofstructures. The damage identification techniques based on these properties’ changes have attractedmuch attention in recent years, and many approaches have been developed[1??5].Nowaday…     

解一类二阶延迟常微分方程连续RKN方法的P-稳定性

In this paper, we study the P-stability of the continuous Runge-Kutta Nystroem method for solving the delayed second order differential equation that does not depend on y′. A general theorem is presented which can be used to obtain complete characterizations of the P-stability regions of these continuous RungeKutta- Nystroem methods. We use the condition to two given RKN methods.     

离散与连续的相互转化

离散系统的教学模型可推广至连续系统;但为了便于计算,连续变量又常常被离散化处理。     

与积分有关的一类函数极限的再探讨

用马克劳林公式探讨带有定积分的函数极限     

时滞Duffing型微分方程周期解的存在唯一性

利用三角级数理论及压缩映射原理研究了时滞Duffing型方程ax″(t) bx(t) g(x(t-τ))=p(t),给出了此类Duffing型方程存在唯一周期解的几个充分条件.