Derivation of a hydrodynamic equation for Ginzburg-Landau models in an external field

The lattice approximation to a time-dependent Ginzburg-Landau equation is investigated in the presence of a small external field. The evolution law conserves the spin, but is not reversible. A nonlinear diffusion equation of divergence type is obtained in the hydrodynamic limit. The proof extends to certain stochastically perturbed Hamiltonian systems.     

冲击加载下孔洞形成微射流的最大侵彻深度

应用二维弹塑性流体力学欧拉程序MEPH,研究冲击载荷作用下孔洞形成的微射流.主要关注孔洞微射流的形成过程,重点分析冲击压力及孔洞半径等因素对于孔洞微射流最大侵彻深度的影响.分析孔洞塌缩形成射流的空间速度分布特征,并应用非定常射流理论,对不同冲击压力及孔洞半径条件下,微射流的最大侵彻深度进行估算,估算结果与数值模拟结果符合较好.     

长径比对长杆弹垂直侵彻能力影响机制的研究

 以长杆弹垂直侵彻半无限靶为研究对象,利用量纲理论,分析了影响侵彻深度的主要因素,采用经验公式和数值仿真对长杆弹侵彻机理进行了系统研究。结果表明：要达到同样的侵彻效率,长径比的增加会增大单位侵彻深度所耗的能量密度;对于具有相同体积的不同弹体,侵彻深度随长径比增加而增大,直至达到某一最大值。研究发现,造成这种现象的主要原因是侵彻过程中后续不稳定阶段产生的漏斗形弹坑和高温影响弹体侵彻,虽然交界面对侵彻深度的影响较大,但与长径比对侵彻效率的影响无明显关系。     

入射速度对长杆弹垂直侵彻行为的影响规律

 以长杆弹垂直侵彻半无限厚靶板为研究对象,分析了弹体最大侵彻深度与入射速度的关系,研究了弹体入射速度对侵彻最大深度的影响规律。研究表明：靶板的强度和界面效应使弹体在侵彻过程中存在一个临界速度,当入射速度大于临界速度时,弹体的侵彻才能通过开坑阶段进入准稳定阶段,它是造成当入射速度较小时侵彻深度随入射速度的提高而几乎不变或缓慢增加的主要原因;准稳定侵彻过程中弹体速度和侵彻速度基本不变,并且两者存在线性关系,这种关系只与弹体和靶板的材料性能有关,是造成当入射速度较大时侵彻深度随入射速度的提高呈快速线性增大的主要原因。     

刚性弹丸撞击下岩石侵彻之理论研究

 对岩石在刚性弹丸撞击下的侵彻问题进行了理论研究。文章包括两个部分。首先,对常用的预测岩石在刚性弹丸撞击下侵彻深度的方程进行了简单回顾和评论;然后,在实验观测的基础上,对最近发表的一些预测在刚性弹丸撞击下,混凝土和土壤的侵彻公式进行了修正,推导出一个较为合理的剪切强度表达式。拟合结果表明：该模型与Frew、Forrestal和Hanchak所得到的石灰岩侵彻的实验数据吻合得很好。     

卵形弹侵彻混凝土靶实验研究

 采用电探针测试技术和分幅照相技术测定了按比例缩小的三种弹丸的着靶速度及侵彻过程，获得了弹丸着靶速度及对应的最大侵彻深度数据。通过对实验数据的分析，给出了估算弹丸着靶速度与最大侵彻深度的经验公式，计算结果与本实验和文献［2, 3, 4］的实验数据相符。     

Coherent Derivation of Equations for Differential Spectroscopy and Spatially Resolved Spectroscopy: An Undergraduate Tutorial

Near-infrared spectroscopy (NIRS) is a spectroscopic method that is frequently used in health care and sports medicine to monitor oxygenation parameters in biological tissue. This tutorial provides a coherent derivation of equations for differential spectroscopy and spatially resolved spectroscopy, from basic theories to implementable equations. The basic theories are applicable to any kind of tissue oximeter but mainly focus on continuous-wave instruments.     

基于离焦的微操作机器人系统光轴方向深度测量

在分析显微物镜成像原理的基础上,提出并实现了一种微操作机器人系统光轴方向深度测量方法,该方法通过显微物镜离焦光学传递函数（optical transfer function, OTF）建立物方离焦程度与显微图像模糊程度的关系,由此实现深度测量.由于考虑了透镜参数与衍射效应的影响,方法具有较高的测量精度和较好的线性度,同时利用条状物体快速辨识算法,对原始方法进行了简化,使深度测量可在线完成.进一步,将上述方法应用于实际微操作机器人系统,通过离焦状态双针互插实验验证了方法的有效性,同时拓展了微操作机器人系统的有效操作空间. 关键词： 深度测量 微操作机器人 显微镜系统成像模型 光学传递函数     

Some New Results for McKean’s Graphs with Applications to Kac’s Equation

The main goal of the present paper is to sharpen some results about the error made when the Wild sums, used to represent the solution of the Kac analog of Boltzmann’s equation, are truncated at the n-th stage. More precisely, in Carlen, Carvalho and Gabetta (J. Funct. Anal. 220: 362–387 (2005)), one finds a bound for the above-mentioned error which depends on (an ^Λ+ε). On the one hand, it is shown that Λ, the least negative eigenvalue of the linearized collision operator, is the best possible exponent. On the other hand, ε is an extra strictly positive number and a a positive coefficient which depends on ε too. Thus, it is interesting to check whether ε can be removed from the above bound. According to the aforesaid reference, this problem is studied here by means of the probability distribution of the depth of a leaf in a McKean random tree. In fact, an accurate study of the probability generating function of such a depth leads to conclude that the above bound can be replaced with (a′ n ^Λ).     

贵金属金的状态方程

 提出了一个热压强的计算公式,从而获得金的状态方程。并结合实验数据与文献中常用的其它两个状态方程进行了比较。结果发现,修正后的状态方程与实验数据吻合很好,略优于其它两个状态方程。     

PETN炸药爆轰产物状态方程的理论研究

 采用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型,计算爆轰气相产物的状态方程;用石墨相、金刚石相、类石墨液相和类金刚石液相4种相态描述凝聚成分,由Gibbs自由能最小原理确定不同状态下的凝聚产物相态。对爆轰产物混合系统采用自由能最小原理,通过化学平衡方程组求解炸药爆轰产物系统的平衡组分。使用该理论计算PETN炸药Chapman-Jouguet（CJ）点的爆轰参数,其值与实验值符合得很好;同时计算了以CJ点为起始点的等熵卸载线,并与传统的Jones-Wilkins-Lee（JWL）状态方程的计算结果进行比较,发现计算的γ值是单调递减的,而JWL状态方程计算的γ值却出现了“双峰”现象。分析认为,传统的JWL状态方程给出的“双峰”变化,是由其函数形式自身决定的,并不对应实际物理过程。     

A Study for Obtaining New and More General Solutions of Special-Type Nonlinear Equation

The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.     

Rigorous Derivation and Analysis of Coupling of Kinetic Equations and Their Hydrodynamic Limits for a Simplified Boltzmann Model

In this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model. We prove the global convergence of the Chapman–Enskog expansion for this model. We then study the existence theory and asymptotic behaviour of the coupled systems. To solve the coupled problems we propose to use the transmission time marching algorithm. We then develop a convergence theory for the resulting algorithms.     

极小景深条件下显微镜大范围聚焦算法

自动聚焦是全自动显微成像中的一项关键技术。为了克服已有聚焦算法对聚焦起始点敏感及聚焦范围过小的问题,从分析大范围聚焦曲线形态入手,依据离焦距离、初始搜索方向和初始搜索范围等参量和曲线形态参数间的制约关系,将聚焦划分为六种类型,极值搜索中结合聚焦函数值的变化信息并通过启发式方式将未知类型转化为基本型,从而实现了大范围聚焦到小范围聚焦的转换。然后在聚焦曲线陡峭区范围内对曲线进行高斯拟合以获取最优焦平面。基于自行研发的全自动显微镜系统对提出的算法进行了验证,实验结果证明了该算法的有效性。     

Variation of Parameters Method for Solving System of Nonlinear Volterra Integro-Differential Equation

It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes, such as nano-hydrodynamics, drop wise condensation, oceanography, earthquake and wind ripple in desert. Inspired and motivated by these facts, we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations. The proposed technique is applied without any discretization, perturbation, transformation, restrictive assumptions and is free from Adomian's polynomials. Several examples are given to verify the reliability and efficiency of the proposed technique.     

Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit

The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.     

用串行迭代算法设计具有长焦深功能的衍射光学元件

提出一种串行迭代算法,将它用于控制波前传播进行衍射光学元件设计.用此算法设计出能使半导体激光束聚焦并具有长焦深功能的衍射光学元件.模拟计算结果表明了此设计方法的有效性.该衍射光学元件已用光刻和离子刻蚀技术制备并进行了光学实验研究,取得了与理论设计一致的实验结果.     

氢及其同位素宽区状态方程的核量子效应

应用大规模第一性原理分子动力学数值模拟方法,系统研究了氢及其同位素在极端条件下的分子解离规律及状态方程,并给出了参数化的解函数拟合公式。结合分子、原子流体量子振动的一阶修正,揭示了氢及其同位素的核量子效应,解析获得了氢、氘分子在温稠密区域分子解离规律的差别。由第一性原理状态方程给出了雨贡纽曲线,与气炮、化学炸药、磁驱动、高能激光等实验数据相符合,并详细讨论了由核量子效应导致的氢、氘雨贡纽曲线的同位素效应。     

New Concepts from the Evans Unified Field Theory. Part One: The Evolution of Curvature,Oscillatory Universe Without Singularity,Causal Quantum Mechanics,and General Force and Field Equations

No Heading The Evans field equation is solved to give the equations governing the evolution of scalar curvature R and contracted energy-momentum T. These equations show that R and T are always analytical, oscillatory, functions without singularity and apply to all radiated and matter fields from the sub-atomic to the cosmological level. One of the implications is that all radiated and matter fields are both causal and quantized, contrary to the Heisenberg uncertainty principle. The wave equations governing this quantization are deduced from the Evans field equation. Another is that the universe is oscillatory without singularity, contrary to contemporary opinion based on singularity theorems. The Evans field equation is more fundamental than, and leads to, the Einstein field equation as a particular example, and so modifies and generalizes the contemporary Big Bang model. The general force and conservation equations of radiated and matter fields are deduced systematically from the Evans field equation. These include the field equations of electrodynamics, dark matter, and the unified or hybrid field.     

Noether Symmetry and Noether Conserved Quantity of Nielsen Equation for Dynamical Systems of Relative Motion

Noether symmetry of Nielsen equation and Noether conserved quantitydeduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.