数字全息干涉相位导数计算的研究

应变测量对材料评估与分析非常重要。通过计算数字全息干涉的相位导数可实现应变测量。本文针对数字全息干涉相位导数提取问题,对数字剪切法和基于二维伪维格纳法进行研究。数字剪切法通过对干涉复相量的数字平移实现剪切,确定干涉相位导数,而二维伪维格纳法则通过对干涉复相量的二维伪维格纳分布变换,由变换模极值对应的频域参数确定相位导数。数字剪切法需干涉复相量的数字剪切过程,还需相位去包裹。由于激光散斑噪声的影响,直接数字剪切法处理效果较差,通过对剪切干涉复相量滤波,能较好消除散斑噪声影响。二维伪维格纳法无需数字剪切和相位去包裹,就可同时得到2个方向的干涉相位导数,但处理时间较长,处理效果较差。最后,用数字全息干涉法对四周固定、中心加载铝圆盘进行了实际测量,并分别用数字剪切法和二维伪维格纳法进行了分析。结果表明,滤波数字剪切法处理时间适中,处理效果较好。     

反平面动态扩展裂纹问题的研究

应用复变函数论，对反平面动态扩展裂纹问题进行了研究。通过自相似函数的方法可以获得若干问题的解析解。应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题，并可以相当简单地得到问题的闭合解。通过叠加原理利用这些解，就可以求得任意复杂问题的解。     

Mixed Plane Problems in Linearized Solid Mechanics: Exact Solutions

The paper analyzes the exact solutions to mixed plane problems of linearized solid mechanics in cases of statics, dynamics, stability, and fracture. The exact solutions have a universal form for compressible and incompressible, elastic and plastic bodies and account for stresses and displacements expressed in terms of analytical functions of complex variables. To obtain these solutions, the use is made of complex variable theory, in particular, the Riemann–Hilbert methods and Keldysh–Sedov formula. When the initial (residual) stresses tend to zero, the exact solutions go over into the corresponding exact solutions of classical linear solid mechanics, which are based on the complex representations due to Muskhelishvili, Lekhnitskii, and Galin     

Ⅲ型界面裂纹面受变载荷Pxmtn作用下的自相似解

通过复变函数论的方法,对Ⅲ型界面裂纹表面受变载荷$Px^mt^n$作用下的动态扩 展问题进行了研究. 采用自相似函数的方法可以获得解析解的一般表达式. 应用 该法可以很容易地将所讨论的问题转化为Riemann-Hilbert问题, 然后应 用Muskhelishvili方法就可以较简单地得到问题的闭合解. 利用这些解 并采用叠加原理,就可以求得任意复杂问题的解.     

Complex function projective synchronization of complex chaotic system and its applications in secure communication

To develop secure communication, the paper presents complex function projective synchronization (CFPS) of complex chaotic systems. Aimed to coupled complex chaotic system, the control law is derived to make the complex state vectors asymptotically synchronize up to a desired complex function matrix. Based on CFPS, a novel communication scheme is further designed in theory. Its main idea is chaotic masking in essence, but the transmitted signal is the derivative of the product of the information signal and chaotic signal. As the complex scaling functions are arbitrary and more unpredictable than real scaling functions, and the product and derivative operations of complex numbers are complicated, the possibility that an interceptor extracts the information from the transmitted signal is greatly reduced. The communication system can transmit analog signal and digital symbols with fast transmission and high security, especially low bit-error rate and the strong robustness to noise for digital symbols. The corresponding numerical simulations are performed to verify and illustrate the analytical results.     

DYNAMIC PROPAGATION PROBLEM ON DUGDALE MODEL OF MODE Ⅲ INTERFACE CRACK

By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.     

On the representation of three-dimensional elasticity solutions with the aid of complex valued functions

In this paper the representation of three-dimensional displacement fields in linear elasticity in terms of six complex valued functions is considered. The representation includes the complex Muskhelishvili formulation for plane strain as a special case. The completeness of the complex representation for regular solutions is shown and a relationship to the Neuber/Papkovich solutions is given.     

Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions

The impact dynamics of water drops on thin films of viscoelastic wormlike micelle solutions is experimentally studied using a high-speed digital video camera at frame rates up to 4000 frame/s. The composition and thickness of the thin film is modified to investigate the effect of fluid rheology on the evolution of crown growth, the formation of satellite droplets and the formation of the Worthington jet. The experiments are performed using a series of wormlike micelle solutions composed of a surfactant, cetyltrimethylammonium bromide (CTAB), and a salt, sodium salicylate (NaSal), in deionized water. The linear viscoelastic shear rheology of the wormlike micelle solutions is well described by a Maxwell model with a single relaxation time while the steady shear rheology is found to shear thin quite heavily. In transient homogeneous uniaxial extension, the wormlike micelle solutions demonstrate significant strain hardening. The size and velocity of the impacting drop is varied to study the relative importance of Weber, Ohnesorge, and Deborah numbers on the impact dynamics. The addition of elasticity to the thin film fluid is found to suppress the crown growth and the formation of satellite drops with the largest effects observed at small film thicknesses. A new form of the splashing threshold is postulated which accounts for the effects of viscoelasticity and collapses the satellite droplet data onto a single master curve dependent only on dimensionless film thickness and the underlying surface roughness. Additionally, a plateau is observed in the growth of the maximum height of the Worthington jet height with increasing impact velocity. It is postulated that the complex behavior of the Worthington jet growth is the result of a dissipative mechanism stemming from the scission of wormlike micelles.     

Polarigraphic measurement of liquid-phase species distributions

In this study, the optical rotatory power of sucrose-water solutions is exploited and digital, spectral image analysis is used to nonintrusively measure one-dimensional species distributions within a liquid. The measurement scheme is described and is used in experiments ranging from one-dimensional isothermal diffusion to layered double-diffusive convection.     

Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.     

Asymmetrical dynamic propagation problems on mode Ⅲ interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of serf-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.     

Analytical study of solitons to nonlinear time fractional parabolic equations

The some of the well-known nonlinear time fractional parabolic partial differential equations is studied in this paper. The fractional complex transform and the first integral method are employed to construct one-soliton solutions of these equations. The power of this manageable method is confirmed. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions.     

正交异性复合材料界面上反平面动态自相似扩展裂纹问题的解

采用复变函数论的方法，对复合材料界面上的裂纹扩展问题进行研究。并根据任意的自相似指数的断裂动力学问题，进行自相似求解，导出解析解的一般表示。应用该法可以迅速地将所论问题转化为Riemann-Hil-bert问题，并可以相当简单地得到问题的闭合解。文中分别对裂纹中心受阶跃载荷，裂纹面受到瞬时脉冲载荷作用下的界面裂纹扩展问题进行求解。得到了裂纹的位移。尖端的应力和动态应力强度因子的解析解。应用该解并通过叠加原理。就可以很容易的求得任意复杂问题的解。     

数字全息粒子图像测速技术(DHPIV)研究进展

全息粒子图像测速技术(DHPIV)是当前非常具有发展潜力的非定常三维流场测量技术,是一种具有点空间分辨力的三维空间三维速度场和时间历程的实验观测方法和技术. 本文介绍了该项技术(数字全息DH和粒子图像测速PIV)的发展背景和近20年来的研究进展,并介绍了已测得的非定常复杂流动的初步结果. 详细论述了DHPIV技术所面临的关键性问题和应用基础问题以及相应的进展:粒子空间场的重建与再现的空间分辨率问题、粒子定位或位移精度问题、信噪比和数字再现的光学与快速算法以及测量空间的扩展等问题.同时讨论了数字离轴全息等有关技术的潜力, 介绍了进一步的研究发展方向.      

基于DSP和CPLD的数字化转台伺服系统的设计与实现

介绍了一种数字化转台伺服系统的设计及其实现．在设计中使用了数字信号处理器(DSP)以及复杂可编程逻辑器件(CPLD)，有效地降低了模拟电路中噪声、漂移等固有因素的影响，使得系统具有较高的精度。实验证明了该方案的实用性和有效性。     

Analytical solutions of dynamic mode I crack under the conditions of displacement boundary

By the approaches of the theory of complex variable functions, the problems of dynamic mode I crack under the condition of displacement boundary are investigated. For this kind of dynamic crack extension problems with arbitrary index of self-similarity, the universal representations of analytical solutions are facilely deduced by the methods of self-similar functions. Analytical solutions of the stresses, displacements and stress intensity factors are readily acquired using the methods of self-similar functions. The problems studied can be very easily translated into Riemann–Hilbert problems and their closed solutions are gained rather straightforward in terms of this technique. According to corresponding material properties, the mutative rule of stress intensity factor was illustrated very well. Using those solutions and superposition theorem, the solutions of arbitrarily complex problems can be attained.     

COMPLEX FUNDAMENTAL SOLUTIONS FOR SEMI-INFINITE PLANE AND INFINITE PLANE WITH HOLE UNDER VARIOUS BOUNDARY CONDITIONS

I.IntroductionBoundaryelementmethod(BEM)hasbeenwidelyusedforlinearandnonlinearanalysisofengineeringstructures.ThetriditionalboundaryelementdiscretizationforthecouplingproblemoftbullditliollandpipeinFig.IisshowninFig.2.ConlparcdwithFEM,BEMIlasmoreadvantages.Inthispaper,thegeneralmethodoffindingthecomplexfundamentalsolutions(CFSs)I'orsemi-illfiniteplanealldintllliteplanewithholeundervariousboundaryconditions(aCs)hasbeenestablishedbyLlsillgRiemann-Schwarzsymmetricprincipleandsuperpositio…     

动态扩展裂纹的若干反平面问题的研究

采用复变函数论,对反平面条件下的动态裂纹扩展问题进行研究。通过自相似函数的方法可以获得解析解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题,并可以相当简单地得到问题的闭合解。文中分别对裂纹面受均布载荷、坐标原点受集中增加载荷、坐标原点受瞬时冲击载荷以及裂纹面受运动集中载荷Px／t作用下的动态裂纹扩展问题进行求解,得到了裂纹扩展位移、裂纹尖端的应力和动态应力强度因子的解析解。应用该解并通过叠加原理,就可以求得任意复杂问题的解。     

Travelling, non-periodic patterns in nonlinear stability problems

In this short note we present results on the existence of several classes of travelling, non-periodic solutions of the complex Ginzburg-Landau equation. First we give a very short introduction to the G-L equation and show its importance in nonlinear stability theory. We then study the G-L equation with complex coefficients and establish the existence of a 2-parameter family of quasi-periodic solutions and two different types of one-parameter families of heteroclinic orbits; all members of these families travel with a well-defined wave-speed. The heteroclinic solutions correspond to (travelling) soliton-like localized structures which connect different (stable) periodic patterns. Mathematically, these families of travelling solutions (quasi-periodic and heteroclinic) are continuations into the complex case of the stationary solutions of the real G-L equation.