Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

Wetting in Potts and Blume-Capel models

We discuss the wetting of the interface between two ordered phases by the disordered one in the Potts model withq large. We argue that a low-temperature expansion can be used in this situation, with logq replacing. This model is analogous to the Blume-Capel model at low temperatures, which we use as an example to review the low-temperature expansions.     

Computation of moisture and temperature profiles in soil—The coupled model

The coupled model has been developed in this study for moisture transport and beat exchange in soil. The model is driven by atmospheric conditions measured in a field. The concept that soil has a surface resistance to evaporation is introduced in order to relate the evaporation from surface with the vapour flux in air. With the use of this concept, the simulation results agree quite well with the measured data.     

Marked Schottky Groups and Representations of Surface Groups

We give a complete condition for any n elements of PSL(2, R)to generate a Fuchsian group which is a Schottky group on thatset of generators, and apply it to a question of Bowditch onrepresentations of surface groups into PSL(2, R). 2000 MathematicalSubject Classification: 20H10, 32G15.     

Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces

We prove that the varieties of complete pairs of zero-dimensional subschemes of lengths d ₁ 2, d ₂ 4 on a smooth irreducible projective algebraic surface are singular.     

New Examples of Willmore Surfaces in S n

A surface x: M S ⁿ is called a Willmore surface if it is a criticalsurface of the Willmore functional _M (S – 2H ²)dv, where H isthe mean curvature and S is the square of the length of the secondfundamental form. It is well known that any minimal surface is aWillmore surface. The first nonminimal example of a flat Willmoresurface in higher codimension was obtained by Ejiri. This example whichcan be viewed as a tensor product immersion of S ¹(1) and a particularsmall circle in S ²(1), and therefore is contained in S ⁵(1) gives anegative answer to a question by Weiner. In this paper we generalize theabove mentioned example by investigating Willmore surfaces in S ⁿ (1)which can be obtained as a tensor product immersion of two curves. We inparticular show that in this case too, one of the curves has to beS ¹(1), whereas the other one is contained either in S ²(1) or in S ³(1). In the first case, we explicitly determine the immersion interms of elliptic functions, thus constructing infinetely many newnonminimal flat Willmore surfaces in S ⁵. Also in the latter casewe explicitly include examples.     

Far infrared surface plasmon propagation

New experimental evidence is presented which shows that, contrary to an earlier report, far-infrared surface plasmons at metal-air interfaces propagate long distances (tens of centimeters or longer).     

近自由面细长体的振荡问题

本文引进细长体的假定,把三维的流体运动问题化成了二维的非定常问题。前面剖面对后面剖面的干扰作用用积分表示,对物体作了适当近似以后,改善了切片理论。根据物面条件把整个问题的求解分解为兴波问题和振荡问题,而振荡问题可由兴波问题的适当组合表示出来。这样,大大简化了问题的求解。作为例子,本文数值计算了细长体的水动力导数,给出了结果。     

基于机器视觉的刀具轮廓在线检测方法的研究

超精密单点金刚石车削过程中需要对刀具参数进行检测。基于机器视觉原理,采用新型的机械结构设计了新型刀具在线检测系统。通过垂直放置的两组由同轴远心镜头和CMOS相机组成的光学系统来获取车刀刀尖正面及侧面的图像,再经图像处理系统来获取刀具的轮廓及位置信息,完成对刀具轮廓及位置的在线检测,实验验证可实现测量的重复性定位精度达1μm。在线检测的方式借助了超精密车床自身的高精度和运动机构,可以保证相机焦点和机床主轴之间的相对位置关系,弥补了目前刀具检测系统稳定性差和重复性精度低的不足,提高了加工的整体效率。