A least‐square weighted residual method for level set formulation

In this paper, a least‐square weighted residual method (LSWRM) for level set (LS) formulation is introduced to achieve interface capturing in two‐dimensional (2D) and three‐dimensional (3D) problems. An LSWRM was adopted for two semi‐discretized advection and reinitialization equations of the LS formulation. The present LSWRM provided good mathematical properties such as natural numerical diffusion and the symmetry of the resulting algebraic systems for the advection and reinitialization equations. The proposed method was validated by solving some 2D and 3D benchmark problems such as those involving a rotating slotted disk, the rotation of a slotted sphere, and a time‐reversed single‐vortex flow and a deformation problem of a spherical fluid. The numerical results were compared with those obtained from essentially non‐oscillatory type formulations and particle LS methods. Further, the proposed LSWRM for the LS formulation was coupled with a splitting finite element method code to solve the incompressible Navier–Stokes equations, and then, the collapse of a 3D broken dam flow was well simulated; in the simulation, the entrapping of air and the splashing of the surge front of water were reproduced. The mass conservation of the present method was found to be satisfactory during the entire simulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Brownian motion on a manifold

The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due to a physical agency that forces the motion to remain on a manifold, or they represent conserved quantities of the equation of motion themselves. Also the Brownian motion is described either by a Smoluchowski diffusion equation or by a Kramers equation. The four cases lead to the following conclusions, (i) Smoluchowski diffusion with a conserved quantity reduces to a diffusion equation on the manifold; (ii) The same is true for diffusion with a physical constraint in three dimensions, but in more dimensions it may happen thatno autonomous equation on the manifold results; (iii) A Kramers equation with a conserved quantity reduces to an equation on the manifold, but in general not of the form of a Kramers equation; (iv) The Kramers equation with a physical constraint reduces to an autonomous Kramers equation on the manifold only for a special shape of that constraint. Throughout, only a certain type of physical constraints has been envisaged, and global questions are ignored. Finally, the customary heuristic construction of a Fokker-Planck equation for a mechanical system on a manifold is demonstrated for the case of Brownian rotation of a rigid body, and its shortcomings are emphasized.     

Diamine的光、电性质及其在有机薄膜电致发光器件中的应用

合成了芳香族二胺类衍生物(diamine),测定了它的光、电性质.制备了diamine作为空穴传输层的二层结构有机薄膜电致发光器件,使器件的发光亮度相对单层器件有了很大的提高.并用不同区域掺杂的方法,探讨了电致发光机理.分析、讨论了激子的形成和复合区域,较好地解释了单、双层器件的不同的电流电压关系和不同的亮度电压关系.从激子的扩散方程出发,对双层掺杂器件的发光强度比数据进行了拟合,确证了激子的扩散模式.     

一类具退化强制的椭圆方程在加权Sobolev空间中重整化解的存在性

运用截断方法研究了一类椭圆方程在加权Sobolev空间中解的存在性.主要采用Marcinkiewicz估计,在得到逼近解序列的截断函数先验估计的基础上,通过选取适当的检验函数,对逼近解序列做合适的估计,以此证明重整化解的存在性.     

黄铜选择性溶解固相扩散机理的研究

采用恒电位暂态和旋转盘环电极等方法研究了α、α＋β以及β黄铜在硫酸钠、硫酸以及氯化钠的稀溶液中的阳极溶解过程．结果表明，在黄铜阳极溶解的初始阶段测得的ｉ－ｔ曲线遵循抛物线定律，求得ｉ－ｔ为一通过坐标原点的直线，证明了黄铜中锌的选择性溶解受固相扩散控制，计算出在上述溶液中黄铜中锌的扩散系数值在１０－１５～１０－１３ｃｍ２·ｓ－１数量级，介质成分和微量合金元素砷对扩散系数值有明显的影响．     

Echo planar imaging of perfluorocarbons

Emulsions of perfluorotributylamine (FTBA) and perflubron were evaluated for their utility in ¹⁹F echo planar imaging. Fluorine images of the emulsions were obtained in a phantom and two mice that had been predosed. Both agents, but particularly perflubron, show potential for fluorine echo planar studies because of the long spin-spin relaxation times of the CF₃ resonances. High resolution thin slice images obtained in as little as 26.6 ms are presented.