Surfaces of Constant Mean Curvature Bounded by Two Planar Curves

In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.     

Au-Au2S复合纳米球壳微粒的空腔谐振及参量讨论

Au-Au2S复合纳米球壳微粒（金纳米球壳），是一种新型复合结构的纳米微粒，其结构为纳米级的Au2S介质球外包裹了一层几个纳米厚的黄金球壳。这种复合纳米球壳微粒可以被抽象为球型谐振腔。报道了它的空腔谐振吸收的实验结果，并且运用经典理论结合介观结构特征，讨论了有关Au-Au2S复合纳米球壳微粒空腔谐振吸收的一些重要参量，其中包括谐振吸收波长、品质因数、谐振能量等。另外，还讨论了金球壳的厚度对这些重要参量的影响。     

The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

R~(n+1)中常高阶平均曲率超曲面

本文给出了Rn+1中超曲面的一些积分公式,并利用这些积分公式得到了以球面为边界的常高阶平均曲率超曲面的一些唯一性结果.     

Letter: Differential Invariants of the Kerr Vacuum

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.     

关于凸曲面的几个定义的关系

本文讨论了凸曲面的几种定义及其关系，发现有的定义是局部凸的定义，有的是整体凸的定义，有的则对于局部凸和整体凸都适合，最后给出了各种定义之间互推的证明，对于局部凸和整体凸定义之间不能推证的，则说明了原因．     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Forces along Equidistant Particle Paths

Two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force acting between the particles. On the other hand, if particles travel at the same speed (initially parallel) along geodesics in the hyperbolic plane, then the particle paths diverge. Imagine two particles in the hyperbolic plane that are bound together at a constant distance with their center of mass traveling along a geodesic path at a constant velocity, then the force due to the curvature of the space acts to break the bond and increases as a quadratic function of the velocity. We consider this problem for the sphere and the hyperbolic plane and we give the exact formula for the apparent force between the particles. This revised version was published online in July 2006 with corrections to the Cover Date.