A Cartesian grid method for two‐phase gel dynamics on an irregular domain

We develop a numerical method for simulating models of two‐phase gel dynamics in an irregular domain using a regular Cartesian grid. The models consist of transport equations for the volume fractions of the two phases, polymer network and solvent; coupled momentum equations for the two phases; and a volume‐averaged incompressibility constraint. Multigrid with Vanka‐type box relaxation scheme is used as a preconditioner for the Krylov subspace solver (GMRES) to solve the momentum and incompressibility equations. Ghost points are used to enforce no‐slip boundary conditions for the velocity field of each phase, and no‐flux boundary conditions for the volume fractions. The behavior of the new method, including its rate of convergence, is explored through numerical experiments for a problem in which strong phase separation develops from an initially (almost) homogeneous phase distribution. We also use the method to explore situations, motivated by biology, which show that imposed boundary velocities can cause substantial redistribution of network and solvent. Copyright © 2010 John Wiley & Sons, Ltd.     

A characterization of generator for multiresolution analysis with composite dilations

In this paper, we will introduce multiresolution analysis with composite dilations and give a characterization of generator for multiresolution analysis with composite dilations.     

基于纳米晶晶格热胀冷缩的高灵敏度荧光纳米温度计

有效测量纳微米尺度范围温度及物体表面温度梯度分布需要研发各种类型的纳米尺度温度计来实现.半导体纳米晶由于具有尺寸效应引起光致发光(荧光)效应,其具有的热胀冷缩的性质会使得温度变化引起纳米晶晶格收缩或膨胀,从而引起荧光光谱的变化,进而为设计制备高灵敏度温度计奠定基础.结合前期相关工作,本文总结了基于纳米晶的各种荧光纳米温度计,阐述不同类型纳米温度计的特性,为这一前沿领域研究提供启发.     

Joint Similarities and Parameterizations for Dilations of Dual g -frame Pairs in Hilbert Spaces

In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.     

Subdivision Schemes and Irregular Grids

The present paper deals with subdivision schemes associated with irregular grids. We first give a sufficient condition concerning the difference scheme to obtain convergence. This condition generalizes a necessary and sufficient condition for convergence known in the case of uniform and stationary schemes associated with a regular grid. Through this sufficient condition, convergence of a given subdivision scheme can be proved by comparison with another scheme. Indeed, when two schemes are equivalent in some sense, and when one satisfies the sufficient condition for convergence, the other also satisfies it and it therefore converges too. We also study the smoothness of the limit functions produced by a scheme which satisfies the sufficient condition. Finally, the results are applied to the study of Lagrange interpolating subdivision schemes of any degree, with respect to particular irregular grids.     

LIR序关系的一些封闭性质

证明了Location Independent Riskier Order随机序关系关于简单随机样本的极小值与可微递增凹变换的封闭性质，并讨论了Dilation序关系的一些矩不等式．     

Uniformly convergent finite difference methods for singularly perturbed problems with turning points

In this work one-dimensional singular perturbation problems with turning points are considered. To resolve these problems numerically we consider a family of finite difference schemes, which includes classical methods in literature, such as the upwind method, the Samarskii method and exponential fitting type methods. Once the uniform convergence of the upwind method on irregular meshes has been established, the same property is easily shown on all the elements of the family.Work supported by a grant of the Diputación General de Aragón.     

Corners of normal matrices

We study various conditions on matricesB andC under which they can be the off-diagonal blocks of a partitioned normal matrix. To Kalyan Sinha on his sixtieth birthday