A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Carathéodory's method for a class of second order differential equations on the half-line

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate boundary value problems for a class of second order differential equations on the half-line. Some applications are presented to illustrate the potential of this method.     

Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.     

Asymptotic behaviors of competitive Lotka-Volterra system with stage structure

In this paper, a two-species competitive model with stage structure is presented and studied. Results on the global extinction and permanence are given, which generalize the well-known three theorems for the two species competitive system and, moreover, they confirm the negative effect of stage structure on the permanence of populations as well as estimate the degree of such effect. Conclusions in this paper suggest that for a competitive community stage structure is also one of the important reasons that cause permanence and extinction.     

Reversible addition–fragmentation transfer (RAFT) copolymerization of methyl methacrylate and styrene in miniemulsion

In the reversible addition–fragmentation transfer (RAFT) copolymerization of two monomers, even with the simple terminal model, there are two kinds of macroradical and two kinds of polymeric RAFT agent with different R groups. Because the structure of the R group could exert a significant influence on the RAFT process, RAFT copolymerization may behave differently from RAFT homopolymerization. The RAFT copolymerization of methyl methacrylate (MMA) and styrene (St) in miniemulsion was investigated. The performance of the RAFT copolymerization of MMA/St in miniemulsion was found to be dependent on the feed monomer compositions. When St is dominant in the feed monomer composition, RAFT copolymerization is well controlled in the whole range of monomer conversion. However, when MMA is dominant, RAFT copolymerization may be, in some cases, out of control in the late stage of copolymerization, and characterized by a fast increase in the polydispersity index (PDI). The RAFT process was found to have little influence on composition evolution during copolymerization. The synthesis of the well‐defined gradient copolymers and poly[St‐b‐(St‐co‐MMA)] block copolymer by RAFT miniemulsion copolymerization was also demonstrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6248–6258, 2004     

Researches of DC—Problem Under the Model S in which the Numbers of Defective Coins are not Fixed

In this paper,we research general Defective Cion Problem under the model S,i.e,the number d of Defective cions is not fixed. For d=O,1,or 2. we get some good results.     

C^＊—模理论的若干结果

本文把代数结构与分析体系结合起来，运用同调的方法，较系统地确定了A上C^*－模的部分理论，这里A为复数域C上的交换C^*－代数。即不仅定义了与C^*－模有关的某些新概念，而且还得到了有关C^*－模的若干结果。     

同输入M/M/∞排队群的联合队长过程

本提出一个偏微分方程方法，用这一方法研究同输入M/M／∞排队群中的联合队长分布。在任意初始条件下，给出了瞬时联合队长分布的多元母函数，也讨论了稳态队长的联合分布及各排队系统之间的相关性。