Error analysis for finite element methods for steady natural convection problems

We analyze the error in finite element methods in approximating, so-called, free or natural convection problems. We also include the effects of conducting solid walls in our analysis. Under a uniqueness condition on the Rayleigh and Prandtl numbers (which we derive), we give direct, quasioptimal error estimates for “div-stable” finite element spaces for the fluid variables and general conforming finite element spaces for the temperature. At larger Rayleigh numbers, we give analogous, asymptotic error estimates, basing this analysis upon local uniqueness properties of the true solution (u p T), which we also establish.     

三维有限差分波束传输法:用于Ti∶ LiNbO_3方向耦合器的模拟

提出求解三维傍轴近似波动方程的交替方向隐式差分格式，并用它模拟Ｔｉ∶ＬｉＮｂＯ３方向耦合器     

Young measure solutions of some nonlinear mixed‐type equations

This contribution deals with measure‐valued solutions to two types of nonlinear partial differential equations for which, in general, the results on the existence of classical or weak solutions fail. These are the potential equation for transonic flow and the associated unsteady problem (forward–backward diffusion equation). The solutions are constructed by an iteration scheme (Katchanov method) and additional time discretization (Rothe method) in the second case. The existence is proved in the sense of spatial gradient Young measures. Copyright © 2010 John Wiley & Sons, Ltd.     

Spin fluctuation effects in substituted CeRu2Si2 and YbPd2Si2 alloys

Effects of chemical substitution in CeRu₂Si₂, a well-studied heavy fermion system and YbPd₂Si₂ have been investigated through magnetic susceptibility and x-ray diffraction in the systems CeRu _x Si₂, CeRu_2−x Os _x Si₂, CeRu₂Si_2−x Ge _x and YbPd₂Si_2−x Ge _x . Replacing silicon by germanium generates normal chemical pressure effect, namely, Ce and Yb atoms in CeRu₂Si₂ and YbPd₂Si₂ became more and less magnetic respectively. With increasing Ge concentration, CeRu₂Si_2−x Ge _x exhibits larger susceptibility at low temperature, goes to an antiferromagnetic state and finally becomes ferromagnetic. In YbPd₂Si_2−x Ge _x , increasing Ge concentration drives Yb atoms to more divalent state. Electronic effects are more pronounced in CeRu_2−x Os _x Si₂ though CeRu₂Si₂ and CeOs₂Si₂ have very nearly the same lattice parameters. It is conjectured that CeRu₂Si_2−x Ge _x may be the first Ce-based heavy fermion having a magnetic ground state. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

On enumeration of polynomial equivalence classes

The isomorphism of polynomials(IP),one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials.Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate public key cryptosystem.In this paper we show the enumeration of the equivalence classes containing ∑n-1 i=0 aiX2qi when char(Fq) = 2,which implies that these polynomials are all weak IP instances.Moreover,we study the cardinality of an equivalence class containing the binomial aX 2q i + bX 2qj(i=j) over Fqn without the restriction that char(Fq) = 2,which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.     

Adaptive control of nonlinear complex Holling II predator–prey system with unknown parameters

In recent years, control of nonlinear complex predator–prey systems has attracted the attention of many researchers. The previous works have some weaknesses such as neglecting the consideration of the effects of both model uncertainties and unknown parameters and having an infinite time of convergence. To overcome the mentioned shortages, this article solves the problem of robust control of nonlinear complex Holling type II predator–prey system in a given finite time. It is assumed that the parameters of the system are fully unknown in advance and some uncertainties perturb the system's dynamics. To tackle the system unknown parameters, some adaptation laws are introduced. Thereafter, a robust switching controller is proposed to finite‐timely stabilize the predator–prey system. An illustrative example demonstrates the efficiency and usefulness of the proposed control strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 260–266, 2016     

对流扩散方程一类改进的特征线修正有限元方法

１引言在地下水污染,地下渗流驱动,核污染,半导体等问题的数值模拟中,均涉及抛物型对流扩散方程（或方程组）的数值求解问题．这些对流扩散型偏微分方程（或方程组）具有共同的特点：对流的影响远大于扩散的影响,即对流占优性,对流占优性给问题的数值求解带来许多困难,因此对流占优问题的有效数值解法一直是计算数学中重要的研究内容．用通常的差分法或有限元法进行数值求解将出现数值振荡．为了克服数值振荡,提出各种迎风方法和修正的特征方法并在这些问题上得到成功的实际应用、８０年代,Ｄｏｕｇｌａｓ和Ｒｕｓｓｅｌｌ［２］等…     

关于“Bubble-隐定化有限元方法”的两点注记

本文针对Ｓｔｏｋｅｓ－问题给出了［１２］发展的基于局部ｂｕｂｂｌｅ－函数稳定化有限元法与Ｇａｌｓ－稳定化有限元法,ｂｕｂｂｌｅ函数扩充元法的等价关系     

Effects of Nb and Si on densities of valence electrons in bulk and defects of Fe3Al alloys

Positron lifetime measurements have been performed in binary Fe₃Al and Fe₃Al doping with Nb or Si alloys. The densities of valence electrons of the bulk and microdefects in all tested samples have been calculated by using the positron lifetime parameters. Density of valence electron is low in the bulk of Fe₃Al alloy. It indicates that, the 3d electrons in a Fe atom have strong-localized properties and tend to form covalent bonds with Al atoms, and the bonding nature in Fe₃Al is a mixture of metallic and covalent bonds. The density of valence electron is very low in the defects of Fe₃Al grain boundary, which makes the bonding cohesion in grain boundary quite weak. The addition of Si to Fe₃Al gives rise to the decrease of the densities of valence electrons in the bulk and the grain boundary thus the metallic bonding cohesion. This makes the alloy more brittle. The addition of Nb to Fe₃Al results in the decrease of the ordering energy of the alloy and increases the density of valence electron and the bonding cohesion of the grain boundary. However, since the radius of Nb atom is larger than that of Fe atom, when Nb atoms substitute for Fe atoms, they will distort the lattice and enlarge the volume of the lattice, which decreases the density of valence electron and the cohesion of metallic bond in the bulk of the alloy. Project supported by the National Natural Science Foundation of China (Grant No. 59561001) and the Foundation of Guangxi Education Committee.