Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation

Abstract  Let Ω be the unit ball centered at the origin in . We study the following problem

Size Effects of the Critical Temperature in Ferroelectric Thin Films

The size effects of the critical behaviors for the systems of interacting spins are discussed extensively in literature. In this paper, the finite-size dependence of the critical temperature and susceptibility of the ferroelectric thin film are investigated numerically based on the four-state Potts model with the nearest-neighbor interactions between the dipole moments. The four orientations of the domains exist in the ferroelectric film and the movement of the domain walls determines the polarization switching process besides the boundary conditions of the film. The critical exponents are obtained and our investigations show that the boundary conditions play the important roles for the ferroelectric properties of the thin films and the critical behavior of the thin films strongly depends on the feature of the surface.     

Dihydrogen bond in C2H4− n Cl n ··· NaH (n = 0, 1, 2, 3) complexes: ab initio,AIM and NBO studies

The dihydrogen-bonded complexes of ethylene and its chlorine derivatives with sodium hydride have been systematically investigated at the MP2/6-311++G(d,p) level. The studied complexes are divided into three groups (including Linear, Five- and Six-membered cyclic structures) based on the optimized structures. The structural, energetic and topological parameters are presented and analysed in terms of their possible correlation with the interaction energies and the intermolecular H?···?H distances. The nature of the electrostatic interaction in this type of dihydrogen bond has also been unveiled by means of atoms in molecules (AIM) and natural bond orbital (NBO) analysis. The effect of ring structure on the dihydrogen bonding systems has been considered by comparing with the corresponding linear structure. NBO analysis suggests that the electron density transfer (EDT) in cyclic structures have dual-channel character.     

表面能与晶体生长/溶解动力学研究的新动向

界面现象使物质在结晶过程中出现了临界现象.但最近的研究指出在物质溶解过程中,在表面能量的控制下也存在着临界现象以及尺寸效应.实验发现,当晶体自身小到一 定的程度时(通常在纳米尺度上并和临界蚀坑的大小相近),在溶解过程中其速度会自发降 低,反应被抑制乃至停止.尽管在热力学上表面能的因素可以赋予小颗粒晶体较大的溶解度 ,但表面能却也能通过对临界条件的控制而使这些微粒在动力学上不被溶解.这个发现不仅 解决了纳米颗粒在水溶液中稳定性的问题,而且还从动力学的角度解释了生物矿物选择纳米 尺度作为其基本构成单元的原因.由于表面能和晶体生长/溶解的动力学有着密切的关系, 我们可以通过对表面能的调节来修改它们的动力学速度和晶体的形貌.反过来,也可以用动力学的方法来测定表面能及表面吸附/脱附常数等.相对于常规的界面研究手段,通过生 长和溶解动力学途径所得的数据有着很好的可靠性及重复性.我们认为,晶体生长和溶解的 动力学和表面能的研究相结合,不仅为界面研究提供了新的思路和方法,而且也会推动晶体生长和材料科学的发展.     

球上一类含临界增长p-Laplace方程的渐近性(英文)

1 IntroductionIn this paper we study the blow--up of positive solutions as A - 0+ fOr thefOllowing boundary value problem of the weighted pLaplacian on the unit ballcenter at the origin B = B1(0) C Rn:where cr5 u > fi --p > --n and p* = p(n + a)/(fi +n --p) is the critical exponentof the embedding Wl"(fl, lxtpdx) - Lp*(fl, lxl"dx) (see, for example, [6]).When u is radially symmetric, y(r) = u(x), fOr r = lxl, satisfieswhere the new exponents cr, g, p and p* satisfyThe existence and non-exi…     

Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form. As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 98–105, September 2006.     

神华煤液化油窄馏分的临界性质

引入Aspen Plus软件,用COAL LIQ模块计算得到神华煤液化油300℃以前8个窄馏分的临界温度、临界压力、临界体积。同时利用MXXC基团贡献法,以GC MS数据为基准对8个馏分的临界性质进行验证计算。结果表明,计算结果与利用化学结构法测定的基本一致。随馏出温度的提高,馏分临界温度逐渐升高,临界压力先升高再降低,临界体积先减小后增大,转折点出现在180℃~200℃馏分段。通过对化合物的结构分析表明,馏分中大量极性化合物的富集是造成计算数据点转折及跳跃的原因。为验证两种计算方法的一致性,引入斯米尔切诺夫统计检验法进行分析。结果表明,两种方法计算结果的总体分布函数在95%的置信区间内一致,表明对于计算临界性质,Aspen Plus计算方法可以代替基团贡献法估算法。此外,Aspen软件计算简便,其结果可为煤液化反应器的放大及过程优化直接引用。     

Existence and multiplicity results for infinitely many solutions for Kirchhoff‐type problems in

In this paper, we deal with existence and multiplicity of solutions of Kirchhoff‐type problems Under more relaxed assumptions on f, we establish some existence criteria to guarantee that the preceding problem has at least one or infinitely many nontrivial solutions by using the genus properties in critical point theory. Copyright © 2013 John Wiley & Sons, Ltd.     

采用正方元胞的Ising模型实空间重正化群解

在二维正方形晶格上,将元胞取为4格点正方形,采用3种不同的规则定义块自旋状态,进行了重正化群计算,得出了更为精确的结果;解决了元胞内格点数为偶数的重正化群计算问题.     

Completely mixed state is a critical point for three-qubit entanglement

Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown that if the reduced density operator of a some qubit is a multiple of the unit operator, than the geometric entanglement measure of the pure three-qubit state is absolutely independent of the polynomial invariants and is a constant for such tripartite states. Hence a one-particle completely mixed state is a critical point for the geometric measure of entanglement.