Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Wormhole solution in Bergmann-Wagoner scalar-tensor gravitational theory

We give a Euclidean wormhole solution in the vacuum Bergmann-Wagoner scalar-tensor gravitational theory. We show that this wormhole, unlike others, has complex charge and is a baby universe (half a wormhole).     

Chemistry of O-Benzoquinones and Masked O-Benzoquinones I. Diels-Alder Reactions of O-Benzoquinones with Dimethyl Acetylenedicarboxylate and Phenylacetylene

Diels-Alder reactions of six o-benzoquinones with dimethyl acetylenedicarboxylate has been examined. The yields of adducts vary with the natures of the o-benzoquinones, 3,4-Di-n-propyl-(1c), 3,6-di-n-propyl (1d). 3. 4-diallyl-(1e) and 3, 6-diallyl-o-benzoquinone (1f) are found to give bicyclic a-diketones exclusively without the formation of 1,4-dioxine derivatives, the yields ranging from 20 to 70%. In the case of 4, 5-dimethoxy-o-benzoquinone, dimethyl 4, 5-dimethoxyphthalate is produced in 42% yield, presumably derived from the decomposition of the corresponding initially formed α-diketone. 3, 6-Di-n-propyl-4, 5-dimethoxy-o-benzoquinone deteriorates without addition to dimethyl acetylenedicarboxylate upon heating. The additions of o-benzoquinones 1c , 1d and 1f to phenylacetylene are also studied. The yields of adducts, α-diketones, range from 23% to 82%.     

聚丙烯与SBS嵌段共聚物共混时的结晶行为

用偏光显微镜,小角光散射,动态力学测量和DSC等方法研究了聚丙烯和SBS共混物的结晶行为。结果表明,SBS的混入可以降低聚丙烯的结晶程度和阻碍球晶的形成,因而有利于提高聚丙烯塑料的抗冲击性能。从DSC实验也看到共混物中的聚丙烯具有较高的结晶速率。     

Theory of solid solubility for rare earth metal based alloys

Both parabola and ellipse separating schemes are used to study the solid solubilities for the binary alloy systems based on the 13 rare earth metals. It has been found that the soluble elements can be separated from the insoluble ones by a parabolyy ₁=a?bx ₁ ² or an ellipse(x ₂?m)²/c²+(y₂?n)²/d²=1. The results show that the overall reliabilities of the solid solubilities for the 897 binary alloys based on the rare earth metals are 89.2% and 92.8% for the parabola and ellipse regularities respectively. The constants a and b in the parabola equation, andm, n, c andd in the ellipse equation are discussed, which can be related to some appropriate parameters for each host metal respectively.     

CHAOS FOR MIXING TRANSFORMATIONS

ＣＨＡＯＳＦＯＲＭＩＸＩＮＧＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳ￥ＬＩＡＯＧＯＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈａｎｇｃｈｕｎ１３００２３,Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｆｏｒａｃｌａｓｓｏｆｍ...     

Mechanism transition of self-pumped phase conjugation in KTa1 −xNbxO3:Fe crystals

Mechanism transitions of Self-Pumped Phase Conjugation (SPPC) with wavelength and doping concentration are observed in KTN:Fe (KTa_{1 –x} Nb _x O₃:Fe with _x = 0.48) crystals. The SPPC mechanism in KTN: Fe (0.4 wt. %) crystal transforms from Stimulated Photorefractive Backscattering and Four-Wave Mixing (SPB-FWM) to cat (or total internal reflection) as the wavelength increases from 514.5 nm to 620 nm. SPPC at 514.5 nm is formed with the cat mechanism in a 0.2 wt. % doped KTN:Fe crystal, while with the SPB-FWM mechanism in a 0.4 wt. % doped one. These mechanism transitions are discussed with respect to the dependence of the backscattering gain coefficient of the crystals on wavelength and doping concentration.     

Stochastic flows on the boundaries of SL(n,R)

Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS ⁿ–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS ⁿ–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China     

Chemistry of O-Benzoquinones and Masked O-Benzoquinones IV. Synthesis of O-Spirodienonelactones from Unsymmetric Catechols

We describe the syntheses of 6, 8-di-tert-butyl-, 7, 9-di-tert-butyl., 6,7-di-n-propyl and 8, 9-di-n-propyl-O-spirodienonelactone from 3, 5-di-tert-butylcatechol and 3, 4-di-n-propylcatechol.