Adaptive Runge–Kutta discontinuous Galerkin method for complex geometry problems on Cartesian grid

A Cartesian grid method using immersed boundary technique to simulate the impact of body in fluid has become an important research topic in computational fluid dynamics because of its simplification, automation of grid generation, and accuracy of results. In the frame of Cartesian grid, one often uses finite volume method with second order accuracy or finite difference method. In this paper, an h‐adaptive Runge–Kutta discontinuous Galerkin (RKDG) method on Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is developed. A ghost cell immersed boundary treatment with the modification of normal velocity is presented. The method is validated versus well documented test problems involving both steady and unsteady compressible flows through complex bodies over a wide range of Mach numbers. The numerical results show that the present boundary treatment to some extent reduces the error of entropy and demonstrate the efficiency, robustness, and versatility of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Greatest Descent Algorithms in Unconstrained Optimization

We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage requirements for the full Hessian matrix in problems with a large number of variables. The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research as well as the referees for helpful comments.     

Improved microhardness and microtribological properties of bismaleimide nanocomposites obtained by enhancing interfacial interaction through carbon nanotube functionalization

Through the functionalization of multiwalled carbon nanotubes (MWCNTs) by 0,0′‐diallylbisphenol A (DBA), the interface situation between MWCNTs and bismaleimide (BMI) was improved, as detected by scanning electron microscope (SEM) and dynamic mechanical analysis (DMA). The improved interface situation was considered to be the main reason for the huge increased microhardness value and greatly improved the microtribological property of MWCNTs/BMI composites. Besides, the wear mechanism for the composite was also believed to be related to the interfacial situation. The rough wavelike worn surface of pure BMI resin is attributed to its poor load capacity. The smoother waterfall‐shape worn surface of MWCNTs/BMI is related to the interface formed by the addition of MWCNTs while the ultrasmooth worn surface of DBA modified MWCNTs/BMI is due to the greatly improved interfacial interaction of the composite. Copyright © 2008 John Wiley & Sons, Ltd.     

Organic/inorganic hybrid nanospheres coated with palladium/P4VP shells from surface‐initiated atom transfer radical polymerization

Crosslinked poly(4‐vinylbenzyl chloride) (PVBC) nanospheres of about 160 nm were first synthesized by emulsion copolymerization of 4‐vinylbenzyl chloride (VBC) in the presence of a crosslinking agent, p‐divinylbenzene. Subsequent modification of the nanosphere surfaces via surface‐initiated atom transfer radical polymerization of 4‐vinylpyridine, using the VBC units of PVBC on the nanosphere surface as the macroinitiators, produced a well‐defined and covalently tethered poly(4‐vinylpyridine) (P4VP) shells of 24–27 nm in thickness. Activation of the P4VP shells in a PdCl₂ solution, followed by reactions with CO or H₂S gas, gave rise to the corresponding P4VP composite shells containing densely dispersed palladium metal or palladium sulfide nanoparticles. The chemical composition of the nanosphere surfaces at various stages of surface modification was characterized by X‐ray photoelectron spectroscopy. Field emission scanning electron microscopy and transmission electron microscopy were used to characterize the morphology of the organic/inorganic hybrid nanospheres coated with palladium/P4VP shells. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2119–2131, 2008     

Influence of permutizers of subgroups on the structure of finite groups

A group G is said to satisfy the maximal permutizer condition if the permutizer of any maximal subgroup M of G in G, P_G(M), is G. In this paper, we characterize the supersolubility of finite groups by using the maximal permutizer condition. We also get some results for when both G/N and N are supersoluble, which implies that G is supersoluble. Our results unify or generalize some known results.     

Used digital speckle correlation method to realize orientation function of optical mouse

Used digital speckle correlation method (DSCM) to realize orientation function of optical mouse is researched. The experiment is designed to obtain the dynamic speckle patterns which are shot by CCD, then the DSCM is used to process the sequential images and also the experiment is simulated. The experimental results show the DSCM can confirm orientation function of the optical mouse, and have a good agreement with the simulation results, and the resolution we obtained is higher than the resolution of mouse on the market.     

Chaos control in an investment model with straight-line stabilization method

With China's entry into the WTO, this article sets up a dynamic model describing a situation in which both foreign enterprises and Chinese financial institutions are investing in Chinese state-owned enterprises while the state-owned assets withdraw gradually. This model may contribute to the control of the chaotic phenomenon. We can apply the straight-line stabilization method to chaos control successfully through controlling parameter perturbation.     

Fabrication of uniform porous alumina materials by radio frequency (RF) magnetron sputtering

Fabrication of porous materials with uniform pore size distribution remains a challenge. In this paper, a kind of uniform porous alumina material was fabricated on a template of polystyrene microspheres by radio frequency (RF) magnetron sputtering. Surface of samples was observed by scanning electron microscopy (SEM), and the phase of porous materials was confirmed by X-ray diffraction (XRD). The pore size distribution of samples was tested by mercury intrusion method.     

Cage strain in nitro-substituted 1,3,5,7-tetraazacubanes

Homodesmotic reactions were designed for the computation of strain energies (SE) for four nitro-substituted 1,3,5,7-tetraazacubane derivatives. Total energies of the optimized geometric structures at the DFT-B3LYP/6-31G* and DFT-B3LYP/6-311G** levels were used to derive the SE. The variation of SE with respect to the number of substituents is similar with both basis sets. The SE value is 237.32 kcal/mol at the B3LYP/6-311G** level for 2,4,6,8-tetranitro-1,3,5,7-tetraazacubane, which is unexpectedly much larger than that of its cubane analogue. The SE increases remarkably with more nitro groups being attached to the cage skeleton of tetraazacubane. The ‘bending’ of the bonds within the cubic skeleton attributes to the increase of strains as the attached number of nitro groups increases.     

一类三阶非线性伪抛物方程的初边值问题

非线性伪抛物方程由于其来源于一些重要的物理过程而成为研究热点.对于一类三阶非线性伪抛物方程的初边值问题,给出了Hilbert空间中相应的强制不等式,利用同胚理论及推广的反函数定理,得到了非线性方程初边值问题解的大范围存在定理.对于相应的半线性方程给出了初边值问题解的大范围存在性、唯一性定理.