A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L ^p setting.     

对探究影响摩擦力大小因素实验的分析及改进

对传统的影响滑动摩擦力大小因素的实验进行改进,把物块的运动变换成下面木板的运动,并用定滑轮改变拉力的方向.使用改进后的装置不但可以降低操作的难度,还可提高实验的准确性.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

Shock waves for the hyperbolic balance laws with discontinuous sources

In this paper, we are concerned with the behavior of shock waves in a 2 × 2 balance law with discontinuous source terms. We obtain the existence of a local shock wave solution of this problem and deduce that the discontinuous source terms create a weak discontinuity in this solution. Copyright © 2013 John Wiley & Sons, Ltd.     

A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore–Penrose inverse

In this paper, a simultaneous canonical form of a pair of rectangular complex matrices is developed. Using this new tool we give a necessary and sufficient condition to assure that the reverse order law is valid for the weighted Moore–Penrose inverse. Additionally, we characterize matrices ordered by the weighted star partial order and adjacent matrices as applications.     

计入孔隙结构影响的复层含油轴承润滑特性分析

基于Darcy定律和Kozeny-Carman孔隙方程,建立多孔质复层含油轴承的流体润滑模型,利用有限差分法数值模拟,分析复层结构和孔隙参数对含油轴承润滑性能的影响.得出结论如下:复层含油轴承润滑性能随轴承高度增大而变差,随孔隙率减小而变好,当总孔隙率一定时,较低的表层孔隙率有利于提高复层含油轴承润滑性能.因此设计复层含油轴承时,在保证一定孔隙含油量的前提下,应尽可能减小表层孔隙率.研究工作为复层含油轴承摩擦学性能分析与结构设计提供一定的理论基础.     

Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces

Uniform spreading of oil on solid surfaces is important in many processes where proper lubrication is required and this can be controlled using surfactants. The role of oil–solid interfacial self-assembled surfactant structure (SASS) in oil spreading is examined in this study for the case of hexadecane-surfactant droplet spreading on a flat horizontal copper surface, with triphenyl phosphorothionate surfactants having varying chain lengths (0 to 9). It is shown that the frictional forces (F_SASS) as determined by the SASS regulate droplet spreading rate according to surfactant chain length; surfactants with longer chains led to higher reduction in the spreading rate. The extent of such forces, F_SASS, depends on the surfactant density of the evolving SASS, and specific configuration the evolving SASS exhibit as per the orientations of the surfactant chains therein. Thus, F_SASS = [k₁ + k_2(t)] Γ_δ(t), where Γ_δ(t) is the surfactant adsorption density of SASS at time ‘t’ during evolution, and, k₁ and k_2(t) are the force coefficients for Γ_δ(t) and orientations (as a function of spreading time) of the surfactant chains respectively. As a SASS evolves/grows along with adsorption of surfactants at the spreading induced fresh interface, the k₁Γ_δ(t) component of F_SASS increases and contributes to reduction in the net spreading force (S). With a decrease in the net spreading force, the existence of a cross-over period, during which the transition of the spatial dynamics of the chains from disordered to realignment/packing induced ordered orientation occurs, has been inferred from the F_SASS vs. chain length relationships. Such relationships also suggested that the rate of realignment/packing is increased progressively particularly due the realignment/packing induced decrease in the net spreading force. Therefore, the realignment process is a self-induced process, which spans a measurable period of time (several minutes), the cross-over period, during which the net spreading force decreases essentially due to such self-induced process.     

Fly‐Ash‐Supported Synthesis of 2‐Mercaptobenzothiazole Derivatives under Microwave Irradiation

Microwave‐assisted, solvent‐free alkylation and acylation of 2‐mercaptobenzothiazole has been attempted using silica gel, alumina, and a new solid support, fly ash. Fly ash, a waste generated at thermal power stations, could be used as solid support just as efficiently as commercial supports. The additional features of methodology include a much faster reaction, easy workup, higher yields, higher purity of the products, and an ecofriendly approach.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245