Non-linear peristaltic transport of a second-order fluid through a porous medium

The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects through a porous space in a channel. The peristaltic motion of a second-order fluid through a porous medium was studied for the case of a planar channel with harmonically undulating extensible walls. The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise and frictional force. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Periodic solutions of singular second order differential equations: Upper and lower functions

In this paper, we continue the study of the periodic problem for the second-order equation u^′′+f(u)u^′+g(u)=h(t,u), where h is a Carathéodory function and f,g are continuous functions on (0,+∞) which may have singularities at zero. Both attractive and repulsive singularities are considered. The method relies on a novel technique of construction of lower and upper functions. As an application, we obtain new sufficient conditions for the existence of periodic solutions to the Rayleigh–Plesset equation.     

Effect of ionic liquid on dielectric, mechanical and dynamic mechanical properties of multi-walled carbon nanotubes/polychloroprene rubber composites

This paper focuses on the influence of ionic liquid on carbon nanotube based elastomeric composites. Multi-walled carbon nanotubes (MWCNTs) are modified using an ionic liquid at room temperature, 1-butyl 3-methyl imidazolium bis (trifluoromethylsulphonyl) imide (BMI) and modified MWCNTs exhibit physical (cation–π/π–π) interaction with BMI. The polychloroprene rubber (CR) composites are prepared using unmodified and BMI modified MWCNTs. The presence of BMI not only increases the alternating current (AC) electrical conductivity and polarisability of the composites but also improves the state of dispersion of the tubes as observed from dielectric spectroscopy and transmission electron microscopy respectively. In addition to the hydrodynamic reinforcement, the formation of improved filler–filler networks is reflected in the dynamic storage modulus (E′) for modified MWCNTs/CR composites in amplitude sweep measurement upon increasing the proportion of BMI. Hardness and mechanical properties are also studied for the composites as a function of BMI.     

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.     

一类二阶积分型发展方程反周期解问题

本文中,我们研究一类带有非单调扰动算子的二阶非线性发展方程的反周期问题,证明方程中的非单调扰动算子为极大单调的,并用极大单调算子的微单调扰动理论来证明此类方程的反周期解的存在性。     

高阶PMD统计特性研究

讨论了三阶偏振模色散(PMD)的统计特性及其对于高阶PMD补偿系统的影响.数值模拟结果表明,随着即时差分群时延(DGD)的增加,二阶PMD单位矢量旋转速率的统计覆盖范围的变化趋势与主偏振态(PSP)旋转斜率的相应变化正好相反.此外,随着即时DGD的增加,二阶PMD模值的统计覆盖范围不断增加,使得高速光通信系统中高阶PMD补偿的实现将更加困难.     

Mathematical approach for the dynamic testing technique

In dealing with phenomena which show a linear response such as viscoelastic or dielectric properties, measurements are carried out by observing the relationship between the stimulus applied to the sample and the response from the sample. Since the Fourier analysis technique is effective in obtaining this relationship, two types of circuitries based on Fourier analysis have been created. Both DMA and dielectric measurement were used to evaluate these circuitries. Results were satisfactory, especially with respect to tanδ precision.

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Zusammenfassung Bei der Arbeit mit Erscheinungen, die wie z.B. viskoelastische oder dielektrische Eigenschaften eine lineare Reaktion zeigen, wurden Messungen durch Beobachtung der Beziehung zwischen der auf die Probe angewendeten Aktion und der von der Probe gezeigten Reaktion durchgeführt. Da die Fourier-Analyse eine effektive Technik zur Ermittlung dieser Beziehung ist, wurden auf der Grundlage der Fourier-Analyse zwei Typen von Schemen geschaffen. Sowohl DMA als auch dielektrische Messungen wurden zur Entwicklung dieser Schemen verwendet. Did Resultate waren zufriedenstellend, insbesondere mit Hinblick auf die Genauigkeit von tanδ.

     

Oscillation and non-oscillation for second-order linear difference equations

We prove new oscillation and non-oscillation theorems for the second-order linear difference equation Δ²x_n−1 + p_nx_n = 0, where is a real sequence with p_n 0. These results are extensions of earlier results of Zhang and Zhou [Comput. Math. Appl. 39 (2000) 1–7].     

Thermal Analysis of Ionizing Radiation Effects on Recycled Polyamide-6

The aim of this work is to study the ionizing radiation effects on thermal properties of there cycled polyamide-6. This polymer was irradiated with an electron beam of 1.5 MeV with different doses. The thermal properties of the samples were determined by TG, DSC and DMA measurements. It was observed that the irradiated samples of recycled polyamide-6undergo a crosslinking process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectral multiplicity of some stochastic processes

In this paper we consider the connection between the canonical and the weak-canonical representations for the given second-order stochastic process in a separable Hilbert space and we extend a well-known theorem of H. Cramer concerning sufficient conditions for a process to be of multiplicity one.