The linear-viscoelastic behaviour of a dispersion of transversely rigid spherical capsules

A rheological model has been derived for the linear-viscoelastic behaviour of a dispersion of transversely rigid spherical capsules. The model incorporates finite thickness of the elastic shell of the capsules, anisotropy of the mechanical properties of the interface and finite volume fraction. The dynamic viscosity of the dispersion is calculated. The influence of the microstructural parameters is considered and the results are compared with those of other models. The model shows that finite thickness of the shell can strongly influence the relaxation times.     

Ergodicity of minimal sets in scalar parabolic equations

Skew product semiflowΠ _t :X ×Y → X × Y generated by $$\left\{ \begin{gathered} u_t = u_{xx} + f(y \cdot t,x,u,u_x ), t > 0 x \in (0,1), y \in Y, \hfill \\ D or N boundary conditions \hfill \\ \end{gathered} \right.$$ is considered, whereX is an appropriate subspace ofH ²(0, 1), (Y, ?) is a compact minimal flow. By analyzing the zero crossing number for certain invariant manifolds and the linearized spectrum, it is shown that a minimal setE?X × Y ofΠ, is uniquely ergodic if and only if (Y, ?) is uniquely ergodic andμ(Y ₀)=1, whereμ is the unique ergodic measure of (Y, ?),Y ₀={ity∈Y} Card(E∩P ^?1(y))=1},P:X × Y → Y is the natural projection (it was proved in an authors' earlier paper thatY ₀ is a residual subset ofY). Moreover, if (E, ?) is uniquely ergodic, then it is topologically conjugated to a subflow ofR ¹ ×Y. A consequence of the last result is the following: in the case that (Y, ?) is almost periodic,Π, is expected to have many purely almost automorphic motions which are not ergodic.     

Social-support moderated stress: a nonlinear dynamical model and the stress-buffering hypothesis

Health psychology has studied the cross-sectional, stationary relationships linking stress, social support, and health. Levels of stress-related illness are generally modeled by including a nonlinear multiplicative or 'buffering' effect, corresponding to the interaction of stressor levels with social support from family and friends. The motivation of the present research is to extend an iterative, dynamic model of this well-investigated psychological process using a dynamical systems model expressed as a set of continuous, nonlinear differential equations similar to those of the 'Oregonator,' a model of a nonlinear dynamic chemical system. This model of the behavior of an individual is amenable to numerical investigation of its stationary-state stability properties, temporal evolution, and cause-effect relationships. The continuous variables in this new approach refer to varying states of an individual; they are Perceived stress (X), Symptoms (Y), and Social support (Z). It is expected that poor health in this model, represented by Symptoms (Y), is directly related to Perceived stress, as well as being tied in more complicated ways to Social support. A number of such models may be envisioned, some including a multiplicative, 'buffering' (- X x Z) effect of social support dependent on stress levels. We explore the behavior of this model over ranges of parameter values and initial conditions and relate these results to how an individual reacts to environmental challenges at various levels of stressors and social-support recruitment. Data generated by the model are in turn analyzed with a traditional cross-sectional statistical technique. Similarities and differences between chemical and psychological systems are discussed.     

碳纤维的长度与取向对聚醚醚酮基复合材料摩擦磨损性能的影响

为了制备性能优异的聚醚醚酮(PEEK)基自润滑耐磨材料，本文作者通过挤出、注塑成型制备了碳纤维(CF)填充PEEK/聚四氟乙烯(PTFE)复合材料，研究了CF的含量、长度及其在复合材料中的取向对复合材料摩擦磨损性能的影响，采用扫描电子显微镜观察了磨痕的微观形貌，并分析了磨损机理. 研究结果表明:复合材料的平均摩擦系数和体积磨损率随CF添加量的增大均呈现先降低后升高的趋势. 当添加的CF质量分数大于10%时，长CF所填充复合材料的平均摩擦系数明显低于短CF填充复合材料. 当固定CF质量分数为10%时，复合材料在不同CF取向方向上的滑动摩擦磨损行为存在较大差异:X向(熔体流动方向)上滑动时，滑动方向与CF取向排列方向一致，平均摩擦系数较低，但体积磨损率较高；在Y滑动方向上(X的垂直方向)滑动时，平均摩擦系数较高，但体积磨损率较低.      

Analysis of sloping elastic pile under arbitrary loads by line-loaded integral equation method

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潮流中污染物离散的理论分析与应用

利用浓度矩法推导了纵向流速分布可分离为空间函数与时间函数相乘型式的二维潮汐流动中剪切离散系数的表达式,获得了对数流速分布下正弦式潮汐流离散系数随时间的变化过程,对离散与潮流特征的关系以及负离散问题进行了分析。最后将理论分析成果应用于珠江黄埔河段,获得了与实测资料相符的结果。     

Gravity Affected Lateral Dispersion and Diffusion in a Stationary Horizontal Porous Medium Shear Flow

Transport of dissolved species by a carrier fluid in a porous medium comprises advection and diffusion/dispersion processes. Hydrodynamic dispersion is commonly characterized by an empirical relationship, in which the dispersion mechanism is described by contributions of molecular diffusion and mechanical dispersion expressed as a function of the molecular Peclét number. Mathematically these two phenomena are modeled by a constant diffusion coefficient and by velocity dependent dispersion coefficients, respectively. Here, the commonly utilized Bear--Scheidegger dispersion model of linear proportionality between mechanical dispersion and velocity, and the more complicated Bear--Bachmat model derived on a streamtube array model porous medium and better describing observed dispersion coefficients in the moderate molecular Peclét number range, will be considered. Analyzing the mixing flow of two parallelly flowing confluent fluids with different concentrations of a dissolved species within the frames of boundary layer theory one has to deal with transverse mixing only. With the Boussinesq approximation being adopted approximate analytical solutions of the corresponding boundary layer system of equations show that there is no effect of density coupling on concentration distributions across the mixing layer in the pure molecular diffusion regime case. With the Peclét number of the oncoming flow growing beyond unity, density coupling has an increasing influence on the mixing zone. When the Peclét number grows further this influence is successively reduced until its disappearance in the pure mechanical dispersion regime.     

WAVE PROPAGATION IN PIEZOELECTRIC/PIEZOMAGNETIC LAYERED PERIODIC COMPOSITES

This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal （i.e. thickness） mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications.     

Instability theory of shock wave in a channel

The instability theory of shock wave was extended from the case with an infinitefront to the case of a channel with a rectangular cross section.First,themathematical formulation of the problem was given which included a system ofdisturbed equations and three kinds of boundary conditions.Then,the general solutionsof the equations upstream and downstream were given and each contained fiveconstants to be determined.Thirdly,under one boundary condition and oneassumption,it was proved that all of the disturbances in front of the shock front andone of the two acoustic disturbances behind the shock front should be zero.Theboundary condition was that all of the disturbed physical quantities should approach tozero at infinity.The assumption was that only the unstable shock wave was concernedhere.So it was reasonable to assumeω=iγ,γwas the instability growth rate andwas a positive real number.Another kind of boundary conditions was that the normaldisturbed velocities should be zero at the solid wall of the cha     

具有记忆的污染物两维分散的描述

在污染物释放后的前期它的扩散过程受出口速度的影响而具有明显的记忆特性，本文将Ｒ．Ｓｍｉｔｈ［８］（１９８１）污染物纵向记忆描述理论推广到两维情况并给出了的解析表达式。     

Second-gradient homogenized model for wave propagation in heterogeneous periodic media

The paper is focused on a homogenization procedure for the analysis of wave propagation in materials with periodic microstructure. By a reformulation of the variational-asymptotic homogenization technique recently proposed by Bacigalupo and Gambarotta (2012a), a second-gradient continuum model is derived, which provides a sufficiently accurate approximation of the lowest (acoustic) branch of the dispersion curves obtained by the Floquet–Bloch theory and may be a useful tool for the wave propagation analysis in bounded domains. The multi-scale kinematics is described through micro-fluctuation functions of the displacement field, which are derived by the solution of a recurrent sequence of cell BVPs and obtained as the superposition of a static and dynamic contribution. The latters are proportional to the even powers of the phase velocity and consequently the micro-fluctuation functions also depend on the direction of propagation. Therefore, both the higher order elastic moduli and the inertial terms result to depend by the dynamic correctors. This approach is applied to the study of wave propagation in layered bi-materials with orthotropic phases, having an axis of orthotropy parallel to the direction of layering, in which case, the overall elastic and inertial constants can be determined analytically. The reliability of the proposed procedure is analysed by comparing the obtained dispersion functions with those derived by the Floquet–Bloch theory.     

Dispersion of reactive species with reversible and irreversible wall reactions

The longitudinal dispersion of a chemical species released in an oscillatory flow through an annular tube has been studied in presence of two kinds of first order reactions between the species and tube-wall. The species is supposed to undergo kinetic reversible phase exchange with the outer-wall material and irreversible absorption into the wall. Due to the variation of velocity across the tube section, the chemical species may spread out axially along the tube at a much faster rate than that produced by the molecular diffusion. A finite-difference implicit scheme has been adopted to solve the unsteady convection-diffusion equation for all time period based on the Aris method of moments. Axial distributions of mean concentration are determined from the first four central moments using Hermite polynomial representation for the periodic flow with and without non-zero mean flow. The study brings forward the coupled effects of reversible phase exchange and irreversible absorption on dispersion coefficient. Both the reversible and irreversible reactions are found to inhabit the dispersion process at early times, but at developed stage dispersion may be enhanced by the reversible phase exchange, provided the velocity comprises time invariant component. The decrease of peak of the mean concentration distribution with the increase of reaction rate is found irrespective of the nature of reaction.     

刚性斜桩顶部受任意力的位移的线载荷积分方程法的分析

刚性斜桩顶部受任意力作用的位移分析可以分解为在倾斜平面xoz及其法平面yoz内受力的位移分析.xoz(或yoz)平面内的位移分析,可以用集度为未知函数X(t)(或Y(t))和Z(t)的Mindlin水平点力(平行x轴(或y轴)),垂直点力,在xoz(或yoz)平面内沿桩轴[0,L]内分布,根据边界条件,可将问题归结为Fredholm第一种积分方程.用离散的方法可获数值解.文中给出数值计算的例子.计算的精度用功的互等定理来检查,并将直桩的结果与别人的直桩结果作比较.     

Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.     

Nonlinear Two-Phase Mixing in Heterogeneous Porous Media

For a two-phase immiscible flow through a heterogeneous porous medium in gravity field but with neglected capillary pressure, a macroscale model of first order is derived by a two-scale homogenization method while capturing the effect of fluid mixing. The mixing is manifested in the form of a nonlinear hydrodynamic dispersion and a transport velocity shift. The dispersion tensor is shown to be a nonlinear function of saturation. In the case offlow without gravity this function is proportional to the fractional flow derivative and depends on the viscosity ratio. For a flow which is one dimensional at the macroscale, the dispersion operator remains three dimensional and can be calculated in an analytical way. In the case of gravity induced flow, the longitudinal dispersion as the function of saturation is negative within some interval of saturation values. Numerical simulations of the microscale problemjustify the theoretical results of homogenization.     

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal (SH) waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe₂O₄ substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that, (i) the effect of the cut orientation on the dispersion curves is very obvious, (ii) the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and (iii) the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.     

Approximate analytical solutions for solute transport in two-layer porous media

Mathematical models for transport in layered media are important for investigating how restricting layers affect rates of solute migration in soil profiles; they may also improve the analysis of solute displacement experiments. This study reports an (approximate) analytical solution for solute transport during steady-state flow in a two-layer medium requiring continuity of solute fluxes and resident concentrations at the interface. The solutions were derived with Laplace transformations making use of the binomial theorem. Results based on this solution were found to be in relatively good agreement with those obtained using numerical inversion of the Laplace transform. An expression for the flux-averaged concentration in the second layer was also obtained. Zero- and first-order approximations for the solute distribution in the second layer were derived for a thin first layer representing a water film or crust on top of the medium. These thin-layer approximations did not perform as well as the binomial solution, except for the first-order approximation when the Peclet number,P, of the first layer, was low (P<5). Results of this study indicate that the ordering of two layers will affect the predicted breakthrough curves at the outlet of the medium. The two-layer solution was used to illustrate the effects of dispersion in the inlet or outlet reservoirs using previously published data on apparatus-induced dispersion.The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

On the backward Lamb waves near thickness resonances in anisotropic plates

A closed-form expression for the leading-order dispersion coefficient, describing the trend of Lamb-wave branches at their onset from thickness resonances, is derived for an arbitrary anisotropic plate. The sign of this coefficient and hence of the in-plane group velocity near cutoffs decides the existence or non-existence of the backward Lamb waves without a necessity to calculate the dispersion branches. A link between the near-cutoff dispersion of Lamb waves and the curvature of bulk-wave slowness curves in a sagittal plane is analyzed. It is established that a locally concave slowness curve of a bulk mode entails the backward Lamb waves at the onset of branches emerging from this bulk mode resonances of high enough order. A simple sufficient condition for no backward Lamb waves near the resonances associated with a convex slowness curve is also noted. Two special cases are discussed: the first involves the coupled resonances of degenerate bulk waves, and the second concerns quasi-degenerate resonances which give rise to pairs of dispersion branches with a quasilinear positive and negative onset. Occasions of the backward Lamb waves in isotropic plate materials are tabulated.     

Theoretical Analyses of the Effects of Solute Dispersion on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

This article deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including solute dispersion effects. Since the solute equilibrium concentration is much smaller than the molar density of the dissolvable mineral in a mineral dissolution system, a limit case, in which the ratio of the solute equilibrium concentration (in the pore fluid) to the molar density of the dissolvable mineral (in the solid matrix of the porous medium) approaches zero, is considered in the theoretical analysis. Under this assumption, the critical condition under which a planar chemical-dissolution front becomes unstable has been mathematically derived when solute dispersion effects are considered. The present theoretical results clearly demonstrated that: (1) the propagation speed of a planar chemical-dissolution front in the case of considering solute dispersion effects is the same as that when solute dispersion effects are neglected. This indicates that solute dispersion does not affect the propagation speed of the planar chemical-dissolution front in a fluid-saturated porous medium. (2) The consideration of solute dispersion can cause a significant increase in the critical Zhao number, which is used to judge whether or not a planar chemical-dissolution front may become unstable in the fluid-saturated porous medium. This means that the consideration of solute dispersion can stabilize a planar chemical-dissolution front, because an increase in the critical Zhao number reduces the likelihood of the planar chemical-dissolution front instability in a fluid-saturated porous medium. In addition, the present results can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of chemical dissolution fronts in two-dimensional fluid-saturated porous media.     

Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov’s exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot’s characteristic frequency to the viscoelastic characteristic frequency. If Biot’s characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel–Biot theory of poroelasticity. In the opposite case when Biot’s characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.