Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

考虑壁面滑移的Z-W流变模型及其应用

总结了聚合物熔体在剪切溶场壁面滑移研究的成果，提出了Z－W模型的物理概念。该模型考虑了界面分子链和固体壁面间解吸－吸附而发生的滑移。界面分子链和内部分子链间解缠－重新缠结而发生的表观滑移以及变形摩擦滑移。在稳态简单剪切流运过程，模型可以化简为应力和应变的二次微分方程，说明了壁面滑移来源于Cohesive滑移和Adhesive滑移两部分，对于自激振荡相关的多重内振荡和多重外振荡进行了归纳，应用统一模型定性地解释了毛细管实验中剪切应力的非线性，瞬态自激振荡、滑－粘转换和鲨鱼皮等现象，在聚合物熔体振动剪切流动（LAOS）中，统一模型可以简化为杜芬方程，通过模拟发现，该模型可解释小应变振幅下振动剪切时的线性流变行为和在大振幅振动流动中的复杂非线性行为。非线性行为与熔体粘弹性以及近壁面界面层的性质有关，统一模型在特殊情况下还可以简化Joshi模型，结构网络模型，Hatzikiriakos或等效的Graham模型，可见，Z－W模型内内涵比较丰富，适用面较广，也从一个侧面说明该模型具有相当的合理性。     

Recent progress in measurements of oscillatory forces and liquid properties under confinement

The present review paper focuses on direct measurements of oscillatory forces. Beside the surface forces apparatus (SFA), atomic force microscopy (AFM) has emerged as the most commonly used technique to measure surface forces. Recent instrumental advances of both methods are highlighted in the review. Different systems, showing oscillatory forces are classified. Principle distinction is made between 1-component liquids (water, organic liquids and liquid crystals), pseudo 1-component liquids (ionic liquids and microemulsions) and 2-component liquids (dispersions containing polyelectrolytes, micelles or nanoparticles). In the last few years, the oscillatory force studies address particle characterisation, synergistic effects in multicomponent systems, the introduction of ‘switchable’ forces, and resolving liquid properties under confinement. Last but not least, the ability of AFM and SFA to measure oscillatory forces is discussed.     

振荡Robin混合边值齐次化问题

该文研究了振荡Robin混合边值齐次化问题解的收敛率.该工作的困难之处在于Robin边值上出现的振荡因子以及边界交叉项的处理.该文利用对偶方法巧妙得对振荡积分进行了估计.文中建立了解的H1和L2收敛率,所得结果明显地依赖于维数.该文可以视为将对偶方法和光滑算子,延拓到处理振荡Robin混合边值问题的情形.     

Application of wake oscillators to two-dimensional vortex-induced vibrations of circular cylinders in oscillatory flows

A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow–cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid–structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan–Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in cases of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.     

On intrinsic oscillation in radiation-affected diffusion flames

A linear stability analysis is conducted to study the onset of near-limit flame oscillation with radiative heat loss in 1-D chambered planar flames using multi-scale activation-energy asymptotics. The oscillatory instability near the radiation-induced extinction limit at large Damköhler numbers is identified, in additional to the one near the kinetic limit at small Damköhler numbers. It is shown that radiative loss assumes a similar role as varying the thermal diffusivity of the reactants. Thus, flame oscillation near the radiative limit is still thermal-diffusive in nature although it may develop under unity Lewis numbers. The unstable range of Damköhler numbers near the radiative limit shows quite similar parametric dependence on the Lewis numbers of reactants, Le_F and Le_O, the stoichiometry, ?, and the radiative loss as that near the kinetic limit. They both increase monotonically with Le_O and ? and increase then decrease with Le_F. Increasing radiative loss extends the parameter range under which flame oscillations may develop. However, they show different dependence on the temperature difference between the supplying reactants. Unless radiative loss approaches its maximum value the system can sustain, flame oscillation near the radiative limit is only possible within a limited range of ΔT, whereas it is promoted monotonically with decreasing ΔT near the kinetic limit. Furthermore, while radiative loss shows small effect on the nondimensional oscillation frequency, the dimensional frequency of flame oscillations near the radiative limit can be substantially smaller than that near the kinetic limit.     

Numerical simulation of the horizontal Bridgman growth. Part II: Three-dimensional flow

We study the steady-state three-dimensional flow which occurs in a horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals. We find that three-dimensional effects can have a dramatic influence upon the flow, which, before the onset of periodic disturbances, differs appreciably from its two-dimensional counterpart. We also investigate the sensitivity of the flow to non-symmetric disturbances.     

Application of differential transform method to non-linear oscillatory systems

In this paper, the differential transform method is proposed for solving non-linear oscillatory systems. These solutions do not exhibit periodicity, which is the characteristic of oscillatory systems. A modification of the differential transform method, based on the use of Padé approximants, is proposed. We use alternative technique by which the solution obtained by the differential transform method is made periodic. The method is described and illustrated with examples. The results reveal that the method is very effective and convenient.     

Comment on the paper: “Forced oscillation of certain neutral hyperbolic equations with continuous distributed deviating arguments” [Math. Comput. Modeling 49 (2009) 1211–1220]

In recent years, many results on oscillation criteria of second-order nonlinear neutral delay differential equations with distributed deviating argument have been obtained, but some of these criteria are incorrect due to a mistake in a crucial auxiliary result. We give two counterexamples.     

The effect of impurities on the viscoelastic response of polycarbonate reinforced with short glass fibers

Observations are reported in oscillatory torsion tests at room temperature on unfilled and fiber-reinforced polycarbonates melt-blended with impurities (acronitrile–butadiene–styrene, high-impact polystyrene, low-density polyethylene, poly(ethylene terephthalate) and Nylon 6,6). Constitutive equations are derived for the viscoelastic behavior of glassy polymers. With reference to the theory of cooperative relaxation, a polymer is treated as an ensemble of meso-regions with arbitrary shapes and sizes. The time-dependent response of the ensemble is attributed to rearrangement of meso-domains. The rearrangement events occur at random times, when meso-regions are excited by thermal fluctuations. Stress–strain relations are derived by using the laws of thermodynamics. The governing equations are determined by four adjustable parameters that are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. The study focuses on the effects of the concentration of impurities and glass fibers on material parameters.