Application of parameter differentiation for flow of a third grade fluid past an infinite porous plate

This article investigates the analytic solution for the flow of a third grade fluid past an infinite porous plate. The method of parameter differentiation is used to linearized the governing flow equation. The solution of the obtained linear equation is developed by differential transform method in combination with the method of superposition. The obtained results are compared with existing results in the literature and an excellent agreement is found. This shows that the parameter differentiation is a powerful technique for solving nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

HF激光脉冲与水柱表面相互作用产生电信号(英文)

研究了脉冲HF激光与水柱表面相互作用下电信号的产生过程。电信号显示了与激光能量线性相关的峰值间有时间间隔的两峰结构,且第二个尖峰在水柱底部的蒸汽腔塌缩后出现。实验还显示电信号的幅值和激光脉冲照射过程中是否存在膨胀和挤压的薄水层密切相关。如果在电池上边缘和石英平板(石英板紧邻电池,并与水柱上表面相接)之间存在一薄水层,电信号强度会增加10倍。     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

矩形毛细微槽中三角形区域接触线特性的研究

利用CCD和宽视场体视显微镜相结合的技术,拍摄了矩形毛细微槽内液体工质在三角形区域的润湿图像,并进行了图像处理,研究结果表明:随着热流密度的增加,三角形区域内的三相接触线向微槽底角收缩,导致三相接触线的长度减小,液膜厚度减小;随着微槽深度的增加,三角形区域的接触线长度减小;随着微槽宽度和倾斜角度的增加,三角形区域内的接触线长度增加,液膜厚度增加.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

An efficient numerical method for the resolution of the Kirchhoff‐Love dynamic plate equation

We solve numerically the Kirchhoff‐Love dynamic plate equation for an anisotropic heterogeneous material using a spectral method. A mixed velocity‐moment formulation is proposed for the space approximation allowing the use of classical Lagrange finite elements. The benefit of using high order elements is shown through a numerical dispersion analysis. The system resulting from this spatial discretization is solved analytically. Hence this method is particularly efficient for long duration experiments. This time evolution method is compared with explicit and implicit finite differences schemes in terms of accuracy and computation time. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Design of phase plates for shaping partially coherent beams by simulated annealing

Taking the Gaussian Schell-model beam as a typical example of partially coherent beams, this paper applies the simulated annealing （SA） algorithm to the design of phase plates for shaping partially coherent beams. A flow diagram is presented to illustrate the procedure of phase optimization by the SA algorithm. Numerical examples demonstrate the advantages of the SA algorithm in shaping partially coherent beams. An uniform flat-topped beam profile with maximum reconstruction error RE 〈 1.74% is achieved. A further extension of the approach is discussed.     

Commutativity of the Arens product in lattice ordered algebras

Let be an Abelian Archimedean lattice ordered algebra. The order bidual furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the up-down-up approximation of positive elements in the order continuous order bidual by elements in the canonical image of in Components of positive elements in are characterized and the result is applied to the Arens product of -and almost -algebras.     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

Continual approximations of displacements in thick layered plates upon decomposition of thermomechanical loads into bilateral symmetric and antisymmetric components

Continual models of deformation of thick layered plates, where the general order of resolving equations does not depend on the number of layers, are constructed with account of the specific character of the unflexural and flexural deformation caused by the symmetric and antisymmetric components of bilateral loads and temperature. Account of the load decomposition during the process of refining a certain reasonable initial solution, consisting in the analytical iterative integration, makes it possible to obtain rather precise continual approximations of stresses and displacements over the transverse coordinate and thus to revise the known continual models.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 743–756, November–December, 1999.