Naive asymptotic expansion of the water wave generated by a slowly moving body

It is pointed out that the naive asymptotic expansion does not satisfy all the body boundary condition. A nonhomogeneous body boundary condition is obtained from this expansion. It is this condition that the additional wave term must satisfy. Moreover, because of this condition, the wave term must appear. It is pointed out that the zeroth approximation in the naive asymptotic expansion has weak singularity and the singularities become still stronger in the subsequent approximations.

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

The asymptotic near-tip solution for mode-iii crack in steady growth in power hardening media

Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.

SOA-based polarity-preserving all-optical wavelength conversion at 80Gbit/s: Wide conversion range, well dynamic characteristics and polarization insensitive

This letter presents the effective design of a tunable 80 Gbit/s wavelength converter with a simple configuration consisting of a single semiconductor optical amplifier (SOA) and an optical bandpass filter (OBPF). Based on both cross-gain and cross-phase modulation in SOA, the polarity-preserved, ultrafast wavelength conversion is achieved by appropriately filtering the blue-chirped spectral component of a probe light. Moreover, the experiments are carried out to investigate into the wavelength tunability and the maximum tuning range of the designed wavelength converter. Our results show that a wide wavelength conversion range of nearly 35 nm is achieved with 21-nm downconversion and 14-nm upconversion, which is substantially limited by the operation wavelength ranges of a tunable OBPF and a tunable continuous-wave laser in our experiment. We also exploited the dynamics characteristics of the wavelength converter with variable input powers and different injection current of SOA. (C) 2008 Wiley Periodicals, Inc.

Discriminative Orthogonal Neighborhood-Preserving Projections for Classification

Orthogonal neighborhood-preserving projection (ONPP) is a recently developed orthogonal linear algorithm for overcoming the out-of-sample problem existing in the well-known manifold learning algorithm, i.e., locally linear embedding. It has been shown that ONPP is a strong analyzer of high-dimensional data. However, when applied to classification problems in a supervised setting, ONPP only focuses on the intraclass geometrical information while ignores the interaction of samples from different classes. To enhance the performance of ONPP in classification, a new algorithm termed discriminative ONPP (DONPP) is proposed in this paper. DONPP 1) takes into account both intraclass and interclass geometries; 2) considers the neighborhood information of interclass relationships; and 3) follows the orthogonality property of ONPP. Furthermore, DONPP is extended to the semisupervised case, i.e., semisupervised DONPP (SDONPP). This uses unlabeled samples to improve the classification accuracy of the original DONPP. Empirical studies demonstrate the effectiveness of both DONPP and SDONPP.

Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Asymptotic weighted-periodicity of the impulsive parabolic equation with time delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

Elliptic Object Detection Based on Shape Preserving and Active Contour

本文通过形状约束方程(组)与一般主动轮廓模型结合,将目标形状与主动轮廓模型融合到统一能量泛函模型中,提出了一种形状保持主动轮廓模型即曲线在演化过程中保持为某一类特定形状。模型通过参数化水平集函数的零水平集控制演化曲线形状,不仅达到了分割即目标的目的,而且能够给出特定目标的定量描述。根据形状保持主动轮廓模型,建立了一个用于椭圆状目标检测的统一能量泛函模型,导出了相应的Euler-Lagrange常微分方程并用水平集方法实现了椭圆状目标检测。此模型可以应用于眼底乳头分割,虹膜检测及相机标定。实验结果表明,此模型不仅能够准确的检测出给定图像中的椭圆状目标,而且有很强的抗噪、抗变形及遮挡性能。

Mathematical Modeling of Near-Wall Flows of Two-Phase Mixture with Evaporating Droplets

In the framework of the two-continuum approach, using the matched asymptotic expansion method, the equations of a laminar boundary layer in mist flows with evaporating droplets were derived and solved. The similarity criteria controlling the mist flows were determined. For the flow along a curvilinear surface, the forms of the boundary layer equations differ from the regimes of presence and absence of the droplet inertia deposition. The numerical results were presented for the vapor-droplet boundary layer in the neighborhood of a stagnation point of a hot blunt body. It is demonstrated that, due to evaporation, a droplet-free region develops near the wall inside the boundary layer. On the upper edge of this region, the droplet radius tends to zero and the droplet number density becomes much higher than that in the free stream. The combined effect of the droplet evaporation and accumulation results in a significant enhancement of the heat transfer on the surface even for small mass concentration of the droplets in the free stream. 在双连续介质理论框架下,采用匹配渐进展开方法导出并求解了具有蒸发液滴的汽雾流中层流边界层方程,给出了控制汽雾流的相似判据。对于沿曲面的流动,边界层方程的形式取决于是否存在液滴的惯性沉积。给出了热钝体验点附近蒸汽。液滴边界层的数值计算结果。它们表明：由于蒸发,在边界层内近壁处形成了一个无液滴区域；在该区上边界处,液滴半径趋于零而液滴数密度急剧增高。液滴蒸发及聚集的联合效应造成了表面热流的显著增加,甚至在自由来流中液滴质量浓度很低时此效应依然存在。

Electrostatic Interactions Between Glycosaminoglycan Molecules

The electrostatic interactions between nearest-neighbouring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains are obtained on the bottle brush conformation of proteoglycan aggrecan based on an asymptotic solution of the Poisson-Boltzmann equation the CS-GAGs satisfy under the physiological conditions of articular cartilage. The present results show that the interactions are associated intimately with the minimum separation distance and mutual angle between the molecular chains themselves. Further analysis indicates that the electrostatic interactions are not only expressed to be purely exponential in separation distance and decrease with the increasing mutual angle but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue, which is in agreement with the existed relevant conclusions.

A generalized self-consistent method accounting for fiber section shape

A three-phase confocal elliptical cylinder model is proposed for fiber-reinforced composites, in terms of which a generalized self-consistent method is developed for fiber-reinforced composites accounting for variations in fiber section shapes and randomness in fiber section orientation. The reasonableness of the fiber distribution function in the present model is shown. The dilute, self-consistent, differential and Mori-Tanaka methods are also extended to consider randomness in fiber section orientation in a statistical sense. A full comparison is made between various micromechanics methods and with the Hashin and Shtrikman's bounds. The present method provides convergent and reasonable results for a full range of variations in fiber section shapes (from circular fibers to ribbons), for a complete spectrum of the fiber volume fraction (from 0 to 1, and the latter limit shows the correct asymptotic behavior in the fully packed case) and for extreme types of the inclusion phases (from voids to rigid inclusions). A very different dependence of the five effective moduli on fiber section shapes is theoretically predicted, and it provides a reasonable explanation on the poor correlation between previous theory and experiment in the case of longitudinal shear modulus.

Unsteady Model of Drop Marangoni Migration in Microgravity

The experiments of drop Marangoni migration have been performed by the drop shift facility of short period of 4.5 s, and the drop accelerates gradually to an asymptotic velocity during the free fall. The unsteady and axisymmetric model is developed to study the drop migration for the case of moderate Reynolds number Re = O(1), and the results are compared with the experimental ones in the present paper. Both numerical and experimental results show that the migration velocity for moderate Reynolds number is several times smaller than that given by the linear YGB theory.

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are delta(2) = 4.69 and delta(4) = 4.6, which are comparable with the theoretical asymptotic value delta = 4.669.

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.