Onset of plane layer magnetoconvection at low Ekman number

We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth's tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra-c and critical wavenumber a(c) are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number. (ratio of the Lorentz force to the Coriolis force). E is varied from 10(-9) to 10(-2) and. from 10(-3) to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E-one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E < 10(-6) and establish a map in the (E, Lambda) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal. (C) 2015 AIP Publishing LLC.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

A new genus and species of arboreal toad with phytotelmonous larvae, from the Andaman Islands, India (Lissamphibia, Anura, Bufonidae)

A new bufonid amphibian, belonging to a new monotypic genus, is described from the Andaman Islands, in the Bay of Bengal, Republic of India, based on unique external morphological and skeletal characters which are compared with those of known Oriental and other relevant bufonid genera. Blythophryne gen. n. is distinguished from other bufonid genera by its small adult size (mean SVL 24.02 mm), the presence of six presacral vertebrae, an absence of coccygeal expansions, presence of an elongated pair of parotoid glands, expanded discs at digit tips and phytotelmonous tadpoles that lack oral denticles. The taxonomic and phylogenetic position of the new taxon (that we named as Blythophryne beryet gen. et sp. n.) was ascertained by comparing its 12S and 16S partial genes with those of Oriental and other relevant bufonid lineages. Resulting molecular phylogeny supports the erection of a novel monotypic genus for this lineage from the Andaman Islands of India.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Three-dimensional warping in strip-based composite four-bar mechanisms

This work intends to demonstrate the effect of geometrically non-linear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting the three-dimensional warping of the cross-section. The only restriction in the present analysis is that the strains within each elastic body remain small (i.e., this work does not deal with materials exhibiting non-linear constitutive laws at the 3-D level). Here, all component bars of the mechanism are made of fiber-reinforced laminates. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction, results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis, the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here. The representative cross-sections of all component bars are analyzed using two different approaches: (1) Numerical Model and (2) Analytical Model. Four-bar mechanisms are analyzed using the above two approaches for Omega = 20 rad/s and Omega = pi rad/s and observed the same behavior in both cases. The noticeable snap-shots of the deformation shapes of the mechanism about 1000 frames are also reported using commercial software (I-DEAS + NASTRAN + ADAMS). The maximum out-of-plane warping of the cross-section is observed at the mid-span of bar-1, bar-2 and bar-3 are 1.5 mm, 250 mm and 1.0 mm, respectively, for t = 0:5 s. (C) 2015 Elsevier Ltd. All rights reserved.

Stabilization of Collective Motion in Synchronized, Balanced and Splay Phase Arrangements on a Desired Circle

This paper proposes a design methodology to stabilize collective circular motion of a group of N-identical agents moving at unit speed around individual circles of different radii and different centers. The collective circular motion studied in this paper is characterized by the clockwise rotation of all agents around a common circle of desired radius as well as center, which is fixed. Our interest is to achieve those collective circular motions in which the phases of the agents are arranged either in synchronized, in balanced or in splay formation. In synchronized formation, the agents and their centroid move in a common direction while in balanced formation, the movement of the agents ensures a fixed location of the centroid. The splay state is a special case of balanced formation, in which the phases are separated by multiples of 2 pi/N. We derive the feedback controls and prove the asymptotic stability of the desired collective circular motion by using Lyapunov theory and the LaSalle's Invariance principle.

A Stochastic Approximation Algorithm for Quantile Estimation

In this paper, we present two new stochastic approximation algorithms for the problem of quantile estimation. The algorithms uses the characterization of the quantile provided in terms of an optimization problem in 1]. The algorithms take the shape of a stochastic gradient descent which minimizes the optimization problem. Asymptotic convergence of the algorithms to the true quantile is proven using the ODE method. The theoretical results are also supplemented through empirical evidence. The algorithms are shown to provide significant improvement in terms of memory requirement and accuracy.

Social optimum in social groups with give-and-take criterion

We consider a Social Group' of networked nodes, seeking a universe' of segments. Each node has a subset of the universe and access to an expensive resource for downloading data. Nodes can also acquire the universe by exchanging copies of segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum cost, some nodes in the group try to exploit the system. We term such nodes as non-reciprocating nodes' and prohibit such behavior by proposing the give-and-take' criterion, where exchange is allowed if each node has segments unavailable with the other. Under this criterion, we consider the problem of maximizing the number of nodes with the universe at the end of local exchanges. First, we present a randomized algorithm that is shown to be optimal in the asymptotic regime. Then, we present greedy links algorithm, which performs well for most of the scenarios and yields an optimal result when the number of nodes is four. The polygon algorithm is proposed, which yields an optimal result when each of the nodes has a unique segment. After presenting some intuitive algorithms (e.g., greedy incremental algorithm and rarest first algorithm), we compare the performances of all proposed algorithms with the optimal. Copyright (c) 2015 John Wiley & Sons, Ltd.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

A micromechanical damage theory for brittle materials with small cracks

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre-existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress-strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress-strain relation curves are evaluated for a rectangular plate containing small cracks.

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.

On applications of high-frequency asymptotics in aeroacoustics.

The aim of this paper is to survey a range of applications of high-frequency asymptotic methods in aeroacoustics. Specifically, we are concerned with problems associated with noise generation, propagation and scattering as found in large modern aeroengines. With regard to noise generation, we consider the interaction between high-frequency vortical waves and thin aerofoils, with particular emphasis being placed on the way in which the vortical waves act on the non-uniform mean flow around the aerofoil. A ray-theoretic description of the resulting sound as it propagates along the engine intake is then presented, followed by consideration of the diffraction of these rays by the (possibly asymmetric) intake lip to produce sound in the far field. A range of more detailed possible extensions is also presented.

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.