Pulsatile flow of a viscous fluid in elliptical pipe of variable cross-section

The pulsatile flow of an incompressible viscous fluid in an elliptical pipe of slowly varying cross-section is considered. Asymptotic series solutions for the velocity distribution and pressure gradient are obtained in terms of Mathieu functions for a low Reynold number flow in which the volume flux is prescribed. An expression for shear stress on the boundary is derived. The physically significant quantities governing the flow are computed numerically and analysed for different types of constrictions. The effect of eccentricity and Womerslay parameter on the flow is discussed.

Synthesis of Layered Perovskite Oxides, ACa2-xLaxNb3-xTix010 (A = K, Rb, Cs), and Characterization of New Solid Acids, HCa2-xLaxNb3-xTixOlo (0 < x d 2), Exhibiting Variable Bronsted Acidity?

Layered perovskite oxides of the formula ACa~,La,Nb3-,Ti,010 (A = K, Rb, Cs and 0 < x d 2) have been prepared. The members adopt the structures of the parent ACazNb3010. Interlayer alkali cations in the niobium-titanium oxide series can be ion-exchanged with Li+, Na+, NH4+, or H+ to give new derivatives. Intercalation of the protonated derivatives with organic bases reveals that the Bronsted acidity of the solid solution series, HC~ ~ , L ~ ,N~ ~ , T ~ ,dOep~eOnd, s on the titanium content. While the x = 1 member (HCaLaNbzTiOlo) is nearly as acidic as the parent HCazNb3010, the x = 2 member (HLazNbTizOlo) is a weak acid hardly intercalating organic bases with pKa - 11.3. The variation of acidity is probably due to an ordering of Nb/Ti atoms in the triple octahedral perovskite slabs, [Ca~,La,Nb~,Ti,0~0], such that protons are attached to NbO6 octahedra in the x = 1 member and to Ti06 octahedra in the x = 2 member.

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

Popular matchings with variable item copies

We consider the problem of matching people to items, where each person ranks a subset of items in an order of preference, possibly involving ties. There are several notions of optimality about how to best match a person to an item; in particular, popularity is a natural and appealing notion of optimality. A matching M* is popular if there is no matching M such that the number of people who prefer M to M* exceeds the number who prefer M* to M. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not admit popular matchings. This motivates the following extension of the popular matchings problem: Given a graph G = (A U 3, E) where A is the set of people and 2 is the set of items, and a list < c(1),...., c(vertical bar B vertical bar)> denoting upper bounds on the number of copies of each item, does there exist < x(1),...., x(vertical bar B vertical bar)> such that for each i, having x(i) copies of the i-th item, where 1 <= xi <= c(i), enables the resulting graph to admit a popular matching? In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c(i) is 1 or 2. We show a polynomial time algorithm for a variant of the above problem where the total increase in copies is bounded by an integer k. (C) 2011 Elsevier B.V. All rights reserved.

Variable Elimination in Linear Constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fourier's original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

Identification of Local Conformational Similarity in Structurally Variable Regions of Homologous Proteins Using Protein Blocks

Structure comparison tools can be used to align related protein structures to identify structurally conserved and variable regions and to infer functional and evolutionary relationships. While the conserved regions often superimpose well, the variable regions appear non superimposable. Differences in homologous protein structures are thought to be due to evolutionary plasticity to accommodate diverged sequences during evolution. One of the kinds of differences between 3-D structures of homologous proteins is rigid body displacement. A glaring example is not well superimposed equivalent regions of homologous proteins corresponding to a-helical conformation with different spatial orientations. In a rigid body superimposition, these regions would appear variable although they may contain local similarity. Also, due to high spatial deviation in the variable region, one-to-one correspondence at the residue level cannot be determined accurately. Another kind of difference is conformational variability and the most common example is topologically equivalent loops of two homologues but with different conformations. In the current study, we present a refined view of the ``structurally variable'' regions which may contain local similarity obscured in global alignment of homologous protein structures. As structural alphabet is able to describe local structures of proteins precisely through Protein Blocks approach, conformational similarity has been identified in a substantial number of `variable' regions in a large data set of protein structural alignments; optimal residue-residue equivalences could be achieved on the basis of Protein Blocks which led to improved local alignments. Also, through an example, we have demonstrated how the additional information on local backbone structures through protein blocks can aid in comparative modeling of a loop region. In addition, understanding on sequence-structure relationships can be enhanced through our approach. This has been illustrated through examples where the equivalent regions in homologous protein structures share sequence similarity to varied extent but do not preserve local structure.

Unsteady nonsimilar two-dimensional and axisymmetric water boundary layers with variable viscosity and prandtl number

The influence of temperature-dependent viscosity and Prandtl number on the unsteady laminar nonsimilar forced convection flow over two-dimensional and axisymmetric bodies has been examined where the unsteadiness and (or) nonsimilarity are (is) due to the free stream velocity, mass transfer, and transverse curvature. The partial differential equations governing the flow which involve three independent variables have been solved numerically using an implicit finite-difference scheme along with a quasilinearization technique. It is found that both the skin friction and heat transfer strongly respond to the unsteady free stream velocity distributions. The unsteadiness and injection cause the location of zero skin friction to move upstream. However, the effect of variable viscosity and Prandtl number is to move it downstream. The heat transfer is found to depend strongly on viscous dissipation, but the skin friction is little affected by it. In general, the results pertaining to variable fluid properties differ significantly, from those of constant fluid properties.

Variable density approach for rotating shallow shell of variable thickness

A new approach based on variable density in conjunction with shallow shell theory is proposed to analyse rotating shallow shell of variable thickness. Coupled non-linear ordinary differential equations governing shallows shells of variable thickness are first derived before applying the variable density approach. Results obtained from the new approach compare well with FEM calculation for a wide range of profiles considered in this paper.

Variable Sparsity Kernel Learning

This paper(1) presents novel algorithms and applications for a particular class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume that the given kernels are grouped and employ l(1) norm regularization for promoting sparsity within RKHS norms of each group and l(s), s >= 2 norm regularization for promoting non-sparse combinations across groups. Various sparsity levels in combining the kernels can be achieved by varying the grouping of kernels-hence we name the formulations as Variable Sparsity Kernel Learning (VSKL) formulations. While previous attempts have a non-convex formulation, here we present a convex formulation which admits efficient Mirror-Descent (MD) based solving techniques. The proposed MD based algorithm optimizes over product of simplices and has a computational complexity of O (m(2)n(tot) log n(max)/epsilon(2)) where m is no. training data points, n(max), n(tot) are the maximum no. kernels in any group, total no. kernels respectively and epsilon is the error in approximating the objective. A detailed proof of convergence of the algorithm is also presented. Experimental results show that the VSKL formulations are well-suited for multi-modal learning tasks like object categorization. Results also show that the MD based algorithm outperforms state-of-the-art MKL solvers in terms of computational efficiency.

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

Variable-speed wind power generation using doubly fed wound rotor induction machine - A comparison with alternative schemes

In this paper, a wind energy conversion system (WECS) using grid-connected wound rotor induction machine controlled from the rotor side is compared with both fixed speed and variable speed systems using cage rotor induction machine. The comparison is done on the basis of (I) major hardware components required, (II) operating region, and (III) energy output due to a defined wind function using the characteristics of a practical wind turbine. Although a fixed speed system is more simple and reliable, it severely limits the energy output of a wind turbine. In case of variable speed systems, comparison shows that using a wound rotor induction machine of similar rating can significantly enhance energy capture. This comes about due to the ability to operate with rated torque even at supersynchronous speeds; power is then generated out of the rotor as well as the stator. Moreover, with rotor side control, the voltage rating of the power devices and dc bus capacitor bank is reduced. The size of the line side inductor also decreasesd. Results are presented to show the substantial advantages of the doubly fed system.

Variable temperature x-ray crystal structure analysis of a type I langbeinite: Rb2Cd2(SO4)(3)

The structure of a type I langbeinite, Rb2Cd2(SO4)(3), displays three different phases, cubic with a = 10.378(5) Angstrom (space group P2(1)3) at room temperature, monoclinic at 120 K with a = 10.328(3), b = 10.322(3), c = 10.325(3) Angstrom, beta = 89.975(1)degrees (space group P2(1)), and orthorhombic at 85 K with a = 10.319(2), b = 10.321(2), c = 10.320(2) Angstrom (space group P2(1)2(1)2(1)), respectively. Precise single-crystal analyses of these phases indicate that Rb2Cd2(SO4)(3) distorts initially from cubic to monoclinic upon cooling followed by a significant reorientation of the SO4 tetrahedra, resulting in an orthorhombic symmetry upon further cooling. The three structures have been established unequivocally using the same crystal. There is no indication of the formation of an intermediate triclinic phase or any lattice disorder as conjectured in several earlier reports on compounds belonging to the type I langbeinite. The bond valence sum analyses of the coordination around the Rb sites indicate asymmetry in the bond strengths which could be the driving force of the ferroelectric behavior in these materials.

A method of tracking the peak power points for a variable speed wind energy conversion system

In this paper, a method of tracking the peak power in a wind energy conversion system (WECS) is proposed, which is independent of the turbine parameters and air density. The algorithm searches for the peak power by varying the speed in the desired direction. The generator is operated in the speed control mode with the speed reference being dynamically modified in accordance with the magnitude and direction of change of active power. The peak power points in the P-omega curve correspond to dP/domega = 0. This fact is made use of in the optimum point search algorithm. The generator considered is a wound rotor induction machine whose stator is connected directly to the grid and the rotor is fed through back-to-back pulse-width-modulation (PWM) converters. Stator flux-oriented vector control is applied to control the active and reactive current loops independently. The turbine characteristics are generated by a dc motor fed from a commercial dc drive. All of the control loops are executed by a single-chip digital signal processor (DSP) controller TMS320F240. Experimental results show that the performance of the control algorithm compares well with the conventional torque control method.