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.

Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle Using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A I-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

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.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

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.

Effect of sliding speed on friction and wear of uni-directional aramid fibre-phenolic resin composite

A previous study on the tribological performance of a compression-moulded aramid fibre-phenolic resin composite, containing 30% continuous fibre, showed that this composite provides a reasonable combination of the friction coefficient and wear rate to be used as a friction component, such as a brake shoe. In the present work, the effect of sliding speed on the friction and wear behaviour of this composite has been investigated. The sliding experiments were conducted in a speed range of 0.1-6 m s(-1) at two normal pressure levels of 1.0 and 4.9 MPa. The coefficient of friction was found to be stable over a wide range of sliding speeds and normal pressures. The wear of the composite was found to be insensitive to changes in the speed in the higher speed range. The results have been supplemented with scanning electron micrographs to help understand possible friction and wear mechanisms.

Effect of Speed and Pressure on Dry Sliding Interactions of Alumina against Steel

Sliding of alumina (87%) pins against a hardened steel disk over a range of pressures (3.3-30.0 MPa) and speeds (0.1-12.0 ms(-1)) has been studied. Four different regions (R1, R2, R3, and R4) of friction as a function of speed have been identified. R1 and RS exhibit single-valued friction while in R2 and R4 the friction exhibits dual behavior. The speed range over which these regions prevail is sensitive to the pressure. R1 and R2 are low-speed and low-temperature regions, and in both, metal transfer and formation and compaction of gamma-Fe2O3 occur. R3 and R4 are associated with high speeds and high interface temperatures. Formation of FeO, FeAl2O4, and FeAlO3 has been observed. The implications of the tribochemical interactions on friction and wear characteristics are discussed.

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.

Queuing strategies for qos management of traffic between lans interconnected by low-speed wan links

We provide a comparative performance evaluation of packet queuing and link admission strategies for low-speed wide area network Links (e.g. 9600 bps, 64 kbps) that interconnect relatively highspeed, connectionless local area networks (e.g. 10 Mbps). In particular, we are concerned with the problem of providing differential quality of service to interLAN remote terminal and file transfer sessions, and throughput fairness between interLAN file transfer sessions. We use analytical and simulation models to study a variety of strategies. Our work also serves to address the performance comparison of connectionless vs. connection-oriented interconnection of CLNS LANS. When provision of priority at the physical transmission level is not feasible, we show, for low-speed WAN links (e.g. 9600 bps), the superiority of connection-oriented interconnection of connectionless LANs, with segregation of traffic streams with different QoS requirements into different window flow controlled connections. Such an implementation can easily be obtained by transporting IP packets over an X.25 WAN. For 64 kbps WAN links, there is a drop in file transfer throughputs, owing to connection overheads, but the other advantages are retained, The same solution also helps to provide throughput fairness between interLAN file transfer sessions. We also provide a corroboration of some of our modelling results with results from an experimental test-bed.

Unsteady laminar compressible swirling flow with massive blowing

THE study of swirling boundary layers is of considerable importance in many rotodynamic machines such as rockets, jet engines, swirl generators, swirl atomizers, arc heaters, etc. For example, the introduction of swirl in a flow acceleration device such as a nozzle in a rocket engine promises efficient mass flow control. In nuclear rockets, swirl is used to retain the uranium atoms in the rocket chamber. With these applications in mind, Back1 and Muthanna and Nath2 have obtained the similarity solutions for a low-speed three-dimensional steady laminar compressible boundary layer with swirl inside an axisymmetric surface of variable cross section. The aim of the present analysis is to study the effect of massive blowing rates on the unsteady laminar swirling compressible boundary-layer flow of an axisymmetric body of arbitrary cross section when the freestream velocity and blowing rate vary with time. The type of swirl considered here is that of a free vortex superimposed on the longitudinal flow of a compressible fluid with variable properties. The analysis is applicable to external flow over a body as well as internal flow along a surface. For the case of external flow, strong blowing can have significant use in cooling the surface of hypervelocity vehicles, particularly when ablation occurs under large aerodynamic or radiative heating, but there may not be such an important application of strong blowing in the case of internal flow. The governing partial differential equations have been solved numerically using an implicit finite difference scheme with a quasilinearization technique.3 High temperature gas effects, such as radiation, dissociation, and ionization, etc., are not investigated. The nomenclature is usually that of Ref. 4 and is listed in the full paper.

Suboptimal Midcourse Guidance of Interceptors for High-Speed Targets with Alignment Angle Constraint

Using the recently developed computationally efficient model predictive static programming and a closely related model predictive spread control concept, two nonlinear suboptimal midcourse guidance laws are presented in this paper for interceptors engaging against incoming high-speed ballistic missiles. The guidance laws are primarily based on nonlinear optimal control theory, and hence imbed effective trajectory optimization concepts into the guidance laws. Apart from being energy efficient by minimizing the control usage throughout the trajectory (minimum control usage leads to minimum turning, and hence leads to minimum induced drag), both of these laws enforce desired alignment constraints in both elevation and azimuth in a hard-constraint sense. This good alignment during midcourse is expected to enhance the effectiveness of the terminal guidance substantially. Both point mass as well as six-degree-of-freedom simulation results (with a realistic inner-loop autopilot based on dynamic inversion) are presented in this paper, which clearly shows the effectiveness of the proposed guidance laws. It has also been observed that, even with different perturbations of missile parameters, the performance of guidance is satisfactory. A comparison study, with the vector explicit guidance scheme proposed earlier in the literature, also shows that the newly proposed model-predictive-static-programming-based and model-predictive-spread-control-based guidance schemes lead to lesser lateral acceleration demand and lesser velocity loss during engagement.