An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Unsteady mixed convection flow of a thermomicropolar fluid on a long thin vertical cylinder

The unsteady laminar mixed convection boundary layer flow of a thermomicropolar fluid over a long thin vertical cylinder has been studied when the free stream velocity varies with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite difference scheme in combination with the quasilinearization technique. The results show that the buoyancy, curvature and suction parameters, in general, enhance the skin friction, heat transfer and gradient of microrotation, but the effect of injection is just opposite. The skin friction and heat transfer for the micropolar fluid are considerably less than those for the Newtonian fluids. The effect of microrotation parameter is appreciable only on the microrotation gradient. The effect of the Prandtl number is appreciable on the skin friction, heat transfer and gradient of microtation.

Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

Optimal design of multiproduct batch chemical plant using NSGA-II

The optimal design of a multiproduct batch chemical plant is formulated as a multiobjective optimization problem, and the resulting constrained mixed-integer nonlinear program (MINLP) is solved by the nondominated sorting genetic algorithm approach (NSGA-II). By putting bounds on the objective function values, the constrained MINLP problem can be solved efficiently by NSGA-II to generate a set of feasible nondominated solutions in the range desired by the decision-maker in a single run of the algorithm. The evolution of the entire set of nondominated solutions helps the decision-maker to make a better choice of the appropriate design from among several alternatives. The large set of solutions also provides a rich source of excellent initial guesses for solution of the same problem by alternative approaches to achieve any specific target for the objective functions

A mixed-split scheme for 2-D DPCM based LSF quantization

In this paper a mixed-split scheme is proposed in the context of 2-D DPCM based LSF quantization scheme employing split vector product VQ mechanism. Experimental evaluation shows that the new scheme is successfully being able to show better distortion performance than existing safety-net scheme for noisy channel even at considerably lower search complexity, by efficiently exploiting LSF trajectory behavior across the consecutive speech frames.

Stability and transition in the flow of polymer solutions

The linear stability analysis of a plane Couette flow of viscoelastic fluid have been studied with the emphasis on two dimensional disturbances with wave number k similar to Re-1/2, where Re is Reynolds number based on maximum velocity and channel width. We employ three models to represent the dilute polymer solution: the classical Oldroyd-B model, the Oldroyd-B model with artificial diffusivity and the non-homogeneous polymer model. The result of the linear stability analysis is found to be sensitive to the polymer model used. While the plane Couette flow is found to be stable to infinitesimal disturbances for the first two models, the last one exhibits a linear instability.

Studies on optical absorption and photoluminescenceproperties of Pr3+ and Nd3+ doped mixed alkali chloroborate glasses

This article presents the optical absorption and emission properties of Pr3+ and Nd3+ doped two different mixed alkali chloroborate glass matrices of the type 70B(2)O(3)center dot xLiCl center dot(30 - x)NaCl and 70B(2)O(3)center dot xLiCl center dot(30 - x)KCl (x = 5, 10, 15.20 and 25). The variation of Judd-Ofelt parameters (Omega(2), Omega(4) and Omega(6)), total radiative transition probabilities (A(T)), radiative lifetimes (tau(R)) and emission cross-sections (sigma(p)) with the variation of alkali contents in the glass matrix have been discussed in detail. The changes in the peak wavelengths of the hypersensitive transition and intensity parameters with x are correlated to the structural changes in the host matrix. The estimated radiative lifetimes of certain excited states of Pr3+ and Nd3+ in these two glass matrices are reported. Peak stimulated emission cross-sections (sigma(p)) are reported for the observed emission transitions of Pr3+ and Nd3+ ions. Branching ratios (beta) of the observed emission transitions obtained from the Judd-Ofelt theory are compared with the values obtained from the emission spectra. (C) 2010 Elsevier B.V. All rights reserved.

Mixed-mode stress intensity factors for arbitrarily oriented cracks in cylindrical shells under axial pull and torsion

Results of photoelastic investigations conducted on cylindrical tubes (made of Araldite material) containing cracks oriented at 0°, 30°, 45°, 60° and 90° to the axis of the tube and subjected to axial and torsional loads are reported. The stress-intensity factors (SIFs) were determined by analysing the crack-tip stress fields. Smith and Smith's method [Engng Fracture Mech.4, 357–366 (1972)] and a new method developed by the authors by modifying Rakesh et al.'s method [Proc. 26th Congress of ISTAM, India (1981)] were employed to evaluate the mixed-mode SIFs.

A simple technique for approximate solutions of the Falkner-Skan equation

A simple, sufficiently accurate and efficient method for approximate solutions of the Falkner-Skan equation is proposed here for a wide range of the pressure gradient parameter. The proposed approximate solutions are obtained utilising a known solution of another differential equation.

ESR studies of X-irradiated strontium mixed calcium tartrate crystals

The electron spin resonance spectra of X-ray irradiated single crystals of strontium doped calcium tartrate tetrahydrate (CST) with molecular formula Ca0.88Sr0.12C4H4O6.4H(2)O grown in gels has been investigated. Only one species of free radical but with two magnetically unequivalent sites was observed at room temperature. The free radical was found to be the result of the splitting of a C-II bond adjacent to both the hydroxyl and carboxyl groups. The a factor was found to be slightly anisotropic. Couplings with two H nuclei, believed to be the proton of the OH group attached directly to the unsaturated asymmetric carbon atom and the proton attached directly to the: other asymmetric carbon atom of the molecule were observed. The principal g-values were found to be 2.0030, 2.0017, 2.0027. The principal elements of the nuclear coupling are 7.45, 6.59, 4.28 and 8.56, 7.22, 18.71 G, respectively. The radical was found to be very stable. (C) 2000 Elsevier Science Ltd. All rights reserved.

Semi-similar solutions of the unsteady compressible second-order boundary layer flow at the stagnation point

Semi-similar solutions of the unsteady compressible laminar boundary layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer are studied for all the second-order boundary layer effects when the free stream velocity varies arbitrarily with time. The set of partial differential equations governing the unsteady compressible second-order boundary layers representing all the effects are derived for the first time. These partial differential equations are solved numerically using an implicit finite-difference scheme. The results are obtained for two particular unsteady free stream velocity distributions: (a) an accelerating stream and (b) a fluctuating stream. It is observed that the total skin friction and heat transfer are strongly affected by the surface mass transfer and wall temperature. However, their variation with time is significant only for large times. The second-order boundary layer effects are found to be more pronounced in the case of no mass transfer or injection as compared to that for suction. Résumé Des solutions semi-similaires d'écoulement variable compressible de couche limite sur des corps bi-dimensionnels thermique, sont étudiées pour tous les effets de couche limite du second ordre, lorsque la vitesse de l'écoulement libre varie arbitrairement avec le temps. Le systéme d'équations aux dérivées partielles représentant tous les effets est écrit pour la premiére fois. On le résout numériquement á l'aide d'un schéma implicite aux différences finies. Les résultats sont obtenus pour deux cas de vitesse variable d'écoulement libre: (a) un écoulement accéléré et (b) un écoulement fluctuant. On observe que le frottement pariétal total et le transfert de chaleur sont fortement affectés par le transfert de masse et la température pariétaux. Néanmoins, leur variation avec le temps est sensible seulement pour des grandes durées. Les effets sont trouvés plus prononcés dans le cas de l'absence du transfert de masse ou de l'injection par rapport au cas de l'aspiration.

Extension of Darken's Quadratic Formalism to Dilute Multicomponent Solutions

Darken's quadratic formalism is extended to multicomponent solutions. Equations are developed for the representation of the integral and partial excess free energies, entropies and enthalpies in dilute multicomponent solutions. Quadratic formalism applied to multicomponent solutions is thermodynamically consistent. The formalism is compared with the conventional second order Maclaurin series or interaction parameter representation and the relations between them are derived. Advantages of the quadratic formalism are discussed.