Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

A Proportional plus Multiresonant Controller for Three-Phase Four-Wire High-Frequency Link Inverter

A new solution for unbalanced and nonlinear loads in terms of power circuit topology and controller structure is proposed in this paper. A three-phase four-wire high-frequency ac-link inverter is adopted to cater to such loads. Use of high-frequency transformer results in compact and light-weight systems. The fourth wire is taken out from the midpoint of the isolation transformer in order to avoid the necessity of an extra leg. This makes the converter suitable for unbalanced loads and eliminates the requirements of bulky capacitor in half-bridge inverter. The closed-loop control is carried out in stationary reference frame using proportional + multiresonant controller (three separate resonant controller for fundamental, fifth and seventh harmonic components). The limitations on improving steady-state response of harmonic resonance controllers is investigated and mitigated using a lead-lag compensator. The proposed voltage controller is used along with an inner current loop to ensure excellent performance of the power converter. Simulation studies and experimental results with 1 kVA prototype under nonlinear and unbalanced loading conditions validate the proposed scheme.

Direct torque control schemes for split-phase induction machine

In this paper, direct torque control (DTC) algorithms for a split-phase induction machine (SPIM) are established. An SPIM has two sets of three-phase stator windings, with a shift of thirty electrical degrees between them. The significant contributions of this paper are: 1) two new methods of DTC technique for an SPIM are developed, called Resultant Flux Control Method and Individual Flux Control Method and 2) advantages and disadvantages of both methods are discussed. High torque ripple is a disadvantage for three-phase DTC. It is found that torque ripple in an SPIM can be significantly reduced without increasing the switching frequency.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Elastic behaviour of matter under very high pressures - Uniform compression

In order to study the elastic behaviour of matter when subjected to very large pressures, such as occur for example in the interior of the earth, and to provide an explanation for phenomena like earthquakes, it is essential to be able to calculate the values of the elastic constants of a substance under a state of large initial stress in terms of the elastic constants of a natural or stress-free state. An attempt has been made in this paper to derive expressions for these quantities for a substance of cubic symmetry on the basis of non-linear theory of elasticity and including up to cubic powers of the strain components in the strain energy function. A simple method of deriving them directly from the energy function itself has been indicated for any general case and the same has been applied to the case of hydrostatic compression. The notion of an effective elastic energy-the energy require to effect an infinitesimal deformation over a state of finite strain-has been introduced, the coefficients in this expression being the effective elastic constants. A separation of this effective energy function into normal co-ordinates has been given for the particular case of cubic symmetry and it has been pointed out, that when any of such coefficients in this normal form becomes negative, elastic instability will set in, with associated release of energy.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

Robust fixed order lateral H-2 controller for micro air vehicle

This paper presents a robust fixed order H-2 controller design using Strengthened discrete optimal projection equations, which approximate the first order necessary optimality condition. The novelty of this work is the application of the robust H-2 controller to a micro aerial vehicle named Sarika2 developed in house. The controller is designed in discrete domain for the lateral dynamics of Sarika2 in the presence of low frequency atmospheric turbulence (gust) and high frequency sensor noise. The design specification includes simultaneous stabilization, disturbance rejection and noise attenuation over the entire flight envelope of the vehicle. The resulting controller performance is comprehensively analyzed by means of simulation.

High temperature mechanical properties of thermal barrier coated superalloy applied to combustor liner of aero engines

High temperature load controlled fatigue, hot tensile and accelerated creep properties of thermal barrier coated (TBC) Superni C263 alloy used as a candidate material in combustor liner of aero engines are highlighted in this paper. Acoustic emission technique has been utilised to characterise the ductile-brittle transition teperature the bond coat. Results revealed that the DBTT (ductile to brittle transition temperature) of this bond coat is around 923 K, which is in close proximity to the value reported for CoCrAlY type of bond coat. Finite element technique, used for analysing the equivalent stresses in the bond coat well within the elastic limit, revealed the highest order of equivalent stress at 1073 K as the bond coat is ductile above 923 K. The endurance limit in fatigue and the life of TBC coated composite under accelerated creep conditions are substantially higher than those of the substrate material. Fractographic features at high stresses under fatigue showed intergranular cleavage whereas those at low stresses were transgranular and ductile in nature. Delamination of the bond coat and spallation of the TBC at high stresses during fatigue was evident. Unlike in the case of fatigue, the mode of fracture in the substrate at very high stresses was transgranular whereas that at low stresses was intergranular in creep.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

NMR study of ammonium halides under high pressure

Wide-line c.w. proton resonance investigations have been carried out on the ammonium halides, namely, ammonium chloride, ammonium bromide and ammonium iodide in the temperature range between 77 and 300 K and in the pressure range between 1 bar and 14 kbar. It has been found that the narrow iodide spectrum at 77 K broadens under the application of hydrostatic pressure. The barrier height for the ammonium ion motion in ammonium iodide under pressure has been estimated by carrying out a temperature variation study. The rotational potential for the motion of ammonium ion in ammonium iodide at 1 bar and 14 kbar has been calculated using earlier theoretical models and compared with values calculated for ammonium chloride and bromide. The barrier height in the case of ammonium iodide under pressure is found to be of the same order of magnitude as the value obtained in the case of ammonium bromide at atmospheric pressure indicating that the high pressure phase of ammonium iodide is likely to have the same structure as the low temperature ordered CsCl phase found in the case of the chloride and the bromide. The increase in the potential barrier height in the case of ammonium iodide under pressure indicates that the reorientational motion executed by the ammonium ions is inhibited by the application of pressure. This is also confirmed by the broadening of the spectral line at 77 K under the application of pressure.

High-Temperature (1023 K to 1273 K 750 degrees C to 1000 degrees C]) Plastic Deformation Behavior of B-Modified Ti-6Al-4V Alloys: Temperature and Strain Rate Effects

A minor addition of B to the Ti-6Al-4V alloy, by similar to 0.1 wt pct, reduces its as-cast prior beta grain size by an order of magnitude, whereas higher B content leads to the presence of in situ formed TiB needles in significant amounts. An experimental investigation into the role played by these microstructural modifications on the high-temperature deformation behavior of Ti-6Al-4V-xB alloys, with x varying between 0 wt pct and 0.55 wt pct, was conducted. Uniaxial compression tests were performed in the temperature range of 1023 K to 1273 K (750 degrees C to 1000 degrees C) and in the strain rate range of 10(-3) to 10(+1) s(-1). True stress-true strain responses of all alloys exhibit flow softening at lower strain rates and oscillations at higher strain rates. The flow softening is aided by the occurrence of dynamic recrystallization through lath globularization in high temperature (1173 K to 1273 K 900 degrees C to 1000 degrees C]) and a lower strain rate (10(-2) to 10(-3) s(-1)) regime. The grain size refinement with the B addition to Ti64, despite being marked, had no significant effect on this. Oscillations in the flow curve at a higher strain rate (10(0) to 10(+1) s(-1)), however, are associated with microstructural instabilities such as bending of laths, breaking of lath boundaries, generation of cavities, and breakage of TiB needles. The presence of TiB needles affected the instability regime. Microstructural evidence suggests that the matrix cavitation is aided by the easy fracture of TiB needles.

A DC-to-Three-Phase-AC High-Frequency Link Converter With Compensation for Nonlinear Distortion

This paper focuses on a new high-frequency (HF) link dc-to-three-phase-ac power converter. The least number of switching devices among other HF link dc-to-three-phase-ac converters, improved power density due to the absence of devices of bidirectional voltage-blocking capability, simple commutation requirements, and isolation between input and output are the integral features of this topology. The commutation process of the converter requires zero portions in the link voltage. This causes a nonlinear distortion in the output three-phase voltages. The mathematical analysis is carried out to investigate the problem, and suitable compensation in modulating signal is proposed for different types of carrier. Along with the modified modulator structure, a synchronously rotating reference-frame-based control scheme is adopted for the three-phase ac side in order to achieve high dynamic performance. The effectiveness of the proposed scheme has been investigated and verified through computer simulations and experimental results with 1-kVA prototype.

On the High Frequency Dielectric Behavior of Castor Oil

The low frequency dielectric behavior of castor oil (a vegetable oil) has been analyzed quite exhaustively in the context of its application as impregnant in capacitors. For the sake of completeness and in order to understand the relaxation phenomena in this liquid dielectric, this high frequency dielectric study was undertaken. In order to compare its properties with a liquid dielectric used in similar application and whose high frequency behavior has been quite well analyzed, Arochlor 1476 was studied. It is observed that both liquids have distributed relaxation times. The distribution parameters together with the two distinct relaxation times have been calculated by measuring the average relaxation time. It has been found that the distinct relaxation times thus calculated represent the dielectric behavior quite satisfactorily. The average dipole moments, dipole radii and thermal activation energies for dipole relaxation have also been evaluated.

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

Two-Fermi liquid model for high Tc superconductivity involving suppression of tunnelling by decoherence

We consider a model system of two interacting Fermi-liquids, one of which is light and the other much heavier. In the normal state the lighter component provides a quantum mechanical bath coupled 'ohmically' to the heavier component in the sense of Caldeira and Leggett, suppressing thereby the band (tunnelling) matrix elements of the heavier component. Thus we lose the energy of delocalization. On the other hand, a superconducting ordering stiffens the bath spectral function at low energies and so restores the tunnelling. The resulting regain of the delocalization energy bootstraps so as to stabilize the superconducting order that caused it. It is conceivable that the motions parallel to the easy ab-plane and along the hard c-axis may also effectively correspond to the light and the heavy Fermi-liquids, respectively.