A numerical technique for solving nonlinear singularly perturbed delay differential equations

This paper presents a numerical technique for solving nonlinear singularly perturbed delay differential equations. Quasilinearization technique is applied to convert the nonlinear singularly perturbed delay differential equation into a sequence of linear singularly perturbed delay differential equations. An exponentially fitted spline method is presented for solving sequence of linear singularly perturbed delay differential equations. Error estimates of the method is discussed. Numerical examples are solved to show the applicability and efficiency of the proposed scheme

A Case of Neglected Bilateral Anterior Shoulder Dislocation: A Rare Entity with Unusual Mechanism of Injury

Bilateral shoulder dislocations are rare, and if they occurred, posterior type of dislocations is common. Bilateral anterior shoulder dislocations are very rare and occur due to trauma with unique mechanism of injury. We report a case of unreduced simultaneous bilateral anterior dislocations of shoulder without associated fractures in a forty-year-old man following a unique mechanism of injury; both hands of the patient were pulled from either side. To the best of our knowledge, this unusual mechanism of injury has not been reported in the literature

Fiber guiding at the Dirac frequency beyond photonic bandgaps

Light trapping within waveguides is a key practice of modern optics, both scientifically and technologically. Photonic crystal fibers traditionally rely on total internal reflection (index-guiding fibers) or a photonic bandgap (photonic-bandgap fibers) to achieve field confinement. Here, we report the discovery of a new light trapping within fibers by the so-called Dirac point of photonic band structures. Our analysis reveals that the Dirac point can establish suppression of radiation losses and consequently a novel guided mode for propagation in photonic crystal fibers. What is known as the Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. We find the unexpected phenomenon of wave localization at this point beyond photonic bandgaps. This guiding relies on the Dirac point rather than total internal reflection or photonic bandgaps, thus providing a sort of advancement in conceptual understanding over the traditional fiber guiding. The result presented here demonstrates the discovery of a new type of photonic crystal fibers, with unique characteristics that could lead to new applications in fiber sensors and lasers. The Dirac equation is a special symbol of relativistic quantum mechanics. Because of the similarity between band structures of a solid and a photonic crystal, the discovery of the Dirac-point-induced wave trapping in photonic crystals could provide novel insights into many relativistic quantum effects of the transport phenomena of photons, phonons, and electrons

The numerical simulation of convection delayed dominated diffusion equation

In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution

The numerical simulation of convection delayed dominated diffusion equation

In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution

Novel Repetitive Control Technique for Three Phase Four Wire Shunt Active Power Filter

This paper presents a discrete dreary control procedure for three stage four wire (3P4W) shunt enthusiastic force channel (SEPF). By and large, the control plan for power gadgets includes two control circles: slow acting external voltage circle and speedy performing inside current control circle. The reference for inward current circle is occasional in climate and can't be basically followed by PI controller. The dreary regulators (RC) are notable for their following capacity of occasional sign and deal high addition at every one of the frequencies. The high increase in higher recurrence reach might lead towards unsteadiness. Hence, in proposed work, the standard RC is changed by square its affectability work. Fluffy rationale regulator is utilized in this task to improve the force quality. This methodology brings about low sufficiency of affectability work while offering profound indents at low to mid frequencies range and more modest scores at high frequencies. This control approach has been reproduced and execute on 3P4W SAPF