Analysis of the nonlinear vibration of a two-mass–spring system with linear and nonlinear stiffness

An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. The main contribution of this research is twofold. First, it introduces the transformation of two nonlinear differential equations for a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment of a nonlinear differential system by linearization coupled with Newton’s method. Secondly, the major section is the solving of the governing nonlinear differential equation where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using a first-order variational approach. The aforementioned approach proposed by J.H. He, who actually developed the method, is exactly He’s variational method. This approach is an explicit method with high validity for resolving strong nonlinear oscillation system problems. Two examples of nonlinear two-degree-of-freedom mass–spring systems are analyzed, and verified with published results and exact solutions. The method can be easily extended to other nonlinear oscillations and so could be widely applicable in engineering and science.     

Ring vortex scenario in engraved champagne glasses

The simple idea this study rests on is that one cannot be concerned by the bubbling and aromatic exhalation events in champagne tasting without being interested in the study of the flow mixing mechanisms inside the glass. Indeed, a key assumption is that a strong link of causality may exist between inherent liquid-phase flow structures due to bubble motion and the flavors exhalation process. This is the reason why, to underscore the impact of glass-shape and glass-engravement conditions on mixing flow phenomena, classical flow visualization techniques were used to capture fluid motion in traditional flutes and coupes poured with champagne. Laser tomography combined with fluorescent dyes and solid tracers have been used to give the quasi-instantaneous velocity field from which streamline patterns are deduced as well as the vorticity convection.     

Metal contacts to n-GaN

Al, Au, Ti/Al and Ti/Au contacts were prepared on n-GaN and annealed up to 900 °C. The structure, phase and morphology were studied by cross-sectional transmission and scanning electron microscopy as well as by X-ray diffraction (XRD), the electrical behaviour by current-voltage measurements. It was obtained that annealing resulted in interdiffusion, lateral diffusion along the surface, alloying and bowling up of the metal layers. The current-voltage characteristics of as-deposited Al and Ti/Al contacts were linear, while the Au and Ti/Au contacts exhibited rectifying behaviour. Except the Ti/Au contact which became linear, the contacts degraded during heat treatment at 900 °C. The surface of Au and Ti/Au contacts annealed at 900 °C have shown fractal-like structures revealed by scanning electron microscopy. Transmission electron microscopy and XRD investigations of the Ti/Au contact revealed that Au diffused into the n-GaN layer at 900 °C. X-ray diffraction examinations showed, that new Ti₂N, Au₂Ga and Ga₃Ti₂ interface phases formed in Ti/Au contact at 900 °C, new Ti₂N phase formed in Ti/Al contact at 700 and 900 °C, as well as new AlN interface phase developed in Ti/Al contact at 900 °C.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.     

Femtosecond time-resolved interferences of resonantly excited excitons in bulk GaN

It is shown that excitonic transients of bulk GaN can be accurately measured by an interferometric correlation technique used in reflection geometry. This is demonstrated for resonantly excited excitons in high quality GaN epilayers. The interferograms exhibit a clear modulation of the signal due the quantum beats between A and B excitons. The period of these beats is in good agreement with the A–B exciton energy splitting measured by means of frequency-resolved reflectivity. The decrease of the overall signal is mainly connected to the crystal quality and strongly dependent on the inhomogeneous broadening which can be extracted from the correlation spectra. These results are in agreement with numerical calculations based on the Fourier transform determination of the time-resolved reflection coefficient in the framework of linear semi-classical theory carried out in order to obtain the autocorrelation response.     

Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.