A precessing and nutating beam with a tip mass

Stability analysis of elastic vibration of a simultaneously precessing and nutating beam with a tip mass is attempted here. A simple two-degree of freedom model is considered to have an understanding of the terms appearing in the parametric equations with precession softening and centrifugal stiffening. The stability margin is determined using a variant of Hill's method using precession and nutation speeds as parameters. It is found that the stability of an only precessing beam depends on the inclination of the beam-centerline with the axis of precession. A precessing beam with very slow nutation is unstable because of its passage through a particular range of nutation angle.     

On Parametric Generalized Quasi-Variational Inequalities

In this paper, by using the projection method of Dafermos (Ref. 1), we study the behavior and sensitivity analysis of the solution set for a class of parametric generalized quasi-variational inequalities. Our approach and results are new and have a strong geometric flavor.     

Optical amplitude multiplexing through parametric amplification in optical fibers

We propose a new technique that uses parametric amplification in optical fibers to combine two binary signals into a single quaternary amplitude-shift keying (4-ASK) signal. We develop a theoretical model to predict the power level distribution of the 4-ASK signals as a function of the extinction ratios of the input binary signals. Computer simulation results agree with the predictions of this theoretical model within a 0.9 dB margin. We also analyze the application of this technique to the generation of quaternary-amplitude optical packets, which are attractive for allowing the label to be transmitted in the same bandwidth and simultaneously to the payload. Our results indicate that such optical packets may be propagated through lengths comparable to those involved in metropolitan area networks.     

Sensitivity Analysis of Asset Flow Differential Equations and Volatility Comparison of Two Related Variables

In this study, I apply forward sensitivity analysis to the dynamical system of nonlinear asset flow differential equations (AFDEs). I find that all parameters in AFDEs are needed and can be estimated from market prices and net asset values data. Moreover, the market price is the most fluctuating state variable, and the coefficient for the trend-based investor' sentiment is the dominant parameter. Furthermore, I define and compare the extreme value-based volatilities of market price and net asset value for closed-end funds. I find that the extreme value-based volatility of market price is higher than that of net asset value for the vast majority of closed-end funds for both overlapping and non-overlapping cases.     

Analysis of parametric oscillatory instability in Fabry-Perot cavity with Gauss and Laguerre-Gauss main mode profile

We calculate the parametric instabilities in Fabry-Perot cavities of advanced VIRGO and LIGO interferometers with different main mode profiles. All unstable combinations of elastic and Stokes modes both for the case with TEM₀₀ and LG₃₃ as a carriers are deduced.     

Quantum effect on parametric amplification characteristics in piezoelectric semiconductors

Using QHD model the parametric interaction of a laser radiation in an unmagnetised piezoelectric semiconductor has been studied. It is found that the Bohm potential in the electron dynamics enhances the gain coefficient of parametrically generated modes whereas reduces the threshold pump intensity.     

Parametric resonance in acoustically levitated water drops

Liquid drops can be suspended in air with acoustic levitation method. When the sound pressure is periodically modulated, the levitated drop is usually forced into an axisymmetric oscillation. However, a transition from axisymmetric oscillation into sectorial oscillation occurs when the modulation frequency approaches some specific values. The frequency of the sectorial oscillation is almost exactly half of the modulation frequency. It is demonstrated that this transition is induced by the parametric resonance of levitated drop. The natural frequency of sectorial oscillation is found to decrease with the increase of drop distortion extent.     

Continuity of solutions for parametric variational inequalities in Banach space

We consider here a type of pseudo-monotone parametric variational inequalities on a class of Banach spaces and show that such problems admit continuous (with respect to the parameter) solutions, as long as generic existence and uniqueness conditions for these solutions are satisfied. In particular, we show that such results are valid on a class of Banach spaces whenever we deal with strong pseudo-monotonicity, while others are valid in Hilbert spaces, whenever strict monotonicity is present. We also provide examples to illustrate the new results.     

Determination of the analytical parametric relationship for output spectrum of Volterra systems based on its parametric characteristics

The output frequency response function (OFRF) of Volterra systems can be described as a polynomial function of model parameters. However, the analytical determination of the OFRF is very computationally intensive, especially for higher order OFRF. To circumvent this problem, a numerical method can be adopted, provided that a series of simulation or experimental data for this polynomial function are given. In this study, it is theoretically shown that the analytical parametric relationship of OFRF up to any order can be determined accurately by using a simple Least Square method and every specific component of the output spectrum can also be determined explicitly, based on the OFRF's parametric characteristics. Practical techniques to obtain a unique and accurate solution for the Least Square method are discussed. This study provides a fundamental result for the determination of the analytical parametric relationship for this kind of system polynomial functions by using numerical methods.