Sharif Digital Repository

The effects of the entanglement of the inflaton field which initially entangled with those of another field on observables like power spectrum are known in the context of the Schrödinger field theory. To clarify this effect in the Heisenberg picture, there were some attempts to construct the initial entangled state by making use of an entangled transformation (like Bogoliubov transformation) between the Bunch-Davies vacuums and squeezed states. We study the role of the time-dependent entangled transformation in the Schrödinger field theory. We derive the relation between two vacuum states which their mode functions are transformed by the entangled transformation in Schrödinger picture. We... 

In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations. © 2009 Elsevier Ltd. All rights reserved  

Wing rock motion can be described as an oscillatory bank angle buildup to a constant amplitude rocking motion. This phenomenon is realized for delta wings with more than 74 degrees leading edge sweep angles, where asymmetric vortex shedding occurs before vortex breakdown. For wings with sweep angles less than 74 degrees, rocking motion occurs if the wing is in a yawed situation. In this paper, a new and simple method has been presented to predict the amplitude and frequency of oscillation of delta wings undergoing rocking motion at high angles of attack. The predicted data are in excellent agreement with those obtained by experimental studies for wings with sweep angles of 76 and 80 degrees  

In this paper, extensive experimental tests were carried out for an aerodynamic characterization of the airfoil cross-section of a wind turbine blade. The wind turbine blade cross-sections are usually exposed to unsteady pitch and plunge oscillations. One way to increase the power of blade, is to improve it's aerodynamic performance, so it is necessary to study and compare the unsteady aerodynamic behavior of the airfoil. The aerodynamic behavior of turbine blades are dependent on several parameters including initial angle of attack, reduced frequency and oscillation amplitude. In this study, reduced frequency and oscillation amplitude assumed constant and the initial angle of attack of the... 

In this paper, a novel method for nonlinear analysis of noise in microwave oscillators is presented. Based on harmonic balance, the method is general from the point-of-view of circuit topology, noise sources spectral distribution, and their cross correlation. In this method, the effects such as frequency conversion and frequency modulation are considered simultaneously in a unified treatment. Relatively precise estimations for the output signal spectral density of an oscillator is practically obtained. © 2000 IEEE  

An alternative approach to analysis, design and implementation of injection-locked quadrature oscillators is proposed in this paper. A novel technique is presented which allows the effects of the mismatches due to imbalances in the I/Q paths in transceivers (TRX) to be mitigated, and hence the orthogonality of the these vectors be maintained. This technique alleviates the effects of imbalances in a transceiver between I/Q paths, which would otherwise pose many threats to the performance of the system, namely image rejection ratio (IRR) degradation, gain reduction in mixers, desensitization of the RX, and ect. As a design example, a CMOS quadrature oscillator (QOSC) at the frequency of 3.5GHz... 

In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques and introduce some new ones in line with QFT methods. Moreover, we investigate the case of more than one oscillator to see how the frequencies of small oscillations change when non-linear terms are added to a linear system and observe an interesting beat phenomenon in degenerate coupled... 

Recently, a class of fractional multi-frequency oscillators, constructed based on using n integrators and n half-order ones, has been introduced, whose steady-state responses contain sinusoidal components with 0.5 (3 n- 1 ) number of selectable frequencies. In this paper, the structure of the introduced multi-frequency oscillator is modified such that, notwithstanding the frequency content preservation, the number of its involved integrators is reduced. With no effect on the frequency content of the generated oscillations, this modification causes that the circuitry implementation of the considered class of multi-frequency oscillators can be done with a less number of energy storage... 

This paper deals with investigating the maximum number of frequencies generated by an oscillator in the case that a half number of integrators in the conventional dynamic structure of this oscillator are replaced by fractional integrators with an identical order. First, an upper bound for the maximum number of frequencies, which can exist in a steady state response of the oscillator, with respect to the number of integrators, is obtained. Then, on the basis of the recent advances in the field of determinant-based representations of bivariate polynomials, a lower bound is found for the maximum number of sinusoidal components in the steady state oscillations generated by the oscillator. A... 

In this paper, an effective way is proposed for reduction of oscillations in the response of dynamical systems. In this regard, it is analytically shown that the undesirable oscillations in the response of dynamical systems can be reduced using a simple input shaping fractional order filter. The effectiveness of the proposed fractional calculus based technique is numerically verified in reduction of oscillations in a mass-spring-damper system, a low-pass Chebyshev filter, and a PI-controlled two-mass drive system  

In this paper, a novel approach is proposed for solving the nonlinear problems based on the collocation and energy balance methods (EBMs). Rational approximation is employed as an initial guess and then it is combined with EBM and collocation method for solving nonlinear oscillators with cubic term. Obtained frequency amplitude relationship is compared with exact numerical solution and subsequently, a very excellent accuracy will be revealed. According to the numerical comparisons, this method provides high accuracy with 0.03% relative error for Duffing equation with strong nonlinearity in the second-order of approximation. Furthermore, achieved results are compared with other types of... 

We consider the nonlinear Euler differential equation t2 x″ + g (x) = 0. Here g (x) satisfies x g (x) > 0 for x ≠ 0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t2 x″ + a (t) g (x) = 0. © 2006 Elsevier Inc. All rights reserved  

This paper presents a digital hardware implementation of a frequency adaptive Hopf oscillator along with investigation on systematic behavior when they are coupled in a population. The mathematical models of the oscillator are introduced and compared in sense of dynamical behavior by using system-level simulations based on which a piecewise-linear model is developed. It is shown that the model is capable to be implemented digitally with high efficiency. Behavior of the oscillators in different network structures to be used for dynamic Fourier analysis is studied and a structure with more precise operation which is also more efficient for FPGA-based implementation is implemented. Conceptual... 

An analytic method to predict the oscillation amplitude and supply current values of a differential CMOS oscillator is presented. A simplified model to predict the phase noise performance for this type of oscillator is developed. Using this method, it becomes possible to design an optimised oscillator in terms of a minimum phase noise and low power consumption. The validity of the method has been verified by designing a LC CMOS oscillator using 0.25 μm CMOS technology. The predictions are in good agreement with simulation results over a wide range of the supply voltage  

Two important drawbacks of parallel coupled LC quadrature oscillators (P-QOSC) which have not heretofore been addressed thoroughly in the literature are obviated simultaneously in this paper. The first, has to do with the inevitable off-tune operation of the tank which results in quality factor (Q) degradation, and hence, phase noise deterioration. The other, stems from process, voltage, and temperature (PVT) variations which exacerbate quadrature accuracy. Here, a feedback loop is presented which generates a control signal by mixing the quadrature outputs and tunes the injection strength in the coupled oscillators autonomously. A complex coupling factor is implemented which compensates the... 

A systematic method to design high power and high efficiency mm-wave fundamental oscillators is presented. By using a linear time variant method, we first obtain the optimum conditions and show that these conditions can be significantly different for high power and high efficiency fundamental oscillation. Next, we propose a modified multistage ring oscillator with interstage passive networks to exploit the full capacity of the transistors in terms of output power or efficiency. Analytical expressions are also derived to determine the value of passive elements used in the oscillator. To verify the validity of the method, a 77-GHz two-stage (differential) VCO is designed in a 65-nm CMOS... 

We use a nonlinear analytic approach to predict the main oscillation mode power and spurious levels in ultrapure microwave optoelectronic oscillators (OEOs). This approach takes into account N simultaneously mode falling inside the RF filter bandwidth and calculates all the dominant InterModulation Products (IMPs) that fall in the fundamental zone. We show that nonlinear microwave photonic links exhibit the capture effect. By considering this effect, we derive analytical expressions that govern the behavior of the OEOs in the steady state. We find that when the small-signal open-loop gain is increased beyond a critical value, OEOs start a multimode operation from which the spurious levels... 

Phase noise is one of the most important specifications of microwave oscillators. External factors such as mechanical vibrations increase the phase noise of the oscillator. A novel technique is introduced to reduce vibration-induced phase noise using inter-injection locking of two coupled oscillators. Two similar oscillators with equal free running frequencies are chosen and are subjected to sinusoidal vibration. The mechanical configuration is such that vibration sensitivity vector increases the frequency of one oscillator and decreases the other one's frequency of oscillation. Coupling these two oscillators using inter-injection locking, the common after-lock frequencies of both...