New phenomenon of nonlinear Regge trajectory and quantum dual string theory

The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.

A linearly-tunable OTA-C sinusoidal oscillator for low-voltage applications

A low-voltage, low-power OTA-C sinusoidal oscillator based on a triode-MOSFET transconductor is here discussed. The classical quadrature model is employed and the transconductor inherent nonlinear characteristic with input voltage is used as the amplitude-stabilization element. An external bias VTUNE linearly adjusts the oscillation frequency. According to a standard 0.8μm CMOS n-well process, a prototype was integrated, with an effective area of 0.28mm2. Experimental data validate the theoretical analysis. For a single 1.8V-supply and 100mV≤VTUNE≤250mV, the oscillation frequency fo ranges from 0.50MHz to 1.125MHz, with a nearly constant gain KVCO=4.16KHz/mV. Maximum output amplitude is 374mVpp @1.12MHz. THD is -41dB @321mVpp. Maximum average consumption is 355μW.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Radial basis function network applied to the linearization of a voltage controlled oscillator

An analog circuit that implements a radial basis function network is presented. The proposed circuit allows the adjustment of all shape parameters of the radial functions, i.e., amplitude, center and width. The implemented network was applied to the linearization of a nonlinear circuit, a voltage controlled oscillator (VCO). This application can be classified as an open-loop control in which the network plays the role of the controller. Experimental results have proved the linearization capability of the proposed circuit. Its performance can be improved by using a network with more basis functions. Copyright 2007 ACM.

Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

A note on non-linear phenomena in a non-ideal oscillator, with a snap-through truss absorber, including parameter uncertainties

This work considers the vibrating system that consists of a snap-through truss absorber coupled to an oscillator under excitation of an electric motor with an eccentricity and limited power, characterizing a non-ideal oscillator. It is aimed to use the non-linearity and quasi-zero stiffness of absorber (snap-through truss absorber) to obtain a significantly attenuation the jump phenomenon. There is also an interest to exhibit the reduction of Sommerfeld effect, to confirm the saturation phenomenon occurrence and show the power transfer in a non-linear structure, evidencing the pumping energy. As shown by simulations in this work, this absorber allows the energy pumping before and during the jump phenomenon, decreasing the higher amplitudes of considered system. Additionally, the occurrence of saturation phenomenon due use of snap-through truss absorber is verified. The analysis of parameter uncertainties was introduced. Sensitivity of system with parametric errors demonstrated a trustable system. © IMechE 2012.

Identification of nonlinear structures using discrete-time Volterra series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear control in an electromechanical transducer with chaotic behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torque

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.

Dynamical changes from harmonic vibrations of a limited power supply driving a Duffing oscillator

The harmonic oscillations of a Duffing oscillator driven by a limited power supply are investigated as a function of the alternative strength of the rotor. The semi-trivial and non-trivial solutions are derived. We examine the stability of these solutions and then explore the complex behaviors associated with the bifurcations sequences. Interestingly, a 3D diagram provides a global view of the effects of alternate strength on the appearance of chaos and hyperchaos on the system.

X-parameters based analytical design of non-linear microwave circuits Application to oscillator design

Resumen El diseño clásico de circuitos de microondas se basa fundamentalmente en el uso de los parámetros s, debido a su capacidad para caracterizar de forma exitosa el comportamiento de cualquier circuito lineal. La relación existente entre los parámetros s con los sistemas de medida actuales y con las herramientas de simulación lineal han facilitado su éxito y su uso extensivo tanto en el diseño como en la caracterización de circuitos y subsistemas de microondas. Sin embargo, a pesar de la gran aceptación de los parámetros s en la comunidad de microondas, el principal inconveniente de esta formulación reside en su limitación para predecir el comportamiento de sistemas no lineales reales. En la actualidad, uno de los principales retos de los diseñadores de microondas es el desarrollo de un contexto análogo que permita integrar tanto el modelado no lineal, como los sistemas de medidas de gran señal y los entornos de simulación no lineal, con el objetivo de extender las capacidades de los parámetros s a regímenes de operación en gran señal y por tanto, obtener una infraestructura que permita tanto la caracterización como el diseño de circuitos no lineales de forma fiable y eficiente. De acuerdo a esta filosofía, en los últimos años se han desarrollado diferentes propuestas como los parámetros X, de Agilent Technologies, o el modelo de Cardiff que tratan de proporcionar esta plataforma común en el ámbito de gran señal. Dentro de este contexto, uno de los objetivos de la presente Tesis es el análisis de la viabilidad del uso de los parámetros X en el diseño y simulación de osciladores para transceptores de microondas. Otro aspecto relevante en el análisis y diseño de circuitos lineales de microondas es la disposición de métodos analíticos sencillos, basados en los parámetros s del transistor, que permitan la obtención directa y rápida de las impedancias de carga y fuente necesarias para cumplir las especificaciones de diseño requeridas en cuanto a ganancia, potencia de salida, eficiencia o adaptación de entrada y salida, así como la determinación analítica de parámetros de diseño clave como el factor de estabilidad o los contornos de ganancia de potencia. Por lo tanto, el desarrollo de una formulación de diseño analítico, basada en los parámetros X y similar a la existente en pequeña señal, permitiría su uso en aplicaciones no lineales y supone un nuevo reto que se va a afrontar en este trabajo. Por tanto, el principal objetivo de la presente Tesis consistiría en la elaboración de una metodología analítica basada en el uso de los parámetros X para el diseño de circuitos no lineales que jugaría un papel similar al que juegan los parámetros s en el diseño de circuitos lineales de microondas. Dichos métodos de diseño analíticos permitirían una mejora significativa en los actuales procedimientos de diseño disponibles en gran señal, así como una reducción considerable en el tiempo de diseño, lo que permitiría la obtención de técnicas mucho más eficientes. Abstract In linear world, classical microwave circuit design relies on the s-parameters due to its capability to successfully characterize the behavior of any linear circuit. Thus the direct use of s-parameters in measurement systems and in linear simulation analysis tools, has facilitated its extensive use and success in the design and characterization of microwave circuits and subsystems. Nevertheless, despite the great success of s-parameters in the microwave community, the main drawback of this formulation is its limitation in the behavior prediction of real non-linear systems. Nowadays, the challenge of microwave designers is the development of an analogue framework that allows to integrate non-linear modeling, large-signal measurement hardware and non-linear simulation environment in order to extend s-parameters capabilities to non-linear regimen and thus, provide the infrastructure for non-linear design and test in a reliable and efficient way. Recently, different attempts with the aim to provide this common platform have been introduced, as the Cardiff approach and the Agilent X-parameters. Hence, this Thesis aims to demonstrate the X-parameter capability to provide this non-linear design and test framework in CAD-based oscillator context. Furthermore, the classical analysis and design of linear microwave transistorbased circuits is based on the development of simple analytical approaches, involving the transistor s-parameters, that are able to quickly provide an analytical solution for the input/output transistor loading conditions as well as analytically determine fundamental parameters as the stability factor, the power gain contours or the input/ output match. Hence, the development of similar analytical design tools that are able to extend s-parameters capabilities in small-signal design to non-linear ap- v plications means a new challenge that is going to be faced in the present work. Therefore, the development of an analytical design framework, based on loadindependent X-parameters, constitutes the core of this Thesis. These analytical nonlinear design approaches would enable to significantly improve current large-signal design processes as well as dramatically decrease the required design time and thus, obtain more efficient approaches.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

All-fiber passively mode-locked Tm-doped NOLM-based oscillator operating at 2-μm in both soliton and noisy-pulse regimes

A self-starting all-fiber passively mode-locked Tm-doped fiber laser based on nonlinear loop mirror (NOLM) is demonstrated. Stable soliton pulses centered at 2017.33 nm with 1.56 nm FWHM were produced at a repetition rate of 1.514 MHz with pulse duration of 2.8 ps and pulse energy of 83.8 pJ. As increased pump power, the oscillator can also operate at noise-like (NL) regime. Stable NL pulses with coherence spike width of 341 fs and pulse energy of up to 249.32 nJ was achieved at a center wavelength of 2017.24 nm with 21.33 nm FWHM. To the best of our knowledge, this is the first 2 μm region NOLM-based mode-locked fiber laser operating at two regimes with the highest single pulse energy for NL pulses. © 2014 Optical Society of America.

Surfing the high energy output branch of nonlinear energy harvesters

Hysteresis and multistability are fundamental phenomena of driven nonlinear oscillators, which, however, restrict many applications such as mechanical energy harvesting. We introduce an electrical control mechanism to switch from the low to the high energy output branch of a nonlinear energy harvester by exploiting the strong interplay between its electrical and mechanical degrees of freedom. This method improves the energy conversion efficiency over a wide bandwidth in a frequency-amplitude-varying environment using only a small energy budget. The underlying effect is independent of the device scale and the transduction method and is explained using a modified Duffing oscillator model.