Oscillator models and collective motion

A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.

Dynamical aspects of coupled Rossler systems: effects of noise

Nonlinear time series analysis is employed to study the complex behaviour exhibited by a coupled pair of Rossler systems. Dimensional analysis with emphasis on the topological correlation dimension and the Kolmogorov entropy of the system is carried out in the coupling parameter space. The regime of phase synchronization is identified and the extent of synchronization between the systems constituting the coupled system is quantified by the phase synchronization index. The effect of noise on the coupling between the systems is also investigated. An exhaustive study of the topological, dynamical and synchronization properties of the nonlinear system under consideration in its characteristic parameter space is attempted.

Suppression of instabilities in burning droplets using preferential acoustic perturbations

Self-induced internal boiling in burning functional droplets has been observed to induce severe bulk shape oscillations in droplets with characteristic bubble ejection events that corrugate the droplet surface. Such bubble-droplet interactions are characterized by a distinct regime of a single bubble growing inside the droplet where evaporative Darrieus-Landau instability occurs at the bubble-droplet interface. In this regime the bubble-droplet system behaves as a self-excited coupled oscillator. In this study, we report the external flame-acoustic interaction with bubbles inside the droplet resulting in controlled droplet deformation. In particular, by exciting the droplet flame in a critical, responsive frequency range (80 Hz <= f(p) <= 120 Hz) the droplet deformation cycle could be altered through suppression of these self-excited instabilities and intensity/frequency of bubble ejection events. This selective acoustic tuning also enabled the control of bubble dynamics, bulk droplet-shape distortion and the final precipitate morphology even in burning nanoparticle laden droplets. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Spatial models of bistability in biological collectives

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion under slow variation of the neighborhood size in which individuals tend to align with one another. In the case that the neighborhood radius is less than the circular motion radius, both circular and parallel motion can occur. We provide Lyapunov-based analysis of bistability of circular and parallel motion in a closed-loop system of self-propelled particles with coupled-oscillator dynamics. ©2007 IEEE.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Chaotic synchronization in general network topology for scene segmentation

Chaotic synchronization has been discovered to be an important property of neural activities, which in turn has encouraged many researchers to develop chaotic neural networks for scene and data analysis. In this paper, we study the synchronization role of coupled chaotic oscillators in networks of general topology. Specifically, a rigorous proof is presented to show that a large number of oscillators with arbitrary geometrical connections can be synchronized by providing a sufficiently strong coupling strength. Moreover, the results presented in this paper not only are valid to a wide class of chaotic oscillators, but also cover the parameter mismatch case. Finally, we show how the obtained result can be applied to construct an oscillatory network for scene segmentation.

Chaotic synchronization in 2D lattice for scene segmentation

Synchronization and chaos play important roles in neural activities and have been applied in oscillatory correlation modeling for scene and data analysis. Although it is an extensively studied topic, there are still few results regarding synchrony in locally coupled systems. In this paper we give a rigorous proof to show that large numbers of coupled chaotic oscillators with parameter mismatch in a 2D lattice can be synchronized by providing a sufficiently large coupling strength. We demonstrate how the obtained result can be applied to construct an oscillatory network for scene segmentation. (C) 2007 Elsevier B.V. All rights reserved.

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.

High performance terahertz resonant tunnelling diode sources and broadband antenna for air-side radiation

Resonant tunnelling diode (RTD) is known to be the fastest electronics device that can be fabricated in compact form and operate at room temperature with potential oscillation frequency up to 2.5 THz. The RTD device consists of a narrow band gap quantum well layer sandwiched between two thin wide band gap barriers layers. It exhibits negative differential resistance (NDR) region in its current-voltage (I-V) characteristics which is utilised in making oscillators. Up to date, the main challenge is producing high output power at high frequencies in particular. Although oscillation frequencies of ~ 2 THz have been already reported, the output power is in the range of micro-Watts. This thesis describes the systematic work on the design, fabrication, and characterisation of RTD-based oscillators in microwave/millimetre-wave monolithic integrated circuits (MMIC) form that can produce high output power and high oscillation frequency at the same time. Different MMIC RTD oscillator topologies were designed, fabricated, and characterised in this project which include: single RTD oscillator which employs one RTD device, double RTDs oscillator which employs two RTD devices connected in parallel, and coupled RTD oscillators which combine the powers of two oscillators over a single load, based on mutual coupling and which can employ up to four RTD devices. All oscillators employed relatively large size RTD devices for high power operation. The main challenge was to realise high oscillation frequency (~ 300 GHz) in MMIC form with the employed large sized RTD devices. To achieve this aim, proper designs of passive structures that can provide small values of resonating inductances were essential. These resonating inductance structures included shorted coplanar wave guide (CPW) and shorted microstrip transmission lines of low characteristics impedances Zo. Shorted transmission line of lower Zo has lower inductance per unit length. Thus, the geometrical dimensions would be relatively large and facilitate fabrication by low cost photolithography. A series of oscillators with oscillation frequencies in the J-band (220 – 325 GHz) range and output powers from 0.2 – 1.1 mW have been achieved in this project, and all were fabricated using photolithography. Theoretical estimation showed that higher oscillation frequencies (> 1 THz) can be achieved with the proposed MMIC RTD oscillators design in this project using photolithography with expected high power operation. Besides MMIC RTD oscillators, reported planar antennas for RTD-based oscillators were critically reviewed and the main challenges in designing high performance integrated antennas on large dielectric constant substrates are discussed in this thesis. A novel antenna was designed, simulated, fabricated, and characterised in this project. It was a bow-tie antenna with a tuning stub that has very wide bandwidth across the J-band. The antenna was diced and mounted on a reflector ground plane to alleviate the effect of the large dielectric constant substrate (InP) and radiates upwards to the air-side direction. The antenna was also investigated for integration with the all types of oscillators realised in this project. One port and two port antennas were designed, simulated, fabricated, and characterised and showed the suitability of integration with the single/double oscillator layout and the coupled oscillator layout, respectively.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using a new approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyse the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

The generator coordinate method for a reaction coordinate coupled to a harmonic oscillator bath

This paper investigates the usefulness of the generator coordinate method (GCM) for treating the dynamics of a reaction coordinate coupled to a bath of harmonic degrees of freedom. Models for the unimolecular dissociation and isomerization process (proton transfer) are analyzed. The GCM results, presented in analytical form, provide a very good description and are compared to other methods Like the basis set method and multiconfiguration time dependent self-consistent field. (C) 1998 American Institute of Physics. [S0021-9606(98)50934-8].

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

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

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

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

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.