Feedback mechanisms for global oscillations in Lure systems

The paper presents two mechanisms for global oscillations in feedback systems, based on bifurcations in absolutely stable systems. The external characterization of the oscillators provides the basis for a (energy-based) dissipativity theory for oscillators, thereby opening new possibilities for rigorous stability analysis of high-dimensional systems and interconnected oscillators. © 2004 Elsevier B.V. All rights reserved.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.

Azimuthal instabilities in annular combustors: Standing and spinning modes

This theoretical study investigates spinning and standing modes in azimuthally symmetric annular combustion chambers. Both modes are observed in experiments and simulations, and an existing model predicts that spinning modes are the only stable state of the system. We extend this model to take into account the effect that the acoustic azimuthal velocity, u, has on the flames, and propose a phenomenological model based on experiments performed on transversely forced flames. This model contains a parameter, ä, that quantifies the influence that the transversal excitation has on the fluctuating heat release. For small values of ä, spinning modes are the only stable state of the system. In an intermediate range of ä, both spinning and standing modes are stable states. For large values of ä, standing modes are the only stable state. This study shows that a flame's response to azimuthal velocity fluctuations plays an important role in determining the type of thermoacoustic oscillations found in annular combustors. © 2013 The Authors.

A novel theoretical approach to passive control of thermo-acoustic oscillations: Application to ducted heat sources

In this paper, we develop a linear technique that predicts how the stability of a thermo-acoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically-heated hot wire and the second contains a diffusion flame. Both heat sources are assumed to be compact so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermo-acoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermo-acoustic system should be changed in order to make it stable. Copyright © 2013 by ASME.

CFD investigation of turbulent premixed flame response to transverse forcing

Screech is a high frequency oscillation that is usually characterized by instabilities caused by large-scale coherent flow structures in the wake of bluff-body flameholders and shear layers. Such oscillations can lead to changes in flame surface area which can cause the flame to burn unsteadily, but also couple with the acoustic modes and inherent fluid-mechanical instabilities that are present in the system. In this study, the flame response to hydrodynamic oscillations is analyzed in a controlled manner using high-fidelity Computational Fluid Dynamics (CFD) with an unsteady Reynolds-averaged Navier-Stokes approach. The response of a premixed flame with and without transverse velocity forcing is analyzed. When unforced, the flame is shown to exhibit a self-excitation that is attributed to the anti-symmetric shedding of vortices in the wake of the flameholder. The flame is also forced using two different kinds of low-amplitude out-of-phase inlet velocity forcing signals. The first forcing method is harmonic forcing with a single characteristic frequency, while the second forcing method involves a broadband forcing signal with frequencies in the range of 500 - 1000 Hz. For the harmonic forcing method, the flame is perturbed only lightly about its mean position and exhibits a limit cycle oscillation that is characteristic of the forcing frequency. For the broadband forcing method, larger changes in the flame surface area and detachment of the flame sheet can be seen. Transition to a complicated trajectory in the phase space is observed. When analyzed systematically with system identification methods, the CFD results, expressed in the form of the Flame Transfer Function (FTF) are capable of elucidating the flame response to the imposed perturbation. The FTF also serves to identify, both spatially and temporally, regions where the flame responds linearly and nonlinearly. Locking-in between the flame's natural self-excited frequency and the subharmonic frequencies of the broadband forcing signal is found to alter the dynamical behaviour of the flame. Copyright © 2013 by ASME.

Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe.

An innovative, simple, compact and low cost approach for phase mapping based on the intrinsic modulation of an aperture Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. Several nanoscale silicon waveguides are phase-mapped using this approach, and the different modes of propagation are obtained via Fourier analysis. The obtained measured results are in good agreement with the effective indexes of the modes calculated by electromagnetic simulations. Owing to its simplicity and effectiveness, the demonstrated system is a potential candidate for integration with current near field systems for the characterization of nanophotonic components and devices.

Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe

An innovative, simple, compact and low cost approach for phase mapping based on the intrinsic modulation of an aperture Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. Several nanoscale silicon waveguides are phase-mapped using this approach, and the different modes of propagation are obtained via Fourier analysis. The obtained measured results are in good agreement with the effective indexes of the modes calculated by electromagnetic simulations. Owing to its simplicity and effectiveness, the demonstrated system is a potential candidate for integration with current near field systems for the characterization of nanophotonic components and devices. © 2011 Optical Society of America.

Near field phase mapping exploiting intrinsic oscillations of NSOM probe

An innovative, simple compact and low cost approach for phase mapping based on the intrinsic modulation of a Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. © OSA/ CLEO 2011.

Monitoring and preventing numerical oscillations in 3D simulations with coupled Monte Carlo codes

Previous studies have reported that different schemes for coupling Monte Carlo (MC) neutron transport with burnup and thermal hydraulic feedbacks may potentially be numerically unstable. This issue can be resolved by application of implicit methods, such as the stochastic implicit mid-point (SIMP) methods. In order to assure numerical stability, the new methods do require additional computational effort. The instability issue however, is problem-dependent and does not necessarily occur in all cases. Therefore, blind application of the unconditionally stable coupling schemes, and thus incurring extra computational costs, may not always be necessary. In this paper, we attempt to develop an intelligent diagnostic mechanism, which will monitor numerical stability of the calculations and, if necessary, switch from simple and fast coupling scheme to more computationally expensive but unconditionally stable one. To illustrate this diagnostic mechanism, we performed a coupled burnup and TH analysis of a single BWR fuel assembly. The results indicate that the developed algorithm can be easily implemented in any MC based code for monitoring of numerical instabilities. The proposed monitoring method has negligible impact on the calculation time even for realistic 3D multi-region full core calculations. © 2014 Elsevier Ltd. All rights reserved.

Magnetic quantum oscillations for the surface states of topological insulator Bi2Se3

We study quantum oscillations of the magnetization in Bi2Se3 (111) surface system in the presence of a perpendicular magnetic field. The combined spin-chiral Dirac cone and Landau quantization produce profound effects on the magnetization properties that are fundamentally different from those in the conventional semiconductor two-dimensional electron gas. In particular, we show that the oscillating center in the magnetization chooses to pick up positive or negative values depending on whether the zero-mode Landau level is occupied or empty. An intuitive analysis of these features is given and the subsequent effects on the magnetic susceptibility and Hall conductance are also discussed.

Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound "4," which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.