Structural sensitivity of spiral vortex breakdown

Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier-Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the m=-1 azimuthal mode is the most unstable and that the wavemaker regions of the m=-1 mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown. © 2013 Cambridge University Press.

Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators

In this paper, we investigate the behavior of pulse-coupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the approximation of infinite populations. In addition to recovering known stability results of finite populations, we also obtain new stability results for infinite populations. In particular, under a weak coupling assumption, we solve for the continuum model a conjecture still prevailing in the finite dimensional case. © 2011 IEEE.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a Stable nonlinear system. It is shown that the instability of the zeros of the linear System can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This paper analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Stability margins of nonlinear receding-horizon control via inverse optimality

Using the nonlinear analog of the Fake Riccati equation developed for linear systems, we derive an inverse optimality result for several receding-horizon control schemes. This inverse optimality result unifies stability proofs and shows that receding-horizon control possesses the stability margins of optimal control laws. © 1997 Elsevier Science B.V.

Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems. © 2013 Elsevier Ltd. All rights reserved.

Observation of locked phase dynamics and enhanced frequency stability in synchronized micromechanical oscillators

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references. © 2013 American Physical Society.