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.

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.

Linear stability of miscible two-fluid flow down an incline

We show that miscible two-layer free-surface flows of varying viscosity down an inclined substrate are different in their stability characteristics from both immiscible two-layer flows, and flows with viscosity gradients spanning the entire flow. New instability modes arise when the critical layer of the viscosity transport equation overlaps the viscosity gradient. A lubricating configuration with a less viscous wall layer is identified to be the most stabilizing at moderate miscibility (moderate Peclet numbers). This also is in contrast with the immiscible case, where the lubrication configuration is always destabilizing. The co-existence that we find under certain circumstances, of several growing overlap modes, the usual surface mode, and a Tollmien-Schlichting mode, presents interesting new possibilities for nonlinear breakdown. © 2013 AIP Publishing LLC.

Global linear stability of the boundary-layer flow over a rotating sphere

We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk. © 2014 Elsevier Masson SAS. All rights reserved.