Analytically-based approach to rotor-stator interaction noise in mean swirling flow

A method for modelling and predicting the noise generated by the interaction between the unsteady wake shed from the rotor and a downstream row of stators in a modern ultra-high bypass ducted turbofan engine is described. An analytically-based model is developed to account for three main features of the problem. First, the way in which a typical unsteady wake disturbance from the rotor interacts and is distorted by the mean swirling flow as it propagates downstream. The analysis allows for the inclusion of mean entropy gradients and entropy perturbations. Second, the effects of real stator-blade geometry and proper representation of the genuinely three-dimensional nature of the problem. Third, to model the propagation of the resulting noise back upstream in mean swirling flow. The analytical nature of the problem allows for the inclusion of all wake harmonics and enables the response at all blade passing frequencies to be determined. Example results are presented for an initial wake distribution corresponding to a genuine rotor configuration. Comparisons between numerical data and the asymptotic model for the wake evolution are made. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Enhancing parametric sensitivity using mode localization in electrically coupled mems resonators

We use vibration localization as a sensitive means of detecting small perturbations in stiffness in a pair of weakly coupled micromechanical resonators. For the first time, the variation in the eigenstates is studied by electrostatically coupling nearly identical resonators to allow for stronger localization of vibrational energy due to perturbations in stiffness. Eigenstate variations that are orders of magnitude greater than corresponding shifts in resonant frequency for an induced stiffness perturbation are experimentally demonstrated. Such high, voltagetunable parametric sensitivities together with the added advantage of intrinsic common mode rejection pave the way to a new paradigm of mechanical sensing. ©2009 IEEE.

Specificity of reflex adaptation for task-relevant variability.

The motor system responds to perturbations with reflexes, such as the vestibulo-ocular reflex or stretch reflex, whose gains adapt in response to novel and fixed changes in the environment, such as magnifying spectacles or standing on a tilting platform. Here we demonstrate a reflex response to shifts in the hand's visual location during reaching, which occurs before the onset of voluntary reaction time, and investigate how its magnitude depends on statistical properties of the environment. We examine the change in reflex response to two different distributions of visuomotor discrepancies, both of which have zero mean and equal variance across trials. Critically one distribution is task relevant and the other task irrelevant. The task-relevant discrepancies are maintained to the end of the movement, whereas the task-irrelevant discrepancies are transient such that no discrepancy exists at the end of the movement. The reflex magnitude was assessed using identical probe trials under both distributions. We find opposite directions of adaptation of the reflex response under these two distributions, with increased reflex magnitudes for task-relevant variability and decreased reflex magnitudes for task-irrelevant variability. This demonstrates modulation of reflex magnitudes in the absence of a fixed change in the environment, and shows that reflexes are sensitive to the statistics of tasks with modulation depending on whether the variability is task relevant or task irrelevant.

Separate representations of dynamics in rhythmic and discrete movements: evidence from motor learning.

Rhythmic and discrete arm movements occur ubiquitously in everyday life, and there is a debate as to whether these two classes of movements arise from the same or different underlying neural mechanisms. Here we examine interference in a motor-learning paradigm to test whether rhythmic and discrete movements employ at least partially separate neural representations. Subjects were required to make circular movements of their right hand while they were exposed to a velocity-dependent force field that perturbed the circularity of the movement path. The direction of the force-field perturbation reversed at the end of each block of 20 revolutions. When subjects made only rhythmic or only discrete circular movements, interference was observed when switching between the two opposing force fields. However, when subjects alternated between blocks of rhythmic and discrete movements, such that each was uniquely associated with one of the perturbation directions, interference was significantly reduced. Only in this case did subjects learn to corepresent the two opposing perturbations, suggesting that different neural resources were employed for the two movement types. Our results provide further evidence that rhythmic and discrete movements employ at least partially separate control mechanisms in the motor system.

Fundamental limits on the suppression of molecular fluctuations.

Negative feedback is common in biological processes and can increase a system's stability to internal and external perturbations. But at the molecular level, control loops always involve signalling steps with finite rates for random births and deaths of individual molecules. Here we show, by developing mathematical tools that merge control and information theory with physical chemistry, that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signalling events, making it extremely expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential; for example, regulatory genes are transcribed tens of thousands of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to the rigorous analysis of poorly characterized biological systems.

Context-dependent partitioning of motor learning in bimanual movements.

Human subjects easily adapt to single dynamic or visuomotor perturbations. In contrast, when two opposing dynamic or visuomotor perturbations are presented sequentially, interference is often observed. We examined the effect of bimanual movement context on interference between opposing perturbations using pairs of contexts, in which the relative direction of movement between the two arms was different across the pair. When each perturbation direction was associated with a different bimanual context, such as movement of the arms in the same direction versus movement in the opposite direction, interference was dramatically reduced. This occurred over a short period of training and was seen for both dynamic and visuomotor perturbations, suggesting a partitioning of motor learning for the different bimanual contexts. Further support for this was found in a series of transfer experiments. Having learned a single dynamic or visuomotor perturbation in one bimanual context, subjects showed incomplete transfer of this learning when the context changed, even though the perturbation remained the same. In addition, we examined a bimanual context in which one arm was moved passively and show that the reduction in interference requires active movement. The sensory consequences of movement are thus insufficient to allow opposing perturbations to be co-represented. Our results suggest different bimanual movement contexts engage at least partially separate representations of dynamics and kinematics in the motor system.

Optimal control: when redundancy matters.

A new experiment provides support for optimal feedback control as a theoretical basis of how the motor system responds to perturbations in a context-dependent manner.

Comparison of different scheduling techniques for H-infinity controllers

Several approaches to designing schedule H-infinity control systems are compared. These include a controller switching approach and also parameter scheduling of an observer representation of the controller. They are illustrated by application to a Generic VSTOI. Aircraft Model (GVAM) supplied by The Royal Aerospace Establishment (RAE) at Bedford. The switched design has been tested on the simulator at RAE Bedford. The linear H-infinity designs make use of a loop-shaping followed by robust stabilisation to additive perturbations of a normalised coprime factorisation of the shaped plans. The different scheduling approaches are compared with respect to achieved robust stability levels. performance and complexity of implementation.

Effect of elastic stresses on free oscillations in ferroelectric liquid crystals

It is shown experimentally that an elastic mechanical stress in a crystal structure is a necessary factor for the appearance of free oscillations of the director of a ferroelectric liquid crystal. Such a mechanical stress arises as a result of internal textural perturbations in the presence of regions with a different orientation of the director or is produced by external pressure applied to one of the cell plates in the appropriate direction. © 1999 American Institute of Physics.

Behaviour of unsteady transonic shock / boundary layer interactions with three-dimensional effects

An experimental investigation into the response of transonic SBLIs to periodic down-stream pressure perturbations in a parallel walled duct has been conducted. Tests have been carried out with a shock strength of M ∞ = 1.5 for pressure perturbation frequencies in the range 16-90 Hz. Analysis of the steady interaction at M∞ = 1.5 has also been made. The principle measurement techniques were high speed schlieren photography and laser Doppler anemometry. The structure of the steady SBLI was found to be highly three-dimensional, with large corner flows and sidewall SBLIs. These aspects are thought to influence the upstream transmission of pressure information through the interaction by affecting the post-shock flow field, including the extent of regions of secondary supersonic flow. At low frequency, the dynamics of shock motion can be predicted using an inviscid analytical model. At increased frequencies, viscous effects become significant and the shock exhibits unexpected dynamic behaviour, due to a phase lag between the upstream transmission of pressure information in the core flow and in the viscous boundary layers. Flow control in the form of micro-vane vortex generators was found to have a small impact on shock dynamics, due to the effect it had on the post-shock flow field outside the viscous boundary layer region. The relationship between inviscid and viscous effects is developed and potential destabilising mechanisms for SBLIs in practical applications are suggested. Copyright © 2009 by Paul Bruce and Holger Babinsky.

An experimental and numerical study of an oscillating transonic shock wave in a duct

A combined experimental and numerical study of a transonic shock wave in a parallel walled duct subject to downstream pressure perturbations has been conducted. Experiments and simulations have been carried out with a shock strength of M∞ = 1.4 for pressure perturbation frequencies in the range 16-90 Hz. The dynamics of unsteady shock motion and the interaction structure between the unsteady transonic shock wave and the turbulent tunnel floor boundary layer have been investigated. It is found that the (experimentally measured) dynamics of shock motion are generally well predicted by the computational scheme, especially at relatively low (≈ 40 Hz) frequencies. However, at higher frequencies (≈ 90 Hz), some subtle differences between the shock dynamics measured in experiments and those predicted by Computational Fluid Dynamics (CFD) exist. There is evidence from experiments that variations in shock / boundary layer interaction (SBLI) structure caused by shock motion are responsible for a change in the nature of shock dynamics between low and high frequency. In contrast, numerical results at low and high frequencies do not differ significantly and this suggests that the numerical method is not fully capturing the physics of the unsteady flow. Possible reasons for this are considered and a number of areas where CFD is unable to replicate experimental observations are identified. Significantly, CFD predicts changes in SBLI structure due to shock motion that are much too large and this may explain why none of the subtle effects on shock dynamics seen in experiments occur in CFD. Further work developing numerical methods that demonstrate a more realistic sensitivity of SBLI structure to unsteady shock motion is required. Copyright © 2010 by P.J.K. Bruce.

Triggering in a thermoacoustic system with stochastic noise

This paper explores the mechanism of triggering in a simple thermoacoustic system, the Rijke tube. It is demonstrated that additive stochastic perturbations can cause triggering before the linear stability limit of a thermoacoustic system. When triggering from low noise amplitudes, the system is seen to evolve to self-sustained oscillations via an unstable periodic solution of the governing equations. Practical stability is introduced as a measure of the stability of a linearly stable state when finite perturbations are present. The concept of a stochastic stability map is used to demonstrate the change in practical stability limits for a system with a subcritical bifurcation, once stochastic terms are included. The practical stability limits are found to be strongly dependent on the strength of noise.

A single-rate context-dependent learning process underlies rapid adaptation to familiar object dynamics.

Motor learning has been extensively studied using dynamic (force-field) perturbations. These induce movement errors that result in adaptive changes to the motor commands. Several state-space models have been developed to explain how trial-by-trial errors drive the progressive adaptation observed in such studies. These models have been applied to adaptation involving novel dynamics, which typically occurs over tens to hundreds of trials, and which appears to be mediated by a dual-rate adaptation process. In contrast, when manipulating objects with familiar dynamics, subjects adapt rapidly within a few trials. Here, we apply state-space models to familiar dynamics, asking whether adaptation is mediated by a single-rate or dual-rate process. Previously, we reported a task in which subjects rotate an object with known dynamics. By presenting the object at different visual orientations, adaptation was shown to be context-specific, with limited generalization to novel orientations. Here we show that a multiple-context state-space model, with a generalization function tuned to visual object orientation, can reproduce the time-course of adaptation and de-adaptation as well as the observed context-dependent behavior. In contrast to the dual-rate process associated with novel dynamics, we show that a single-rate process mediates adaptation to familiar object dynamics. The model predicts that during exposure to the object across multiple orientations, there will be a degree of independence for adaptation and de-adaptation within each context, and that the states associated with all contexts will slowly de-adapt during exposure in one particular context. We confirm these predictions in two new experiments. Results of the current study thus highlight similarities and differences in the processes engaged during exposure to novel versus familiar dynamics. In both cases, adaptation is mediated by multiple context-specific representations. In the case of familiar object dynamics, however, the representations can be engaged based on visual context, and are updated by a single-rate process.

Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.

Short- and long-term changes in joint co-contraction associated with motor learning as revealed from surface EMG.

In the field of motor control, two hypotheses have been controversial: whether the brain acquires internal models that generate accurate motor commands, or whether the brain avoids this by using the viscoelasticity of musculoskeletal system. Recent observations on relatively low stiffness during trained movements support the existence of internal models. However, no study has revealed the decrease in viscoelasticity associated with learning that would imply improvement of internal models as well as synergy between the two hypothetical mechanisms. Previously observed decreases in electromyogram (EMG) might have other explanations, such as trajectory modifications that reduce joint torques. To circumvent such complications, we required strict trajectory control and examined only successful trials having identical trajectory and torque profiles. Subjects were asked to perform a hand movement in unison with a target moving along a specified and unusual trajectory, with shoulder and elbow in the horizontal plane at the shoulder level. To evaluate joint viscoelasticity during the learning of this movement, we proposed an index of muscle co-contraction around the joint (IMCJ). The IMCJ was defined as the summation of the absolute values of antagonistic muscle torques around the joint and computed from the linear relation between surface EMG and joint torque. The IMCJ during isometric contraction, as well as during movements, was confirmed to correlate well with joint stiffness estimated using the conventional method, i.e., applying mechanical perturbations. Accordingly, the IMCJ during the learning of the movement was computed for each joint of each trial using estimated EMG-torque relationship. At the same time, the performance error for each trial was specified as the root mean square of the distance between the target and hand at each time step over the entire trajectory. The time-series data of IMCJ and performance error were decomposed into long-term components that showed decreases in IMCJ in accordance with learning with little change in the trajectory and short-term interactions between the IMCJ and performance error. A cross-correlation analysis and impulse responses both suggested that higher IMCJs follow poor performances, and lower IMCJs follow good performances within a few successive trials. Our results support the hypothesis that viscoelasticity contributes more when internal models are inaccurate, while internal models contribute more after the completion of learning. It is demonstrated that the CNS regulates viscoelasticity on a short- and long-term basis depending on performance error and finally acquires smooth and accurate movements while maintaining stability during the entire learning process.