Dynamics of in-plane arch rocking: An energy approach

This study employs an analytical model to describe the rocking response of a masonry arch to in-plane seismic loading. Through evaluation of the rate of energy input to the system, the model reveals the ground motions that cause maximum rocking amplification. An experimental investigation of small-scale masonry arches subjected to past earthquake time histories is used to evaluate the analytical model and to explore arch rocking behaviour. The results demonstrate that rocking amplification can occur, but is highly sensitive to slight variations in the ground motion. Thus, the accuracy to which the arch response can be predicted is brought into perspective. The concept that the primary impulse of an expected ground motion is fundamentally important in predicting arch collapse is evaluated in light of the developed energy approach. Finally, a statistical method is proposed for predicting the probability of arch collapse during seismic loading.

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.

Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model.

This study compared adaptation in novel force fields where trajectories were initially either stable or unstable to elucidate the processes of learning novel skills and adapting to new environments. Subjects learned to move in a null force field (NF), which was unexpectedly changed either to a velocity-dependent force field (VF), which resulted in perturbed but stable hand trajectories, or a position-dependent divergent force field (DF), which resulted in unstable trajectories. With practice, subjects learned to compensate for the perturbations produced by both force fields. Adaptation was characterized by an initial increase in the activation of all muscles followed by a gradual reduction. The time course of the increase in activation was correlated with a reduction in hand-path error for the DF but not for the VF. Adaptation to the VF could have been achieved solely by formation of an inverse dynamics model and adaptation to the DF solely by impedance control. However, indices of learning, such as hand-path error, joint torque, and electromyographic activation and deactivation suggest that the CNS combined these processes during adaptation to both force fields. Our results suggest that during the early phase of learning there is an increase in endpoint stiffness that serves to reduce hand-path error and provides additional stability, regardless of whether the dynamics are stable or unstable. We suggest that the motor control system utilizes an inverse dynamics model to learn the mean dynamics and an impedance controller to assist in the formation of the inverse dynamics model and to generate needed stability.

Impedance control and internal model use during the initial stage of adaptation to novel dynamics in humans.

This study investigated the neuromuscular mechanisms underlying the initial stage of adaptation to novel dynamics. A destabilizing velocity-dependent force field (VF) was introduced for sets of three consecutive trials. Between sets a random number of 4-8 null field trials were interposed, where the VF was inactivated. This prevented subjects from learning the novel dynamics, making it possible to repeatedly recreate the initial adaptive response. We were able to investigate detailed changes in neural control between the first, second and third VF trials. We identified two feedforward control mechanisms, which were initiated on the second VF trial and resulted in a 50% reduction in the hand path error. Responses to disturbances encountered on the first VF trial were feedback in nature, i.e. reflexes and voluntary correction of errors. However, on the second VF trial, muscle activation patterns were modified in anticipation of the effects of the force field. Feedforward cocontraction of all muscles was used to increase the viscoelastic impedance of the arm. While stiffening the arm, subjects also exerted a lateral force to counteract the perturbing effect of the force field. These anticipatory actions indicate that the central nervous system responds rapidly to counteract hitherto unfamiliar disturbances by a combination of increased viscoelastic impedance and formation of a crude internal dynamics model.

Learning the dynamics of the external world: Brain inspired learning for robotic applications

Humans have exceptional abilities to learn new skills, manipulate tools and objects, and interact with our environment. In order to be successful at these tasks, our brain has become exceptionally well adapted to learning to deal not only with the complex dynamics of our own limbs but also with novel dynamics in the external world. While learning of these dynamics includes learning the complex time-varying forces at the end of limbs through the updating of internal models, it must also include learning the appropriate mechanical impedance in order to stabilize both the limb and any objects contacted in the environment. This article reviews the field of human learning by examining recent experimental evidence about adaptation to novel unstable dynamics and explores how this knowledge about the brain and neuro-muscular system can expand the learning capabilities of robotics and prosthetics. © 2006.

Synchronization in climate dynamics and other extended systems

Synchronization is now well established as representing coherent behaviour between two or more otherwise autonomous nonlinear systems subject to some degree of coupling. Such behaviour has mainly been studied to date, however, in relatively low-dimensional discrete systems or networks. But the possibility of similar kinds of behaviour in continuous or extended spatiotemporal systems has many potential practical implications, especially in various areas of geophysics. We review here a range of cyclically varying phenomena within the Earth's climate system for which there may be some evidence or indication of the possibility of synchronized behaviour, albeit perhaps imperfect or highly intermittent. The exploitation of this approach is still at a relatively early stage within climate science and dynamics, in which the climate system is regarded as a hierarchy of many coupled sub-systems with complex nonlinear feedbacks and forcings. The possibility of synchronization between climate oscillations (global or local) and a predictable external forcing raises important questions of how models of such phenomena can be validated and verified, since the resulting response may be relatively insensitive to the details of the model being synchronized. The use of laboratory analogues may therefore have an important role to play in the study of natural systems that can only be observed and for which controlled experiments are impossible. We go on to demonstrate that synchronization can be observed in the laboratory, even in weakly coupled fluid dynamical systems that may serve as direct analogues of the behaviour of major components of the Earth's climate system. The potential implications and observability of these effects in the long-term climate variability of the Earth is further discussed. © 2010 Springer-Verlag Berlin Heidelberg.

Exploring the process of whole system design

This paper explores the adoption of a whole system approach to a more sustainable and innovative design. A case study methodology was utilised to gain improved understanding of whole system design and those factors that substantially influence its success. The paper presents a framework of those factors including the requirement for trans-disciplinary skills, the dynamics of a flattened hierarchy and the need to identify relationships between parts of the system to ultimately optimise the whole. Knowing the factors that influence the process of whole system design provides designers with the knowledge necessary to more effectively work within, manage and facilitate that process. This paper uses anecdotes taken from operational cases, across design contexts, to demonstrate those factors. © 2010 Elsevier Ltd. All rights reserved.

Visuomotor feedback gains upregulate during the learning of novel dynamics.

At an early stage of learning novel dynamics, changes in muscle activity are mainly due to corrective feedback responses. These feedback contributions to the overall motor command are gradually reduced as feedforward control is learned. The temporary increased use of feedback could arise simply from the large errors in early learning with either unaltered gains or even slightly downregulated gains, or from an upregulation of the feedback gains when feedforward prediction is insufficient. We therefore investigated whether the sensorimotor control system alters feedback gains during adaptation to a novel force field generated by a robotic manipulandum. To probe the feedback gains throughout learning, we measured the magnitude of involuntary rapid visuomotor responses to rapid shifts in the visual location of the hand during reaching movements. We found large increases in the magnitude of the rapid visuomotor response whenever the dynamics changed: both when the force field was first presented, and when it was removed. We confirmed that these changes in feedback gain are not simply a byproduct of the change in background load, by demonstrating that this rapid visuomotor response is not load sensitive. Our results suggest that when the sensorimotor control system experiences errors, it increases the gain of the visuomotor feedback pathways to deal with the unexpected disturbances until the feedforward controller learns the appropriate dynamics. We suggest that these feedback gains are upregulated with increased uncertainty in the knowledge of the dynamics to counteract any errors or disturbances and ensure accurate and skillful movements.

Physical consequences of a nonparametric uncertainty model in structural dynamics

One of the main claims of the nonparametric model of random uncertainty introduced by Soize (2000) [3] is its ability to account for model uncertainty. The present paper investigates this claim by examining the statistics of natural frequencies, total energy and underlying dispersion equation yielded by the nonparametric approach for two simple systems: a thin plate in bending and a one-dimensional finite periodic massspring chain. Results for the plate show that the average modal density and the underlying dispersion equation of the structure are gradually and systematically altered with increasing uncertainty. The findings for the massspring chain corroborate the findings for the plate and show that the remote coupling of nonadjacent degrees of freedom induced by the approach suppresses the phenomenon of mode localization. This remote coupling also leads to an instantaneous response of all points in the chain when one mass is excited. In the light of these results, it is argued that the nonparametric approach can deal with a certain type of model uncertainty, in this case the presence of unknown terms of higher or lower order in the governing differential equation, but that certain expectations about the system such as the average modal density may conflict with these results. © 2012 Elsevier Ltd.

Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization. © 2012 Kadiallah et al.

Attenuated Salmonella Typhimurium lacking the pathogenicity island-2 type 3 secretion system grow to high bacterial numbers inside phagocytes in mice.

Intracellular replication within specialized vacuoles and cell-to-cell spread in the tissue are essential for the virulence of Salmonella enterica. By observing infection dynamics at the single-cell level in vivo, we have discovered that the Salmonella pathogenicity island 2 (SPI-2) type 3 secretory system (T3SS) is dispensable for growth to high intracellular densities. This challenges the concept that intracellular replication absolutely requires proteins delivered by SPI-2 T3SS, which has been derived largely by inference from in vitro cell experiments and from unrefined measurement of net growth in mouse organs. Furthermore, we infer from our data that the SPI-2 T3SS mediates exit from infected cells, with consequent formation of new infection foci resulting in bacterial spread in the tissues. This suggests a new role for SPI-2 in vivo as a mediator of bacterial spread in the body. In addition, we demonstrate that very similar net growth rates of attenuated salmonellae in organs can be derived from very different underlying intracellular growth dynamics.

Vowel normalisation: Time-domain processing of the internal dynamics of speech

Human listeners can identify vowels regardless of speaker size, although the sound waves for an adult and a child speaking the ’same’ vowel would differ enormously. The differences are mainly due to the differences in vocal tract length (VTL) and glottal pulse rate (GPR) which are both related to body size. Automatic speech recognition machines are notoriously bad at understanding children if they have been trained on the speech of an adult. In this paper, we propose that the auditory system adapts its analysis of speech sounds, dynamically and automatically to the GPR and VTL of the speaker on a syllable-to-syllable basis. We illustrate how this rapid adaptation might be performed with the aid of a computational version of the auditory image model, and we propose that an auditory preprocessor of this form would improve the robustness of speech recognisers.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Time-optimal control of a 3-level quantum system and its generalization

We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: ℤ × S3 discrete symmetry and 51 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system. Copyright ©2007 Watam Press.

Feedback control of impact dynamics: The bouncing ball revisited

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The proposed control law uses the impact times as the sole feedback information. We show that the acceleration of the table at impact plays no role in the stability analysis but is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution. © 2006 IEEE.