Partial synchronization of non-identical chaotic systems via adaptive control, with applications to modelling coupled nonlinear systems

We consider the coupling of two nonidentical dynamical systems using an adaptive feedback linearization controller to achieve partial synchronization between the two systems. In addition we consider the case where an additional feedback signal exists between the two systems, which leads to bidirectional coupling. We demonstrate the stability of the adaptive controller, and use the example of coupling a Chua system with a Lorenz system, both exhibiting chaotic motion, as an example of the coupling technique. A feedback linearization controller is used to show the difference between unidirectional and bidirectional coupling. We observe that the adaptive controller converges to the feedback linearization controller in the steady state for the Chua– Lorenz example. Finally we comment on how this type of partial synchronization technique can be applied to modeling systems of coupled nonlinear subsystems. We show how such modeling can be achieved where the dynamics of one system is known only via experimental time series measurements

Radio observations of the cool gas, dust, and star formation in the first galaxies

We summarize cm through submm observations of the host galaxies of z ~ 6 quasars. These observations reveal the cool molecular gas (the fuel for star formation), the warm dust (heated by star formation), the fine structure line emission (tracing the CNM and PDRs), and the synchrotron emission. Our results imply active star formation in ~ 30% of the host galaxies, with star formation rates ~ 10^3 M_sun/year, and molecular gas masses ~ 10^10 M_sun. Imaging of the [CII] emission from the most distant quasar reveals a 'maximal starburst disk' on a scale ~ 1.5 kpc. Gas dynamical studies suggest a departure of these galaxies from the low-z M_{BH} -- M_{bulge} relation, with the black holes being, on average, 15 times more massive than expected. Overall, we are witnessing the co-eval formation of massive galaxies and supermassive black holes within 1 Gyr of the Big Bang.Comment: First Stars and Galaxies: Challenges in the Next Decade, AIP, 2010; Austin TX (eds Whelan, Bromm, Yoshida); 7 page

A Meta-Learning Approach to Population-Based Modelling of Structures

A major problem of machine-learning approaches in structural dynamics is the frequent lack of structural data. Inspired by the recently-emerging field of population-based structural health monitoring (PBSHM), and the use of transfer learning in this novel field, the current work attempts to create models that are able to transfer knowledge within populations of structures. The approach followed here is meta-learning, which is developed with a view to creating neural network models which are able to exploit knowledge from a population of various tasks to perform well in newly-presented tasks, with minimal training and a small number of data samples from the new task. Essentially, the method attempts to perform transfer learning in an automatic manner within the population of tasks. For the purposes of population-based structural modelling, the different tasks refer to different structures. The method is applied here to a population of simulated structures with a view to predicting their responses as a function of some environmental parameters. The meta-learning approach, which is used herein is the model-agnostic meta-learning (MAML) approach; it is compared to a traditional data-driven modelling approach, that of Gaussian processes, which is a quite effective alternative when few data samples are available for a problem. It is observed that the models trained using meta-learning approaches, are able to outperform conventional machine learning methods regarding inference about structures of the population, for which only a small number of samples are available. Moreover, the models prove to learn part of the physics of the problem, making them more robust than plain machine-learning algorithms. Another advantage of the methods is that the structures do not need to be parametrised in order for the knowledge transfer to be performed

CO(1-0) line imaging of massive star-forming disc galaxies at z=1.5-2.2

We present detections of the CO(J= 1-0) emission line in a sample of four massive star-forming galaxies at z~1.5-2.2 obtained with the Karl G. Jansky Very Large Array (VLA). Combining these observations with previous CO(2-1) and CO(3-2) detections of these galaxies, we study the excitation properties of the molecular gas in our sample sources. We find an average line brightness temperature ratios of R_{21}=0.70+\-0.16 and R_{31}=0.50+\-0.29, based on measurements for three and two galaxies, respectively. These results provide additional support to previous indications of sub-thermal gas excitation for the CO(3-2) line with a typically assumed line ratio R_{31}~0.5. For one of our targets, BzK-21000, we present spatially resolved CO line maps. At the resolution of 0.18'' (1.5 kpc), most of the emission is resolved out except for some clumpy structure. From this, we attempt to identify molecular gas clumps in the data cube, finding 4 possible candidates. We estimate that <40 % of the molecular gas is confined to giant clumps (~1.5 kpc in size), and thus most of the gas could be distributed in small fainter clouds or in fairly diffuse extended regions of lower brightness temperatures than our sensitivity limit

System identification of a mechanical system with impacts using model reference adaptive control

A single degree of freedom mechanical spring-mass system was considered where the motion of the mass is constrained by an adjustable rigid impact stop. A model reference adaptive control algorithm combined with interspike interval techniques was used to consider the viability of identifying system parameters when impacts are present. The unmodified adaptive control algorithm destabilizes during vibro-impact motion, so three modified control algorithms were tested experimentally. The first, the gain reset, was found to be of limited use and system identification could not be successfully carried out. The second and third used a gain pause strategy. The second algorithm used acceleration triggering and represented an improvement on the gain reset method. The third approach used displacement triggering and was found to be partially successful in identifying system parameters in the presence of vibro-impact motion

Modeling a helical fluid inerter system with time-invariant mem-models

In this paper, experimental data from tests of a helical fluid inerter are used to model the observed hysteretic behavior. The novel idea is to test the feasibility of employing mem-models, which are time-invariant herein, to capture the observed phenomena by using physically meaningful state variables. Firstly we use a Masing model concept, identified with a multilayer feedforward neural network to capture the physical characteristics of the hysteresis functions. Following this, a more refined problem formulation based on the concept of a multi-element model including a mem-inerter is developed. This is compared with previous definitions in the literature and shown to be a more general model. Through-out this paper, numerical simulations are used to demonstrate the type of dynamic responses anticipated using the proposed time-invariant mem-models. Corresponding experimental measurements are processed to demonstrate and justify the new mem-modeling concepts. Focusing on identifying the unknown function forms in the proposed problem formulations, the results show that it is possible to formulate a unified model constructed using both the damper and inerter from the mem-model family. This model captures many of the more subtle features of the underlying physics, not captured by other forms of existing model

Chatter, sticking and chaotic impacting motion in a two-degree of freedom impact oscillator

We consider the dynamics of a two-degree of freedom impact oscillator subject to a motion limiting constraint. These systems exhibit a range of periodic and nonperiodic impact motions. For a particular set of parameters, we consider the bifurcations which occur between differing regimes of impacting motion and in particular those which occur due to a grazing bifurcation. Unexpected resonant behavior is also observed, due to the complexity of the dynamics. We consider both periodic and chaotic chatter motions and the regions of sticking which exist. Finally we consider the types of chaotic motion that occur within the parameter range. We discuss the possibility in relating successive low velocity impacts, especially with respect to possible low dimensional mappings for such a system