The effect of an applied electric potential on the dynamics of gas bubble formation from a single nozzle in glycerol was studied experimentally. Dry nitrogen was bubbled into glycerol through a nozzle having an electrified tip while pressure measurements were made upstream of the nozzle. As the applied electric potential was increased from zero, bubble size reduced, bubble shape became more spherical, and bubbling frequency increased. At constant gas flow, bubble-formation exhibited a classic period-doubling route to chaos with increasing potential. We defined an electric Bond number assuming that both the liquid and gas phases are conducting. This is in contrast to previous studies where one phase was considered a perfect conductor and the other one a perfect nonconductor or insulator. Although electric potential and gas flow appear to have similar effects on the period-doubling bifurcation process for this system, the relative impact of electrostatic forces, as measured in terms of electric Bond number for conducting liquid and gas phases, is smaller. However, the relative impact of electrostatic forces for the case of insulating liquid and conducting gas phases is comparable to flow forces. Further data collection is required for different nozzle geometries and liquid column heights in order to verify the relative impacts of electrostatic and flow forces, and would allow us to ascertain if electrostatic potential is a feasible manipulated variable for controlling this system.

A Principal Curve is a hypercurve that passes through the center of the data cloud. We adapt and expand the principal curve algorithm to develop a non-parametric approach called Cluster-linked Principal Curves (CLPC) that locally approximates the structure and scatter in a distribution of data points. The iterative algorithm is based on Expectation-Maximization (E-M) principle. The projections of data points on the principal curve or arc lengths are capable of characterizing the data in fewer dimensions and with greater accuracy than PCA. The distribution of arc lengths is used for gauging stationarity and reversibility, and monitoring. For illustration we use the embeddings formed from chaotic gas pressure time series measurements collected before an electrified capillary nozzle that injects bubbles into a liquid-filled column.

It has been suggested that rising bubbles in dense fluids resemble an inverted dripping faucet and that they undergo analogues period-doubling bifurcations to chaos. We present experimental results that demonstrate that this analogy is weak because the dominant source of instability in the bubble train is inherently different — mutual interactions between spatially separated bubbles as opposed to nozzle dynamics. Unlike the dripping faucet, the initial instability in a bubble train develops at a location far from the injection nozzle and progresses toward the nozzle with increasing gas flow. From qualitative and rigorous quantitative observations, we conclude that rising-bubble dynamics are best described as ‘small-box spatio-temporal chaos’ with a flow instability. Such dynamics can superficially appear to be simple temporal chaos when considering spatially localized measurements. We show similarity between our experimental results and a bubble-interaction model that accounts for drag and coalescence effects without considering any nozzle dynamics.

The recently developed WaveARX neural network has its methodology extended to include net adaptation and on-line implementation in real time. The net evolves by changing its architecture: generation, annihilation, or change in location of neurons. Systematic design procedures remove the traditional network problems of no guidelines to define the architecture and the often strong dependence of the trained network parameters on their initial conditions. In addition, the design procedures provide network information needed for evolution. Two demonstrations are implemented on-line using process simulations of a chaotic map and a pH CSTR model. These provide illustrations of several capabilities of the new network, along with comparisons to other identification techniques.

We present experimental evidence that a complex system of particles suspended by upward-moving gas can exhibit low-dimensional bulk behavior. Specifically, we describe large-scale collective particle motion referred to as slugging in an industrial device known as a fluidized bed. As gas flow increases from zero, the bulk motion evolves from a fixed point to periodic oscillations to oscillations intermittently punctuated by ''stutters,'' which become more frequent as the flow increases further. At the highest flow tested, the behavior becomes extremely complex (''turbulent'').

The WaveARX network, a new neural network architecture, is introduced. Its development was motivated by the opportunity to capitalize on recent research results that allow some shortcomings of the traditional artificial neural net (ANN) to be addressed. ANN has been shown to be a valuable tool for system identification but suffers from slow convergence and long training time due to the globalized activation function. The structure of ANN is derived from trial and error procedures, and the trained network parameters often are strongly dependent on the random selection of the initial values. There are not even guidelines on the number of neurons needed. Also, few identification techniques are available for distinguishing linear from nonlinear contributions to a system's behavior. The WaveARX integrates the multiresolution analysis concepts of the wavelet transform and the traditional AutoRegressive eXternal input model (ARX) into a three-layer feedforward network. Additional network design problems are solved as the WaveARX formalisms provide a systematic design synthesis for the network architecture, training procedure, and excellent initial values of the network parameters. The new structure also isolates and quantifies the linear and nonlinear components of the training data sets. The wavelet function is extended to multidimensional input space using the concept of a norm. The capabilities of the network are demonstrated through several examples in comparison with some widely used linear and nonlinear identification techniques. Separately, the wavelet network of the WaveARX model is shown for the example investigated to have a better performance than two other existing wavelet-based neural networks.

Multivariable model reduction is applied to two processes for simulation, multivariable single input-single output controller design, and singular value decomposition controller design. The model reduction tech-niques investigated fail to maintain some of the dominant characteristics of the full system. More-over, the controllers designed with the reduced models are all unstable when applied to control the full model. Insight into the causes of the failures are discussed in terms of the characteristics maintained by the reduction techniques and the structure of the controllers.