The nonlinear charge storage property of driven Si p-n junction passive resonators gives rise to chaotic dynamics: period doubling, chaos, periodic windows, and an extended period-adding sequence corresponding to entrainment of the resonator by successive subharmonics of the driving frequency. The physical system is described; equations of motion and iterative maps are reviewed. Computed behavior is compared to data, with reasonable agreement for Poincare sections, bifurcation diagrams, and phase diagrams in parameter space (drive voltage, drive frequency). N = 2 symmetrically coupled resonators are found to display period doubling, Hopf bifurcations, entrainment horns ("Arnol'd tongues"), breakup of the torus, and chaos. This behavior is in reasonable agreement with theoretical models based on the characteristics of single-junction resonators. The breakup of the torus is studied in detail, by Poincart sections and by power spectra. Also studied are oscillations of the torus and cyclic crises. A phase diagram of the coupled resonators can be understood from the model. Pincare sections show self-similarity and fractal structure, with measured values of fractal dimension d = 2.03 and d = 2.23 for N = 1 and N = 2 resonators, respectively. Two line-coupled resonators display first a Hopf bifurcation as the drive parameter is increased, in agreement with the model. For N = 4 and N = 12 line-coupled resonators complex quasiperiodic behavior is observed with up to 3 and 4 incommensurate frequencies, respectively. I . I N T R O D U C T I O NMany physical systems can be viewed as a collection of coupled oscillators or modes. In this paper we report the behavior of N driven nonlinear oscillators, coupled in several ways, for N= 1, 2, 4, 12. The oscillator is a passive resonator comprised of a silicon p-n junction used as a nonlinear chargestorage element, together with an external inductance. This physical system can be approximately modeled as a driven damped oscillator with a very nonlinear asymmetric restoring force, and has been used previously, first by Linsay' who found that it exhibited a period-doubling sequence with convergence ratio S and power spectra as predicted by Feigenbaum.' It was shown to display other universal behavior patterns3 and has been much studied;4 in particular, intermittency,' effects of added noise,6*' and cri~es~~~ have been reported. For two or more coupled resonators (which we also refer to as "oscillators") the system displays a much richer dynamical structure:'O~'l period doubling, Hopf bifurcations to quasiperiodicity, entrainment horns, and breakup of the invariant torus. This is the main subject of this paper. We view the junction oscillator as an interesting physical system from the viewpoint of contemporary nonlinear dynamics theory." It is not an analog computer and is to be clearly distinguished from the numerical solutions of mathematical models that approximately represent it.

There exists considerable evidence that manufacturing costs and consumer prices of residential appliances have decreased in real terms over the last several decades. This phenomenon is generally attributable to manufacturing efficiency gained with cumulative experience producing a certain good, and is modeled by an empirical experience curve. The technical analyses conducted in support of U.S. energy conservation standards for residential appliances and commercial equipment have, until recently, assumed that manufacturing costs and retail prices remain constant during the projected 30-year analysis period. This assumption does not reflect real market price dynamics. Using price data from the Bureau of Labor Statistics, we present U.S. experience curves for room air conditioners, clothes dryers, central air conditioners, furnaces, and refrigerators and freezers. These experience curves were incorporated into recent energy conservation standards analyses for these products. Including experience curves increases the national consumer net present value of potential standard levels. In some cases a potential standard level exhibits a net benefit when considering experience, whereas without experience it exhibits a net cost. These results imply that past energy conservation standards analyses without experience curves may have undervalued the economic benefits of potential standard levels, possibly resulting in less stringent standards and reduced energy savings than was economically justified.

No abstract

No abstract