No abstract

An experimental investigation of entrainment and the phenomenon known as periodic pulling is described. Periodic pulling refers to the incomplete entrainment of an oscillatory nonlinear system by a periodically varying driving force. The process whereby the system s oscillation frequency is pulled toward the driving frequency stops short of complete synchronization and is interrupted at regular intervals. In this way, periodic pulling produces pulselike amplitude and frequency modulation in the system s oscillatory response. Associated with these combined, nonsinusoidal modulations is an asymmetric, or single-sided, spectral peak made up of spectral components at frequencies incommensurate with the undriven {spontaneous) and driving frequencies. The system being investigated uses a unijunction transistor as the nonlinear element in an electrical circuit. The behavior of the system is shown to resemble that predicted for a forced van der Pol oscillator with an adjustable nonlinear restoring force.For certain ranges of driving frequency and amplitude, when the system is not entrained to the driving force, periodic pulling is shown to alter the system's oscillatory response significantly from that expected for conventional amplitude modulation involving two sinusoids. The essential features of the periodic pulling phenomenon are observed and compared, with good agreement, to a model.

The experimental verification of spatiotemporal periodic pulling, a specific but universal phenomenon associated with driven, nonlinear, spatiotemporal systems, is reported as part of a study characterizing the ability of dc and chopped laser light to induce periodic pulling in ionization waves propagating in a neon glow-discharge plasma. The degree to which a single-mode laser beam at a metastable transition of 6401 A (1s(5)-2p(9)) influences the discharge is found to depend on the location and magnitude of the perturbation. Cases of ac (chopping the light) and dc perturbation are presented. In a range of chopping frequencies above and below the ionization wave's undriven frequency, the wave can become synchronized to the perturbation. This entrainment range is shown to depend on the frequency difference between the wave and the perturbation, as well as on the perturbation distance from the cathode. Hysteresis is found in the value of the perturbation frequency associated with transitions into and out of entrainment. Outside of entrainment, periodic pulling of a self-excited, propagating, ionization wave by the laser perturbation is observed. This is a case of frequency pulling, or temporal periodic pulling. Inside of entrainment, the chopped laser light controls the frequency and amplitude of the mode. By properly adjusting the frequency and amplitude of one mode with respect to a second mode, periodic pulling of one ionization wave by the mode-locked, propagating, original ionization wave is demonstrated. This is a case of spatiotemporal pulling, involving both wavelength pulling and frequency pulling. Under proper conditions, competition between temporal and spatiotemporal periodic pulling results in a modulation in the dynamics of the system, a process referred to as dynamics modulation.

Useful prediction of the kinematics, dynamics, and chemistry of a system relies on precision and accuracy in the quantification of component properties, operating mechanisms, and collected data. In an attempt to emphasize, rather than gloss over, the benefit of proper characterization to fundamental investigations of multiphase systems incorporating solid particles, a set of procedures were developed and implemented for the purpose of providing a revised methodology having the desirable attributes of reduced uncertainty, expanded relevance and detail, and higher throughput. Better, faster, cheaper characterization of multiphase systems result. Methodologies are presented to characterize particle size, shape, size distribution, density (particle, skeletal and bulk), minimum fluidization velocity, void fraction, particle porosity, and assignment within the Geldart Classification. A novel form of the Ergun equation was used to determine the bulk void fractions and particle density. Accuracy of properties-characterization methodology was validated on materials of known properties prior to testing materials of unknown properties. Several of the standard present-day techniques were scrutinized and improved upon where appropriate. Validity, accuracy, and repeatability were assessed for the procedures presented and deemed higher than present-day techniques. A database of over seventy materials has been developed to assist in model validation efforts and future designs.

Using measurements of spatiotemporal patterns in the light-emission fluctuations of the positive column of a neon glow discharge, the spatiotemporal nature of the nonlinear interaction, known as periodic pulling, which occurs between pairs of self-excited, propagating, ionization waves, is characterized. Transitions occur between discrete longitudinal ionization-wave modes if the discharge current is smoothly ramped. At a given discharge current, multiple modes coexist along the entire plasma column with one mode dominating over all others. As the current is incremented towards the transition from one dominant mode to another, the prospective dominant mode grows and interacts with the dominant mode in space and time. Spatiotemporal periodic pulling is experimentally demonstrated. Characteristic modulation in both time and space of both frequency and wave-number spectra are presented. This phase modulation is low frequency and long wavelength. It maximizes at the instant of transition when both modes are of comparable amplitudes. The transition involves an Eckhaus instability that triggers the spatiotemporal dislocation, which represents the creation or annihilation of a mode number.