Feedback Control of Traveling Wave Solutions of the Complex Ginzburg Landau Equation

Through a linear stability analysis, we investigate the effectiveness of a noninvasive feedback control scheme aimed at stabilizing traveling wave solutions of the one-dimensional complex Ginzburg Landau equation (CGLE) in the Benjamin-Feir unstable regime. The feedback control is a generalization of the time-delay method of Pyragas, which was proposed by Lu, Yu and Harrison in the setting of nonlinear optics. It involves both spatial shifts, by the wavelength of the targeted traveling wave, and a time delay that coincides with the temporal period of the traveling wave. We derive a single necessary and sufficient stability criterion which determines whether a traveling wave is stable to all perturbation wavenumbers. This criterion has the benefit that it determines an optimal value for the time-delay feedback parameter. For various coefficients in the CGLE we use this algebraic stability criterion to numerically determine stable regions in the (K,rho) parameter plane, where rho is the feedback parameter associated with the spatial translation and K is the wavenumber of the traveling wave. We find that the combination of the two feedbacks greatly enlarges the parameter regime where stabilization is possible, and that the stability regions take the form of stability tongues in the (K,rho)--plane. We discuss possible resonance mechanisms that could account for the spacing with K of the stability tongues.Comment: 33 pages, 12 figure

Secondary instabilities of hexagons: a bifurcation analysis of experimentally observed Faraday wave patterns

We examine three experimental observations of Faraday waves generated by two-frequency forcing, in which a primary hexagonal pattern becomes unstable to three different superlattice patterns. We use the symmetry-based approach developed by Tse et al. to analyse the bifurcations involved in creating the three new patterns. Each of the three examples reveals a different situation that can arise in the theoretical analysis.Comment: 14 pages LaTeX, Birkhauser style, 5 figures, submitted to the proceedings of the conference on Bifurcations, Symmetry and Patterns, held in Porto, June 200

Observational and Theoretical Investigation of Cylindrical Line Source Blast Theory Using Meteors

During their passage through the atmosphere meteoroids produce a hypersonic shock which may be recorded at the ground in the form of infrasound. The first objective of this project was to use global infrasound measurements to estimate the influx of large (meter/decameter) objects to Earth and investigate which parameters of their ablation and disruption can be determined using infrasound records. A second objective was to evaluate and extend existing cylindrical line source blast theory for meteoroids by combining new observations with earlier analytical models, and validate these against centimetre-sized optical meteor observations. The annual terrestrial influx of large meteoroids (kinetic energies above a threshold E) was found to be N=4.5E–0.6 where E is expressed in kilotons of TNT equivalent. This indicates that estimates of the influx derived from telescopic surveys of small asteroids near Earth are too low. Infrasound records from an event over Indonesia in 2009 were used to develop a technique to estimate the altitude of meteoroid terminal bursts and their energies. The burst altitude in this case was determined to be near 20 kilometers and the energy between 8 – 67 kilotons of TNT equivalent. Using a network of optical cameras and an Infrasound Array in southern Ontario, Canada, 71 centimetre-sized meteoroids were optically detected and associated with infrasonic signals recorded at the ground. The shock source height and its uncertainty along the meteor trail from raytracing was determined including wind effects due to gravity waves perturbations, which were found to be significant for such short range (km) infrasound propagation. Approximately 75% of signals were attributed to cylindrical line source geometry, while ray deviation angles greater than 117° were associated with spherical shocks. The ReVelle (1974) meteor infrasound model was found to be accurate when using infrasound period measurements, but systematically under-predicted blast radii when amplitude is used. The latter can be better modelled assuming the wave distortion distance is “\u3c6%, as opposed to the 10% adopted by ReVelle. Infrasonic masses found from ReVelle’s theory deviate from photometric estimates largely due to meteoroid fragmentation

Broken symmetries and pattern formation in two-frequency forced Faraday waves

We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the effects of time translation, time reversal and Hamiltonian structure for three illustrative examples: hexagons, two-mode superlattices, and two-mode rhomboids. By means of explicit parameter symmetries, we show how the size of various three-wave resonant interactions depends on the frequency ratio m:n and on the relative temporal phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.Comment: 4 pages, 6 figure

Simultaneous IUE, EXOSAT and optical observations of the unusual AM Her type variable H058+608

Simultaneous observations of the AM Her type variable H0538+608 made with IUE, EXOSAT, and a 1.3 m ground based telescope, and subsequent optical spectrophotometry at high and low resolution are discussed. The X-ray and optical data show clear evidence of a 3.30 + or - 0.03 hr period. Three SWP spectra were taken outside of eclipse and during overlapping phase intervals. The UV spectra contain strong emission lines characteristic of this class of objects and a flat continuum which appears to be deficient, given the brightness of source at optical and X-ray wavelengths. There is evidence for intensity variations in emission lines, particularly C IV. The X-ray light curves for H0538+608 reveal behavior which may be related to irregularities in its accretion flow