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

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

Chow's theorem and universal holonomic quantum computation

A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, these conditions determine that the holonomy group of the two-qubit interaction model contains $SU(2) \times SU(2)$. In particular, a universal two-qubit logic gate is attainable for this model.Comment: 13 page

Driving in ZZ Ceti stars - Problem solved?

There is a fairly tight correlation between the pulsation periods and effective temperatures of ZZ Ceti stars (cooler stars have longer periods). This seems to fit the theoretical picture, where driving occurs in the partial ionization zone, which lies deeper and deeper within the star as it cools. It is reasonable to assume that the pulsation periods should be related to the thermal timescale in the region where driving occurs. As that region sinks further down below the surface, that thermal timescale increases. Assuming this connection, the pulsation periods could provide an additional way to determine effective temperatures, independent of spectroscopy. We explore this idea and find that in practice, things are not so simple.Comment: 4 pages, 3 figure

Haptic feedback in the training of veterinary students

This paper reports on an initial study into the use of haptic (or touch) technology in the training of veterinary students. One major problem faced in veterinary education is that animals can be harmed by inexperienced students who are trying to learn the skills they need. The aim of the work described here is to provide haptic models to simulate internal examinations of horses so that students can learn the basic skills required on computer and then transfer to real animals with much less risk of doing them injury

Maternal smoking during pregnancy and appetite control in offspring

Aims: Intrauterine exposure to tobacco smoke products has been associated with long-term neurobehavioral effects. Modified appetite control might explain the recently observed association between maternal smoking during pregnancy and obesity in offspring. Methods: Some 10,557 British adults aged 42 years born between 3-9 March 1958 were followed up in a birth cohort study (NCDS). The main outcome measure was self-reported poor appetite at age 42 years and main exposure was maternal smoking during pregnancy. Results: The proportion of offspring with poor appetite increased with maternal smoking during pregnancy: nonsmoking 4.5%; (4.0% - 5.0%), medium smoking 5.6%; (4.5 % - 6.8 %), variable smoking 6.8 %; (4.9 % - 9.1 %) and heavy smoking 7.7 %; (6.3 % - 9.4 %). The unadjusted odds ratios for maternal smoking during pregnancy (ever/never) and poor appetite is 1.49 (1.25 - 1.77) and after adjustment for BMI at 42 years and other potential confounding factors it is 1.22 (1.07 - 1.48). Conclusions: Offspring of mothers who smoked during pregnancy were more likely to report a poor appetite independent of a number of potential confounding factors. Although not in the expected direction, the results suggest maternal smoking during pregnancy may influence appetite perception through a developmental influence or through confounding by social factors

Wildfire Risk Management on a Landscape with Public and Private Ownership: Who Pays?

Resource /Energy Economics and Policy,