Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force

We identify a novel route to the birth of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the birth of the SNA which we term as the \emph{bubbling route to SNA}. We characterize and confirm this birth from both experimental and numerical data by maximal Lyapunov exponents and their variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution function. We also strongly confirm the birth of SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.Comment: 11 pages. 11 figures, Accepted for publication in Phys. Rev.

Method of complex paths and general covariance of Hawking radiation

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semi-classical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation. This also shows that there is no correspondence between the particles detected by the model detector and the particle spectrum obtained by the quantum field theoretic analysis -- a result known in other contexts as well.Comment: 9 pages, uses MPLA Style file, Accepted for publication in Mod. Phys. Letts.

Tribological properties of sintered polycrystalline and single crystal silicon carbide

Tribological studies and X-ray photoelectron spectroscopy analyses were conducted with sintered polycrystalline and single crystal silicon carbide surfaces in sliding contact with iron at various temperatures to 1500 C in a vacuum of 30 nPa. The results indicate that there is a significant temperature influence on both the friction properties and the surface chemistry of silicon carbide. The main contaminants on the as received sintered polycrystalline silicon carbide surfaces are adsorbed carbon, oxygen, graphite, and silicon dioxide. The surface revealed a low coefficient of friction. This is due to the presence of the graphite on the surface. At temperatures of 400 to 600 C graphite and copious amount of silicon dioxide were observed on the polycrystalline silicon carbide surface in addition to silicon carbide. At 800 C, the amount of the silicon dioxide decreased rapidly and the silicon carbide type silicon and carbon peaks were at a maximum intensity in the XPS spectra. The coefficients of friction were high in the temperature range 400 to 800 C. Small amounts of carbon and oxygen contaminants were observed on the as received single crystal silicon carbide surface below 250 C. Silicon carbide type silicon and carbon peaks were seen on the silicon carbide in addition to very small amount of graphite and silicon dioxide at temperatures of 450 to 800 C

Do promotions benefit manufacturers, retailers or both ?.

While there has been strong managerial and academic interest in price promotions, much of the focus has been on the impact of such promotions on category sales, brand sales and brand choice. In contrast, little is known about the long-run impact of price promotions on manufacturer and retailer revenues and margins, although both marketing researchers and practitioners consider this a priority area (Marketing Science Institute 2000). Do promotions generate additional revenue and for whom? Which brand, category and market conditions influence promotional benefits and their allocation across manufacturers and retailers?To answer these questions, we conduct a large-scale econometric investigation of the effects of price promotions on manufacturer revenues, retailer revenues and margins. This investigation proceeds in two steps. First, persistence modeling reveals the short- and long-run effects of price promotions on these performance measures. Second, weighted least-squares analysis shows to what extent brand and promotion policies, as well as market-structure and category characteristics, influence promotional impact. A first major finding of our paper is that price promotions do not have permanent monetary effects for either party. Second, in terms of the cumulative, over-time, promotional impact on their revenues, we find significant differences between the manufacturer and retailer. Price promotions have a predominantly positive impact on manufacturer revenues, but their effects on retailer revenues are mixed. Retailer (category) margins, in contrast, are typically reduced by price promotions. Even when accounting for cross-category and store-traffic effects, we still find evidence that price promotions are typically not beneficial to the retailer. Third, our results indicate that manufacturer revenue elasticities are higher for promotions of small-share brands and for frequently promoted brands. Moreover, they are higher for storable products and lower in categories with a high degree of brand proliferation. Retailer revenue elasticities, in turn, are higher for brands with frequent and shallow promotions, for storable products and in categories with a low extent of brand proliferation. As such, from a revenue-generating point of view, manufacturer and retailer interests are often aligned in terms of which categories and brands to promote. Finally, retailer margin elasticities are higher for promotions of small-share brands and for brands with infrequent and shallow promotions. Thus, the implications with respect to the frequency of promotions depend upon the performance measure the retailer chooses to emphasize. The paper discusses the managerial implications of our results for both manufacturers and retailers and suggests various avenues for future research.

A circular dielectric grating for vertical extraction of single quantum dot emission

We demonstrate a nanostructure composed of partially etched annular trenches in a suspended GaAs membrane, designed for efficient and moderately broadband (approx. 5 nm) emission extraction from single InAs quantum dots. Simulations indicate that a dipole embedded in the nanostructure center radiates upwards into free space with a nearly Gaussian far-field, allowing a collection efficiency > 80 % with a high numerical aperture (NA=0.7) optic, and with 12X Purcell radiative rate enhancement. Fabricated devices exhibit an approx. 10 % photon collection efficiency with a NA=0.42 objective, a 20X improvement over quantum dots in unpatterned GaAs. A fourfold exciton lifetime reduction indicates moderate Purcell enhancement.Comment: (3 pages

Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits

We report the first experimental demonstration of chaotic phase synchronization (CPS) in unidirectionally coupled time-delay systems using electronic circuits. We have also implemented experimentally an efficient methodology for characterizing CPS, namely the localized sets. Snapshots of the evolution of coupled systems and the sets as observed from the oscilloscope confirming CPS are shown experimentally. Numerical results from different approaches, namely phase differences, localized sets, changes in the largest Lyapunov exponents and the correlation of probability of recurrence ($C_{CPR}$), corroborate the experimental observations.Comment: Physical_Review_E_82_065201(R) 201