Correction of finite element estimates for Sturm-Liouville eigenvalues

Summary It is shown that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k ⁴ h ²) toO(k h ²). The result still holds when the matrix elements are evaluated by Simpson's rule, but if the trapezoidal rule is used the error isO(k ² h ²). Numerical results demonstrate the usefulness of the correction even for low values ofk.     

Microstructure and composition analysis of group III nitrides by X-ray scattering

The importance of Group III-nitride structures for both light-emitting devices and high-power field effect transistors is well known (J.W. Orton, C.T. Foxon, Rep. Prog. Phys. 61 (1998) 1). In both cases, different alloy composition and doping levels or type are utilised and the device performance also depends critically on the interface quality and defect density. We have used high resolution X-ray scattering to measure the state of strain in the individual layers on an absolute scale to derive the alloy composition, i.e. we have avoided the conventional method of using the substrate as an internal reference since it could be strained. The composition and individual layer thickness are derived through simulation of the profile with this additional strain information and the best-fit profile is obtained with an automatic procedure. These structures are laterally inhomogeneous arising from defects breaking up the structure into narrow vertical columns of nearly perfect material and this produces significant broadening of the diffraction pattern. This broadening in the diffraction pattern has been modelled using an extended dynamical scattering model (P.F. Fewster, X-Ray Scattering from Semiconductors, Imperial College Press, World Scientific, Singapore, 2000) to yield the size distribution of perfect crystal regions. The measurement of the rotation about an axis defined by the growth direction of the GaN with respect to the sapphire is determined and is found to be small. However, a poor quality sample indicates that a large range of rotations is possible in these structures.     

Binaural weighting of monaural spectral cues for sound localization

For human listeners, cues for vertical-plane localization are provided by direction-dependent pinna filtering. This study quantified listeners' weighting of the spectral cues from each ear as a function of stimulus lateral angle, interaural time difference (ITD), and interaural level difference (ILD). Subjects indicated the apparent position of headphone-presented noise bursts synthesized in virtual auditory space. The synthesis filters for the two ears either corresponded to the same location or to two different locations separated vertically by 20 deg. Weighting of each ear's spectral information was determined by a multiple regression between the elevations to which each ear's spectrum corresponded and the vertical component of listeners' responses. The apparent horizontal source location was controlled either by choosing synthesis filters corresponding to locations on or 30 deg left or right of the median plane or by attenuating or delaying the signal at one ear. For broadband stimuli, spectral weighting and apparent lateral angle were determined primarily by ITD. Only for high-pass stimuli were weighting and lateral angle determined primarily by ILD. The results suggest that the weighting of monaural spectral cues and the perceived lateral angle of a sound source depend similarly on ITD, ILD, and stimulus spectral range.     

Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture

We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.     

Feedback localization of freely diffusing fluorescent particles near the optical shot-noise limit

We report near-optimal tracking of freely diffusing fluorescent particles in a quasi-two-dimensional geometry via photon counting and real-time feedback. We present a quantitative statistical model of our feedback network and find excellent agreement with the experiment. We monitor the motion of a single fluorescent particle with a sensitivity of 15 nm/sqrt Hz while collecting fewer than 5000 fluorescence photons/s. Fluorescent microspheres (diffusion coefficient 1.3 microm2/s) are tracked with a root-mean-square tracking error of 170 nm, within a factor of 2 of the theoretical limit set by photon counting shot noise.     

Optimum intermediate fibers for reducing interconnection loss: exact solution

We derive an exact analytical solution for a transmission line of N single-mode intermediate optical fibers that minimize the interconnection loss between any two dissimilar fiber modes that are well described by that paraxial scalar wave equation. Our solution shows that N optimum intermediate fibers reduce the original interconnection loss by a factor of least 1/(N+1) and that the total interconnection loss is only a function of N and the original direct interconnection loss. Our solution is not restricted to axisymmetric fibers or mode fields and therefore could be useful for reducing the interconnection loss between microstructured optical fibers, between certain slab waveguides, or between fibers and optical sources or detectors.     

Sensing and compensation of femtosecond waveform distortion induced by all-order polarization mode dispersion at selected polarization states

We demonstrate full characterization of femtosecond pulse distortion induced by all-order polarization mode dispersion (PMD) at selected polarization states via second-harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements at an average power of under 28 nW. By applying the inverse of the measured spectral phase via a programmable pulse shaper, we compress the distorted pulses from more than 3 ps to nearly bandwidth-limited durations of less than 500 fs. Our results show that SHG FROG measurements performed by using fiber-pigtailed aperiodically poled lithium niobate waveguides can serve as a robust and sensitive tool for characterization of PMD-induced spectral phase.     

Plasma Photocathodes

Plasma wakefield accelerators offer accelerating and focusing electric fields three to four orders of magnitude larger than state-of-the-art radiofrequency cavity-based accelerators. Plasma photocathodes can release ultracold electron populations within such plasma waves and thus open a path toward tunable production of well-defined, compact electron beams with normalized emittance and brightness many orders of magnitude better than state-of-the-art. Such beams will have far-reaching impact for applications such as light sources, but also open up new vistas on high energy and high field physics. This paper reviews the innovation of plasma photocathodes, and reports on the experimental progress, challenges, and future prospects of the approach. Details of the proof-of-concept demonstration of a plasma photocathode in 90° geometry at SLAC FACET within the E-210: Trojan Horse program are described. Using this experience, alongside theoretical and simulation-supported advances, an outlook is given on future realizations of plasma photocathodes such as the upcoming E-310: Trojan Horse-II program at FACET-II with prospects toward excellent witness beam parameter quality, tunability, and stability. Future installations of plasma photocathodes also at compact, hybrid plasma wakefield accelerators, will then boost capacities and open up novel capabilities for experiments at the forefront of interaction of high brightness electron and photon beams.     

Multivariate dynamic modeling for Bayesian forecasting of business revenue

Forecasting enterprise-wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large-scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi-scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context-relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi-scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross-category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.