Error estimation for numerical differential equations

Given a capable human being and a computer, it is possible to make an approximation to the solution of a nonlinear differential equation. However, under the (usually correct) assumption that the equation is analytically intractable, the result of the computation is not the exact solution; indeed it may be so far from the exact solution as to be completely useless. We are interested in the relationship between the effort expended by the human and the computer, and the duality of the computed approximation to a partial or ordinary differential equation. To be specific, we would like to think in terms of a cost-benefit analysis. The cost of the computation is a combination of the human effort and computer resources used to obtain the approximation. The benefit includes, of course, the computed approximation, but it also includes an estimate of the quality of the approximation, that is, an error estimate. It is our opinion that in computational science, as with the experimental sciences, results should always be presented with some estimate of their accuracy. In addition, however, there is another facet to error estimation: one cannot even attempt a cost-benefit analysis or efficiency comparison of methods without an error estimate to evaluate the results     

Fundamental properties of radiation from a leaky mode excited on a planar transmission line

By using a specific normalization, it is shown that the TM/sub 0/ radiation field from a leaky mode that is excited by a source on any printed-circuit structure can be represented in a unified manner. The general properties of the normalized leaky-mode radiation field are examined in detail for a variety of phase and attenuation constants, as well as distances from the source, and for different types of source excitations. The normalized leaky-mode radiation field is compared to similarly normalized geometrical-optics and far-field radiation expressions to provide further insight into the nature of the radiation fields in the near- and far-field regions. The results provide a general view of leaky-mode radiation properties independent of the type of planar transmission line or background structure.     

CW high power single-lobed far-field operation of long-cavityAlGaAs-GaAs single-quantum-well laser diodes grown by MOCVD

Data on long-cavity 100-μm-wide broad-stripe laser diodes that lase with a barrow single-lobed far-field pattern in continuous room-temperature operation are presented. Diodes with a cavity length of 1250 μm emit a power of 200 mW per facet into a 2.5° lobe (full width at half maximum). Short-cavity devices (cavity length of 350 μm) lase with a continuously increasing number of lateral modes right from threshold, and exhibit a far-field divergence that is over three times greater than that of 1250-μm diodes. Explanations for the effect of increasing cavity length on the field patterns of these devices are proposed, based on the measured increase in injected carrier diffusion length in long-cavity diodes and the influence of thermal waveguiding and mirror losses on intermodel discrimination     

Millimeter-wave components and subsystems built using microstriptechnology

The author describes the evaluation of microstrip as a transmission medium for components and subsystems operating in the millimeter wavebands. The manufacturing process for thin-film MICs on single-crystal quartz is described. The microwave integrated circuit (MIC) manufacturing process is suitable for high-value manufacturing of highly integrated subsystems since manufacturing costs for the circuits are almost independent of the number of circuit functions. Designs for various circuit elements are discussed, and an integrated subsystem is described in which MIC techniques are used to produce a miniature millimeter-wave distance-measuring sensor. Range measurement results for the miniature sensor are presented     

The importance of choosing attractors for optimizing chaotic communications

In this brief, we consider methods to improve the performance of chaotic communication schemes. We study a system using a receiver which explicitly includes the presence of noise in the channel. We show how the choice of chaotic dynamical system generating the transmitted signal is crucial. We observe a large variation in bit error rate performance of the system as parameters in the maps are changed, and we propose a simple explanation for this variation.     

Ultrasonic wave propagation in cancellous and cortical bone: prediction of some experimental results by Biot's theory.

Pulse transmission ultrasound was used to determine the longitudinal wave speed along the direction of trabecular alignment in 32 water-saturated anisotropic tibial bovine cancellous bone samples and in one cortical bone sample also from the bovine tibia. These results are compared to published ultrasound wave-speed data obtained from bovine femoral specimens. Nonlinear regression was used to fit Biot's theory to the data. The correlation coefficient for regression analysis between the experimental ultrasound velocities and the velocities predicted by Biot's theory was r = 0.78.     

Ultraviolet photoemission spectroscopy of hydrogen complex deactivation on InP:Zn(1 0 0) surfaces

Ultraviolet photoemission spectroscopy is used to study the kinetics of the H-Zn complex deactivation in Zn doped InP(1 0 0). Hydrogen injected into the material electronically passivates the local carrier concentration. Reverse-biased anneals of the InP under ultra-high vacuum show a dramatic change in the work function of the material with increasing temperature. Spectral features are also shown to be sensitive to sample temperature. To our knowledge, we show the first view of hydrogen retrapping at the surface using photoemission spectroscopy. A simple photoelectron threshold energy analysis shows the state of charge compensation of the material.