Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule

A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the “fuzzy sum rule” of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,Du,D²u)=0 is under consideration.     

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.