Steepest Descent, CG, and Iterative Regularization of Ill-Posed Problems

The state of the art iterative method for solving large linear systems is the conjugate gradient (CG) algorithm. Theoretical convergence analysis suggests that CG converges more rapidly than steepest descent. This paper argues that steepest descent may be an attractive alternative to CG when solving linear systems arising from the discretization of ill-posed problems. Specifically, it is shown that, for ill-posed problems, steepest descent has a more stable convergence behavior than CG, which may be explained by the fact that the filter factors for steepest descent behave much less erratically than those for CG. Moreover, it is shown that, with proper preconditioning, the convergence rate of steepest descent is competitive with that of CG.This revised version was published online in October 2005 with corrections to the Cover Date.     

Investigations in the amplitude of sounded piano tones

The relationship between final hammer velocity and maximum amplitude of radiated piano sound was investigated. Piano tones with varying hammer velocities were produced by a computer-monitored acoustic piano containing optical sensors and solenoids, and the sounded tones were recorded and digitized for analysis. Maximum amplitudes over the duration of the sounded tones were linearly proportional to piano hammer velocities for a range of frequencies and hammer velocities. Changes in room acoustics did not alter the linear relationship. Measurements of maximum amplitudes of individual tones and combined tones (dyads) also indicated a linear relationship between the sum of the maximum amplitudes of the individual tones and the maximum amplitude of the dyads. These findings indicate that the principle of superposition holds for peak amplitudes of sounded piano tones. Findings are discussed with regard to production and perception of musical dynamics.     

A novel detection scheme for vibration monitoring using optical techniques

An all-fibre interferometer which allows the measurement of the movement (speed and distance) of a vibrating body is presented. An electronic signal processing scheme is used and this is contrasted with the measurement of velocity through an optical processing technique, which is however, more complex and expensive to implement. The overall simplicity of the electronic technique, the low cost of components and the use of an all-fibre arrangement make this an attractive system to implement where the more limited information available is sufficient for monitoring purposes.     

Low-threshold interband cascade lasers operating above room temperature

Mid-IR type-II interband cascade lasers were demonstrated in pulsed mode at temperatures up to 325 K and in continuous mode up to 200 K. At 80 K, the threshold current density was 8.9 A/cm² and a continuous wave output power of 140 mW/facet was obtained.     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.