The detection of the onset of electrode-electrolyte interfaceimpedance nonlinearity: a theoretical study

The equivalent series resistance and reactance of the electrode-electrolyte interface impedance have both been used to detect the onset of signal amplitude induced nonlinearity. Using a theoretical model, it is shown that the choice of the most sensitive indicator depends on the phase angle of the “polarization” impedance and on the applied frequency     

Algorithm for cosine transform of Toeplitz matrices

An algorithm for calculating the 2D cosine transform of a Toeplitz matrix is presented. The algorithm is based on the application of 1D cosine transforms. More specifically, four 1D cosine transforms of size N are needed to obtain the transform of a Toeplitz matrix of size N×N. This is an improvement over previously published algorithms. The algorithm is also simple and regular     

Chemical composition and reaction analysis of single aerosol particles

In situ measurements of gas-liquid surface reactions of single aerosol microdroplets are presented. By means of optical levitation in combination with elastic (Mie) and inelastic (Raman) light scattering it is possible to get information on the chemistry of e.g. acid/base reactions as well as the physical behavior of single microparticles.     

Multidimensional augmented current equation including velocityovershoot

The augmented drift-diffusion current equation, which includes velocity overshoot effects through the space derivatives of the electric field, cannot be directly extended beyond one dimension. A new formalism is developed which considers the carrier heating and the distribution relaxation effects to obtain a multidimensional augmented drift diffusion current equation. The equivalent mobility containing the velocity overshoot correction is derived from the perturbation analysis on the carrier temperature using the energy balance equation. The issues related to the numerical implementation of this generalized model and the validity of the assumptions are also discussed     

On the RLSA antenna optimum design for DBS reception

An optimal design for the RLSA (radial line slot array) antenna useful for DBS reception is presented. Classical geometries and structures given in the literature are first used. It is found that in some cases these are not suitable. So, optimization techniques by using the right objective functions have been applied. Two different methods were developed and three antennas were designed. Numerical results and comparisons with other similar antennas give the advantages of our design     

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

THE USE OF THERMOELASTICITY TO EVALUATE STRESS REDISTRIBUTION AND NOTCH SENSITIVITY IN CERAMIC MATRIX COMPOSITES

Thermoelastic stress analysis was used to document the effect of composite damage on the stress distribution in three ceramic matrix composites. Composite damage was found to significantly alter the thermoelastic response of each material, with the greatest effect noted in SiC/CAS. Thermoelastic imaging of these materials affords a more complete picture of how the various damage mechanisms affect the stress distribution. In particular, a stress concentration factor computed from thermoelastic images, serves as an indicator of stress redistribution. The stress concentration factors were computed by comparing notch root to far field temperatures, and monitored after the introduction of various amounts of damage. In each material, the stress concentration factor diminished as the damaging load approached the ultimate stress. Reduction in the stress concentration is associated with local changes in modulus, mechanistically arising from combinations of fiber, matrix and interface fracture. Stress redistribution occurs as a consequence of modulus changes, leading to lower notch sensitivity in each of the tested composites.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.