Electrochemical Frequency Modulation: New Approach and Revision of Previous Model

A careful evaluation of the earlier model (1-2) for electrochemical frequency modulation (EFM) involving two sinusoidal applied potentials for the determination of corrosion parameters shows an algebraic error. Although the missing term in the original derivation appears to be insignificant, it is found that errors involved in corrosion current determination, and especially in evaluation of the Tafel slopes can be very significant, which is of consequence because of the rising popularity of this technique. The magnitude of error is found to be a function of the inherent corrosion characteristics (anodic and cathodic Tafel slopes) of the corroding material as well as the applied peak potential of the modulation. A corrected model with detailed steps showing the appropriate math is presented. In addition, using the experimental data available in the literature, the errors involved in estimating the corrosion parameters by the earlier EFM model of Bosch et al (1-2) are evaluated. The corrected corrosion current and the Tafel slopes can be recovered from the incorrect model without the benefit of the harmonic currents, as shown in this paper.The analysis is also presented for the case of only one applied sinusoidal frequency modulation, which offers several advantages over the multiple frequency modulation.

Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media

We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized Fourier basis and excluding cut-off frequen- cies (also known as Rayleigh-Wood frequencies), we rigorously establish the well-posedness of both continuous and discrete problems, and prove super-algebraic error convergence rates for the proposed scheme. Through several numerical examples, we confirm our findings and show performances competitive to those attained via Nystr\"om methods.

Correcting the Correction: A Revised Formula to Estimate Partial Correlations between True Scores

Bohrnstedt’s (1969) attempt to derive a formula to compute the partial correlation coefficient and simultaneously correct for attenuation sought to simplify the process of performing each task separately. He suggested that his formula, developed from algebraic and psychometric manipulations of the partial correlation coefficient, produces a corrected partial correlation value. However, an algebraic error exists within his derivations. Consequently, the formula proposed by Bohrnstedt does not appropriately represent the value he intended it to estimate. By correcting the erroneous step and continuing the derivation based upon his proposed procedure, the steps outlined in this paper ultimately produce the formula that Bohrnstedt desired.

Adaptive linear solution process for single-phase Darcy flow

This article presents an adaptive approach for solving linear systems arising from self-adjoint Partial Differential Equations (PDE) problems discretized by cell-centered finite volume method and stemming from single-phase flow simulations. This approach aims at reducing the algebraic error in targeted parts of the domain using a posteriori error estimates. Numerical results of a reservoir simulation example for heterogeneous porous media in two dimensions are discussed. Using the adaptive solve procedure, we obtain a significant gain in terms of the number of time steps and iterations compared to a standard solve.