A fast multipole method for the evaluation of elastostatic fields in a half-space with zero normal stress

In this paper, we present a fast multipole method (FMM) for the half-space Green’s function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (Physics 7, 195–202 1936). The image structure of this Green’s function is unbounded, so that standard outgoing representations are not easily available. We introduce two such representations here, one involving an expansion in plane waves and one involving a modified multipole expansion. Both play a role in the FMM implementation.     

Determining optimal replacement time for metal cutting tools

Traditional tool life models do not take into account the variation inherent in metal cutting processes. As a consequence, the real tool life rarely matches the predicted values. To compensate for this uncertainty, tools are usually replaced prematurely, which leads to unnecessarily high tool costs. In some cases, however, wear-out occurs earlier than predicted, which imposes a risk of workpiece damage or rework and can lead to other extra charges. To balance these costs, this paper proposes an age replacement model. It is assumed that penalty costs are incurred each time a tool fails before the planned replacement. The probability of such an event is determined from the tool reliability function, which models the wear-out by a mixture of Weibull distributions, while failures due to external stresses are accounted for by a homogeneous Poisson process. The optimal replacement time is then determined from a total time on test (TTT) plot. The adequacy of the proposed approach for practical application is tested and confirmed in a case study on turning of Inconel 718 with cubic boron nitride (CBN) tools.     

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A ,φ in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a well‐conditioned second‐kind Fredholm integral equation that has no spurious resonances, avoids low‐frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, φ^scat, is determined entirely by the incident scalar potential φ^inc. Likewise, the unknown vector potential defining the scattered field, A ^scat is determined entirely by the incident vector potential A^inc. This decoupled formulation is valid not only in the static limit but for arbitrary ω ≥ 0$. © 2016 Wiley Periodicals, Inc.     

Capillary electrophoretic determination of thiosulfate,sulfide and sulfite using in-capillary derivatization with iodine

A new capillary electrophoresis (CE) method was developed for the rapid, simple and selective determination of thiosulfate, sulfide and sulfite species. The proposed method is based on the in-capillary derivatization of separated sulfur anions by mixing their zones with the iodine zone during the electrophoretic migration and direct UV detection of iodide formed. The optimal conditions for the separation and derivatization reaction were established by varying electrolyte pH, electrolyte counter-ion, concentration of iodine, and applied voltage. The optimized separations were carried out in 20 mmol/L Tris-chloride electrolyte (pH 8.5) using direct UV detection at 214 nm. All three sulfur species were well resolved in less than 4 min. The method gives repeatability comparable or even better than this obtained for sulfur anions using standard CE technique. The proposed CE system was applied to the monitoring of sulfur anions in spent fixing solutions during the electrolytic oxidation.     

Boundary integral equation analysis on the sphere

We present a systematic analysis of the integral operators of potential theory that arise when solving the Helmholtz or Maxwell equations in the exterior (or interior) of a sphere in the frequency domain. After obtaining expressions for the signatures of layer potentials in the spherical harmonic or vector spherical harmonic basis, we turn to a consideration of various integral equations that have been proposed in the literature for problems of acoustic and electromagnetic scattering. The selection of certain parameters in “combined field” and “Calderon-preconditioned” formulations is shown to have a significant impact on condition number, extending earlier work by Kress and others.     

A Nyström method for weakly singular integral operators on surfaces

We describe a modified Nyström method for the discretization of the weakly singular boundary integral operators which arise from the formulation of linear elliptic boundary value problems as integral equations. Standard Nyström and collocation schemes proceed by representing functions via their values at a collection of quadrature nodes. Our method uses appropriately scaled function values in lieu of such representations. This results in a scheme which is mathematically equivalent to Galerkin discretization in that the resulting matrices are related to those obtained by Galerkin methods via conjugation with well-conditioned matrices, but which avoids the evaluation of double integrals. Moreover, we incorporate a new mechanism for approximating the singular integrals which arise from the discretization of weakly singular integral operators which is considerably more efficient than standard methods. We illustrate the performance of our method with numerical experiments.