Analytic and Numerical Aspects of the Nonsingular Laplacian Representation of the Asymptotic Part of the Layered-Medium Green Function in the Mixed Potential Formulation

We report on developments in the evaluation of matrix elements of the electric and magnetic field operators involving the asymptotic (large transverse wave-number or small transverse distances) components of the mixed-potential Green's function of a layered medium. Subtracting these asymptotic terms significantly accelerates numerical computation of the Sommerfeld-type integrals required in constructing Green's function and then the matrix elements [1]

New Simplified Analytic Expressions for the Matrix Elements of the Asymptotic Part of the Layered Medium Green Function in the Mixed Potential Formulation

We report new developments in the analytical evaluation of the near-field contribution to the matrix elements of the electric and magnetic field operators for planar conducting structures embedded in a layered medium. The method is applicable to Rao-Wilton-Glisson (RWG) basis functions supported on parallel interfaces in the medium. Our method is an extension of the approach described in [1] of representing a Green function as a two-dimensional Laplacian of an auxiliary function. Such Laplacian representations can be obtained for the asymptotic forms of the Green functions, which are being subtracted in order to regularize the behavior of the Sommerfeld-type integrals. Matrix elements resulting from these asymptotic forms, given originally as quadruple surface integrals with singular integrands, are then reduced to double contour integrals over the perimeters of the surface elements, involving simple closed-form non-singular auxiliary functions

Noise thermometry and electron thermometry of a sample-on-cantilever system below 1 Kelvin

We have used two types of thermometry to study thermal fluctuations in a microcantilever-based system below 1 K. We measured the temperature of a cantilever's macroscopic degree-of-freedom (via the Brownian motion of its lowest flexural mode) and its microscopic degrees-of-freedom (via the electron temperature of a metal sample mounted on the cantilever). We also measured both temperatures' response to a localized heat source. We find it possible to maintain thermal equilibrium between these two temperatures and a refrigerator down to at least 300 mK. These results are promising for ongoing experiments to probe quantum effects using micromechanical devices

Array Decomposition‐Fast Multipole Method for finite array analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95440/1/rds5001.pd

High sensitivity cantilevers for measuring persistent currents in normal metal rings

We propose a new approach to measuring persistent currents in normal metal rings. By integrating micron-scale metal rings into sensitive micromechanical cantilevers and using the cantilevers as torque magnetometers, it should be possible to measure the rings' persistent currents with greater sensitivity than the SQUID-based and microwave resonator-based detectors used in the past. In addition, cantilever-based detectors may allow for measurements in a cleaner electromagnetic environment. We have fabricated ultra sensitive cantilevers with integrated rings and measured their mechanical properties. We present an estimate of the persistent current sensitivity of these cantilever-based detectors, focusing on the limits set by the cantilever's Brownian motion and the shot noise in the laser interferometer that monitors the cantilever

Two-step contribution to the spin-longitudinal and spin-transverse cross sections of the quasielastic (p,n) reactions

The two-step contribution to the spin-longitudinal and the spin-transverse cross sections of ^{12}C,^{40}Ca(p,n) reactions at 494 MeV and 346 MeV is calculated. We use a plane-wave approximation and evaluate the relative contributions from the one-step and the two-step processes. We found that the ratios of the two-step to the one-step processes are larger in the spin-transverse cross sections than in the spin-longitudinal ones. Combining these results with the distorted-wave impulse approximation (DWIA) results we obtained considerable two-step contributions to the spin-longitudinal and the spin-transverse cross sections. The two-step processes are important in accounting for the underestimation of the DWIA results for the spin-longitudinal and the spin-transverse cross sections.Comment: LaTeX 11 pages, 10 figure