Regularization matrices for discrete ill-posed problems in several space-dimensions

Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space dimensions. The matrix that defines these problems is very ill conditioned and generally numerically singular, and the right-hand side, which represents measured data, is typically contaminated by measurement error. Straightforward solution of these problems is generally not meaningful due to severe error propagation. Tikhonov regularization seeks to alleviate this difficulty by replacing the given linear discrete ill-posed problem by a penalized least-squares problem, whose solution is less sensitive to the error in the right-hand side and to roundoff errors introduced during the computations. This paper discusses the construction of penalty terms that are determined by solving a matrix nearness problem. These penalty terms allow partial transformation to standard form of Tikhonov regularization problems that stem from the discretization of integral equations on a cube in several space dimensions

Calibrating dipolar interaction in an atomic condensate

We revisit the topic of a dipolar condensate with the recently derived more rigorous pseudo-potential for dipole-dipole interaction [A. Derevianko, Phys. Rev. A {\bf 67}, 033607 (2003)]. Based on the highly successful variational technique, we find that all dipolar effects estimated before (using the bare dipole-dipole interaction) become significantly larger, i.e. are amplified by the new velocity-dependent pseudo-potential, especially in the limit of large or small trap aspect ratios. This result points to a promising prospect for detecting dipolar effects inside an atomic condensate.Comment: 5 figures, to be publishe

Use of high-resolution measurements for the retrieval of temperature and gas-concentration profiles from outgoing infrared spectra in the presence of cirrus clouds

We explore ways in which high-spectral-resolution measurements can aid in the retrieval of atmospheric temperature and gas-concentration profiles from outgoing infrared spectra when optically thin cirrus clouds are present. Simulated outgoing spectra that contain cirrus are fitted with spectra that do not contain cirrus, and the residuals are examined. For those lines with weighting functions that peak near the same altitude as the thin cirrus, unique features are observed in the residuals. These unique features are highly sensitive to the resolution of the instrumental line shape. For thin cirrus these residual features are narrow (≤0.1 cm-1), so high spectral resolution is required for unambiguous observation. The magnitudes of these unique features are larger than the noise of modern instruments. The sensitivities of these features to cloud height and cloud optical depth are also discussed. Our sensitivity studies show that, when the errors in the estimation of temperature profiles are not large, the dominant contribution to the residuals is the misinterpretation of cirrus. An analysis that focuses on information content is also presented. An understanding of the magnitude of the effect and of its dependence on spectral resolution as well as on spectral region is important for retrieving spacecraft data and for the design of future infrared instruments for forecasting weather and monitoring greenhouse gases

Single-Walled Carbon Nanotubes as Shadow Masks for Nanogap Fabrication

We describe a technique for fabricating nanometer-scale gaps in Pt wires on insulating substrates, using individual single-walled carbon nanotubes as shadow masks during metal deposition. More than 80% of the devices display current-voltage dependencies characteristic of direct electron tunneling. Fits to the current-voltage data yield gap widths in the 0.8-2.3 nm range for these devices, dimensions that are well suited for single-molecule transport measurements