Comparison of eigenanalysis and Ritz vector approaches for response spectrum analysis of soil-pile-bridge systems

Frequency-based analysis techniques such as response spectrum analysis (RSA) are widely used for designing bridges in seismically active regions. Two well-known analysis procedures that underlie RSA are the solution of the eigenproblem and the approximation of the solution to the eigenproblem (i.e., approximation of eigenvectors and eigenvalues) through use of force-dependent Ritz vectors. While frequency-based methods have achieved widespread adoption in practice, certain simplifications remain common, such as neglecting soil-structure interaction (SSI) due to a fixed-base assumption. In the present study, frequency-based techniques packaged within a research version of a design-oriented computational tool are employed to analyze, assess, and compare results obtained from RSA with use of the eigenanalysis, and separately, Ritz vector approaches. Importantly, for the bridge configurations analyzed, SSI is taken into account. As outcomes, the potential benefits of the Ritz vector approach (as well as modeling strategies) are demonstrated. The study outcomes are intended to aid practicing engineers when the need to account for SSI is recognized as pertinent to a given bridge seismic design application.

Analysis of Polarimetric Mini-SAR and Mini-RF Datasets for Surface Characterization and Crater Delineation on Moon

The hybrid polarimetric architecture of Mini-SAR and Mini-RF onboard Indian Chandrayaan-1 and LRO missions were the first to acquire shadowed polar images of the Lunar surface. This study aimed to characterize the surface properties of Lunar polar and non-polar regions containing Haworth, Nobile, Gioja, an unnamed crater, Arago, and Moltke craters and delineate the crater boundaries using a newly emerged approach. The Terrain Mapping Camera (TMC) data of Chandrayaan-1 was found useful for the detection and extraction of precise boundaries of the craters using the ArcGIS Crater tool. The Stokes child parameters estimated from radar backscatter like the degree of polarization (m), the relative phase (δ), Poincare ellipticity (χ) along with the Circular Polarization Ratio (CPR), and decomposition techniques, were used to study the surface attributes of craters. The Eigenvectors and Eigenvalues used to measure entropy and mean alpha showed distinct types of scattering, thus its comparison with m-δ, m-χ gave a profound conclusion to the lunar surface. The dominance of surface scattering confirmed the roughness of rugged material. The results showed the CPR associated with the presence of water ice as well as a dihedral reflection inside the polar craters.

The field of values of Jones matrices: classification and special cases

The concept of field of values (FoV), also known as the numerical range, is applied to the 2 × 2 Jones matrices used in polarization optics. We discover the relevant interplay between the geometric properties of the FoV, the algebraic properties of the Jones matrices and the representation of polarization states on the Poincaré sphere. The properties of the FoV reveal hidden symmetries in the relationships between the eigenvectors and eigenvalues of the Jones matrices. We determine the main mathematical properties of the FoV, discuss the special cases that are relevant to polarization optics, and describe its application to calculate the Pancharatnam-Berry phase introduced by an optical system to the input state.

Gravitational fields of the magnetic-type

Local conformal symmetry introduces the conformal curvature (Weyl tensor) that gets split into its (gravito-) electric and magnetic (tensor) parts. Newtonian tidal forces are expected from the gravitoelectric field, whereas general-relativistic frame-dragging effects emerge from the gravitomagnetic field. The symmetric, traceless gravitoelectric and gravitomagnetic tensor fields can be visualized by their eigenvectors and eigenvalues. In this paper, we depict the gravitoelectric and gravitomagnetic fields around a slowly rotating black hole. This suggests that the phenomenon of ultra-fast outflows observed at the centers of active galaxies may give evidence for the gravitomagnetic fields of spinning supermassive black holes. We also question whether the current issues in our contemporary observations might be resolved by the inclusion of gravitomagnetism on large scales in a perturbed FLRW model.