Computation of the Modes of Elliptic Waveguides with a Curvilinear 2D Frequency-Domain Finite-Difference Approach

A scalar Frequency-Domain Finite-Difference approach to the mode computation of elliptic waveguides is presented. The use of an elliptic cylindrical grid allows us to take exactly into account the curved boundary of the structure and a single mesh has been used both for TE and TM modes. As a consequence, a high accuracy is obtained with a reduced computational burden, since the resulting matrix is highly sparse

A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes

AbstractThis paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented

Forecasting Using Time Varying Meta-Elliptical Distributions with a Study of Commodity Futures Prices

We propose a methodological approach to the forecast and evaluation of multivariate distributions with time varying parameters. For reasons related to feasible inference attention is restricted to meta-elliptical distributions. We use our approach for the study of a large data set of 16 commodity prices. Our approach leads to a theory for model validation avoiding common problems caused by discontinuities, time variation of parameters and nuisance parameters

Aberrations of the point spread function of a multimode fiber

We investigate the point spread function of a multimode fiber. The distortion of the focal spot created on the fiber output facet is studied for a variety of the parameters. We develop a theoretical model of wavefront shaping through a multimode fiber and use it to confirm our experimental results and analyze the nature of the focal distortions. We show that aberration-free imaging with a large field of view can be achieved by using an appropriate number of segments on the spatial light modulator during the wavefront-shaping procedure. The results describe aberration limits for imaging with multimode fibers as in, e.g., microendoscopy.Comment: 10 pages, 6 figure