Every .nite two-dimensional partially ordered set has an inclusion representation by similar noncircular ellipses centered at the origin. The representing ellipses have the same ratio r of minor axis length to major axis length, and any r ∈ (0; 1) can be used for the representation. c © 2002 Elsevier Science B.V. All rights reserved.

We discuss numerical integration formulas with polynomial exactness for noncircular pupils, based on subperiodic trigonometric Gaussian quadrature and compression of discrete measures. Such formulas can be useful in optical design (numerical ray-tracing in obscured and vignetted pupils for accurate spot size computation), and in optical diffraction theory under conditions of partial coherence (...

A practical procedure is described for implementing Spencer’s method of slices with varying side force inclination. The search for the noncircular critical slip surface is accomplished using spreadsheet-automated constrained optimization. The deterministic formulation is then extended probabilistically to compute the Hasofer-Lind reliability index via constrained optimization of the dispersion ...

We present a numerical framework to simulate pedestrian dynamics in highly competitive conditions by means of a force-based model implemented with spherocylindrical particles instead of the traditional, symmetric disks. This modification of the individuals' shape allows one to naturally reproduce recent experimental findings of room evacuations through narrow doors in situations where the conta...

The growth of two dimensional noncircular flaws was studied by three independent methods: transfer function analysis, equivalent area approximation, and direct fracture mechanics calculation. All three methods yield results varying within a few percent of one another for the simpler elliptical and rectangular geometries. Results of transfer function and equivalent area methods agree also within...