Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmololgies ar...

Barchan dunes — crescent-shaped dunes that form in areas of unidirectional winds and low sand availability — commonly display an asymmetric shape, with one limb extended downwind. Several factors have been identified as potential causes for barchan dune asymmetry on Earth and Mars: asymmetric bimodal wind regime, topography, influx asymmetry and dune collision. However, the dynamics and potenti...

A primary unresolved issue for cosmological singularities is whether or not their behavior is locally of the Mixmaster type (as conjectured by Belinskii, Khalatnikov, and Lifshitz (BKL)). The Mixmaster dynamics first appears in spatially homogeneous cosmologies of Bianchi Types VIII and IX. A multiple of the spatial scalar curvature acts as a closed potential leading, in the evolution toward th...

Crouzeix’s conjecture states that for all polynomials p and matrices A, the inequality ‖p(A)‖ ≤ 2 ‖p‖W (A) holds, where the quantity on the left is the 2-norm of the matrix p(A) and the norm on the right is the maximum modulus of the polynomial p on W (A), the field of values of A. We report on some extensive numerical experiments investigating the conjecture via nonsmooth minimization of the C...

understanding how a cutout influences the load bearing capacity and buckling behavior of cylindrical shells is fundamental in the design of structural components used in automobiles, aircrafts, and marine structures. in this article, simulation and analysis of steel cylindrical shells with various lengths, include quasi elliptical cutout, subjected to axial compression were systematically carri...