15 research outputs found
Geodesic motion in the Kundt spacetimes and the character of envelope singularity
We investigate geodesics in specific Kundt type N (or conformally flat)
solutions to Einstein's equations. Components of the curvature tensor in
parallelly transported tetrads are then explicitly evaluated and analyzed. This
elucidates some interesting global properties of the spacetimes, such as an
inherent rotation of the wave-propagation direction, or the character of
singularities. In particular, we demonstrate that the characteristic envelope
singularity of the rotated wave-fronts is a (non-scalar) curvature singularity,
although all scalar invariants of the Riemann tensor vanish there.Comment: 21 pages, 3 figures. To appear in Class. Quantum Gra
Finite element analysis of free material optimization problem
summary:Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included