Cylindrical Behavior Research Articles

Type II singularities on complete non-compact Yamabe flow

Abstract This work concerns with the existence and detailed asymptotic analysis of type II singularities for solutions to complete non-compact conformally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate of the maximum curvature and show that the solution converges, after blowing-up around the curvature maximum points, to a rotationally symmetric steady soliton. It is the first time that the steady soliton is shown to be a finite time singularity model of the Yamabe flow.

3-D Thin-Wire FDTD Approach for Resistively Loaded Cylindrical Antennas Fed by Coaxial Lines

For the efficient finite-difference time-domain (FDTD) analysis of electrically thin and resistively loaded cylindrical antennas, the 2-D cylindrical thin-wire approach with circular symmetry is extended to the 3-D Cartesian FDTD with non-cubic cells for asymmetric cases. The axial geometry of the antenna is represented as a set of piecewise-linear lumped resistors. And the near fields around the antenna and the coaxial feed aperture are approximated to the quasi-static fields with the cylindrical behavior. From the cylindrical-to-Cartesian coordinate transformation of the quasi-static fields and the contour-path integration along FDTD unit cells in the vicinity of the antenna and its feed, the 3-D Cartesian FDTD equations are derived. These equations may correspond to a full coarse-grid FDTD approach with the equivalent corrections. For some numerical examples, the proposed approach provides comparable accuracy to the reference data with fine-grid resolution. Effects of the cell size and the resistive loading profile are investigated numerically.