The tangent splash in \PG(6,q)

Let B be a subplane of PG(2,q^3) of order q that is tangent to $\ell_\infty$. Then the tangent splash of B is defined to be the set of q^2+1 points of $\ell_\infty$ that lie on a line of B. In the Bruck-Bose representation of PG(2,q^3) in PG(6,q), we investigate the interaction between the ruled surface corresponding to B and the planes corresponding to the tangent splash of B. We then give a geometric construction of the unique order-$q$-subplane determined by a given tangent splash and a fixed order-$q$-subline.Comment: arXiv admin note: substantial text overlap with arXiv:1303.550

Exterior splashes and linear sets of rank 3

In \PG(2,q^3), let $\pi$ be a subplane of order $q$ that is exterior to \li. The exterior splash of $\pi$ is defined to be the set of $q^2+q+1$ points on \li that lie on a line of $\pi$. This article investigates properties of an exterior \orsp\ and its exterior splash. We show that the following objects are projectively equivalent: exterior splashes, covers of the circle geometry $CG(3,q)$, Sherk surfaces of size $q^2+q+1$, and \GF(q)-linear sets of rank 3 and size $q^2+q+1$. We compare our construction of exterior splashes with the projection construction of a linear set. We give a geometric construction of the two different families of sublines in an exterior splash, and compare them to the known families of sublines in a scattered linear set of rank 3

Antarctic impulsive transient antenna (ANITA) instrumentation

Journal ArticleWe will report on the details of the ANITA instrument. This instrument is fundamentally a broadband antenna, which is arrayed and constructed in such a way as to be optimized for the detection and characterization of high-energy neutrino cascades [1]. The requirement to maximize the detector view of the Antarctic ice fields implies low gain antennas yet the need for maximum sensitivity dictates using the highest gain possible. Since the Cherenkov signal increases quadratically at higher frequencies suggesting that the optimal selection is an antenna with constant gain as a function of frequency. The baseline design will be a linearly polarized log-periodic zigzag (LPZZ) antenna