Particle Candidates of Ultrahigh Energy Cosmic Rays

We discuss candidates for trans-GZK cosmic rays observed in a variety of detectors. Three types of primaries are represented among the abstracts submitted to this meeting: neutrin os causing a Z-burst, protons arising from the decay of ultra-heavy metastable particles and neutrinos within the framework of low scale string-like models of unification. We attempt to evaluate the relative merits of these schemes. No definite conclusion can be reached at this time. However, we point out that some schemes are more credible/predictive than others. Data to be gathered by the Pierre Auger observatories as well as orbiting detectors (OWL, Airwatch...) should be able to decide between the various schemes.Comment: 15 pages, LaTex. Substantially revised to take into account the discussion at HEP2001, Budapest July 200

Signatures of Precocious Unification in Orbiting Detectors

It has been conjectured that the string and unification scales may be substantially lower than previously believed, perhaps a few TeV. In scenarios of this type, orbiting detectors such OWL or AIRWATCH can observe spectacular phenomena at trans-GZK energies. We explore measurable signatures of the hypothesis that trans-GZK air showeres (``anomalous showers'') are originated by strongly interacting neutrinos. The results of a MC simulation of such air showers is described. A distinction between proton induced and ``anomalous'' showers becomes possible once a substantial sample of trans-GZK showers will be available.Comment: LaTeX 2e, 14 pages, 5 figures. Revised and expanded version: MC rerun, figures redrawn, text revised and expande

The robustness of equilibria on convex solids

We examine the minimal magnitude of perturbations necessary to change the number $N$ of static equilibrium points of a convex solid $K$. We call the normalized volume of the minimally necessary truncation robustness and we seek shapes with maximal robustness for fixed values of $N$. While the upward robustness (referring to the increase of $N$) of smooth, homogeneous convex solids is known to be zero, little is known about their downward robustness. The difficulty of the latter problem is related to the coupling (via integrals) between the geometry of the hull \bd K and the location of the center of gravity $G$. Here we first investigate two simpler, decoupled problems by examining truncations of \bd K with $G$ fixed, and displacements of $G$ with \bd K fixed, leading to the concept of external \rm and internal \rm robustness, respectively. In dimension 2, we find that for any fixed number $N=2S$, the convex solids with both maximal external and maximal internal robustness are regular $S$-gons. Based on this result we conjecture that regular polygons have maximal downward robustness also in the original, coupled problem. We also show that in the decoupled problems, 3-dimensional regular polyhedra have maximal internal robustness, however, only under additional constraints. Finally, we prove results for the full problem in case of 3 dimensional solids. These results appear to explain why monostatic pebbles (with either one stable, or one unstable point of equilibrium) are found so rarely in Nature.Comment: 20 pages, 6 figure