Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces

We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a topologically typical $Z$-periodic surface with boundary are recurrent.Comment: 34 pages, 13 figures. To be published in V. V. Kozlov's Festschrif

Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

Formation of a stable deacagonal quasicrystalline Al-Pd-Mn surface layer

We report the in situ formation of an ordered equilibrium decagonal Al-Pd-Mn quasicrystal overlayer on the 5-fold symmetric surface of an icosahedral Al-Pd-Mn monograin. The decagonal structure of the epilayer is evidenced by x-ray photoelectron diffraction, low-energy electron diffraction and electron backscatter diffraction. This overlayer is also characterized by a reduced density of states near the Fermi edge as expected for quasicrystals. This is the first time that a millimeter-size surface of the stable decagonal Al-Pd-Mn is obtained, studied and compared to its icosahedral counterpart.Comment: Submitted to Phys. Ref. Lett. (18 July 2001

Square-tiled cyclic covers

A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichm\"uller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichm\"uller curve with respect to the geodesic flow. This paper includes a new example (announced by G. Forni and C. Matheus in \cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover in a stratum of Abelian differentials in genus four with a maximally degenerate Kontsevich--Zorich spectrum (the only known example found previously by Forni in genus three also corresponds to a square-tiled cyclic cover \cite{ForniSurvey}). We present several new examples of Teichm\"uller curves in strata of holomorphic and meromorphic quadratic differentials with maximally degenerate Kontsevich--Zorich spectrum. Presumably, these examples cover all possible Teichm\"uller curves with maximally degenerate spectrum. We prove that this is indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments. In particular, a gap in the previous version was corrected. This file uses the journal's class file (jmd.cls), so that it is very similar to published versio

The Year of Polar Prediction in the Southern Hemisphere (YOPP-SH)

The Year of Polar Prediction in the Southern Hemisphere (YOPP-SH) had a Special Observing Period (SOP) that ran from November 16, 2018 to February 15, 2019, a period chosen to span the austral warm season months of greatest operational activity in the Antarctic. Some 2200 additional radiosondes were launched during the 3-month SOP, roughly doubling the routine program, and the network of drifting buoys in the Southern Ocean was enhanced. An evaluation of global model forecasts during the SOP and using its data has confirmed that extratropical Southern Hemisphere forecast skill lags behind that in the Northern Hemisphere with the contrast being greatest between the southern and northern polar regions. Reflecting the application of the SOP data, early results from observing system experiments show that the additional radiosondes