A series of coverings of the regular n-gon

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To appear in Geometriae Dedicata.

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

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

Irreversible Structural Transformation of five fold i-AlPdMn Quasicrystals after Ion Bombardment and Annealing

Five fold i-AlPdMn surface prepared under UHV by ion bombardment and annealing was so far considered to be bulk terminated. This result was substantially based on a quantitative LEED analyses [1]. Analysis of the specular rod in a X ray diffraction experiment at grazing incidence supported this result [2]. We present a new study of this surface by high resolution X ray diffraction at normal incidence. In this Bragg configuration the diffraction peak 18 – 29 for instance is at a photon energy of 2.873keV, the 72 – 116 reflection at 5.725keV. This results in an analyzed thickness of the sample surface of a few micrometers. The surface was cleaned by ion bombardment. During annealing (T≅880K), we clearly observed the progressive disappearance of the initial Bragg peak characteristic of the as cast bulk sample. Conversely a new Bragg peak grows at an energy position shifted by 1eV compared to the position of the original Bragg peak. This is a clear signature for an irreversible structural transformation which takes place on at least the micron thickness. On the transformed surface, both, a LEED pattern and a RHEED pattern, characteristic for a five fold surface were easily obtained. This high resolution experiment (the relative Bragg peak shift is 3ׁ10−4) was reproduced on samples from different initial compositions. This shows that five fold i-AlPdMn surface changes after preparation by ion bombardment and annealing at 900K on a micrometer thickness. This is not consistent with the conclusion that the surface is simply terminated by a cut of the original bulk. We conclude that a reorganization process of the quasicrystalline structure during annealing proceeds in the surface vicinity (probed depth is close to a few microns)

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

Meteorological conditions during the ACLOUD/PASCAL field campaign near Svalbard in early summer 2017

The two concerted field campaigns, Arctic CLoud Observations Using airborne measurements during polar Day (ACLOUD) and the Physical feedbacks of Arctic planetary boundary level Sea ice, Cloud and AerosoL (PASCAL), took place near Svalbard from 23 May to 26 June 2017. They were focused on studying Arctic mixed-phase clouds and involved observations from two airplanes (ACLOUD), an icebreaker (PASCAL) and a tethered balloon, as well as ground-based stations. Here, we present the synoptic development during the 35-day period of the campaigns, using near-surface and upper-air meteorological observations, as well as operational satellite, analysis, and reanalysis data. Over the campaign period, short-term synoptic variability was substantial, dominating over the seasonal cycle. During the first campaign week, cold and dry Arctic air from the north persisted, with a distinct but seasonally unusual cold air outbreak. Cloudy conditions with mostly low-level clouds prevailed. The subsequent 2 weeks were characterized by warm and moist maritime air from the south and east, which included two events of warm air advection. These synoptical disturbances caused lower cloud cover fractions and higher-reaching cloud systems. In the final 2 weeks, adiabatically warmed air from the west dominated, with cloud properties strongly varying within the range of the two other periods. Results presented here provide synoptic information needed to analyze and interpret data of upcoming studies from ACLOUD/PASCAL, while also offering unprecedented measurements in a sparsely observed region.</p

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