Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Environment and climate of the last 51,000 years – new insights from the Potrok Aike maar lake Sediment Archive Drilling prOject (PASADO)

In this introductory paper we summarize the history and achievements of the Potrok Aike maar lake Sediment Archive Drilling prOject (PASADO), an interdisciplinary project embedded in the International Continental Scientific Drilling Program (ICDP). The stringent multiproxy approach adopted in this research combined with radiocarbon and luminescence dating provided the opportunity to synthesize a large body of hydrologically relevant data from Laguna Potrok Aike (southern Patagonia, Argentina). At this site, lake level was high from 51 ka until the early Holocene when the Southern Hemisphere Westerlies (SHW) were located further to the north. At 9.3 ka cal. BP the SHW moved southward and over the latitude of the study area (52 degrees S) causing a pronounced negative water balance with a lake level decrease of more than 50 m. Two millennia later, the SHW diminished in intensity and lake level rose to a subsequent maximum during the Little Ice Age. Since the 20th century, a strengthening of the SHW increased the evaporative stress resulting in a more negative water balance. A comparison of our data with other hydrological fluctuations at a regional scale in south-eastern Patagonia, provides new insights and also calls for better chronologies and high-resolution records of climate variability.

Correlating the Ancient Maya and Modern European Calendars with High-Precision AMS 14C Dating

The reasons for the development and collapse of Maya civilization remain controversial and historical events carved on stone monuments throughout this region provide a remarkable source of data about the rise and fall of these complex polities. Use of these records depends on correlating the Maya and European calendars so that they can be compared with climate and environmental datasets. Correlation constants can vary up to 1000 years and remain controversial. We report a series of high-resolution AMS C-14 dates on a wooden lintel collected from the Classic Period city of Tikal bearing Maya calendar dates. The radiocarbon dates were calibrated using a Bayesian statistical model and indicate that the dates were carved on the lintel between AD 658-696. This strongly supports the Goodman-Martinez-Thompson (GMT) correlation and the hypothesis that climate change played an important role in the development and demise of this complex civilization.

Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite’s solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case. Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The reasons are threefold: The direct SRP is about a factor of 30–40 smaller for typical geodetic SLR satellites than for GNSS satellites, allowing it in most cases to not solve for SRP parameters (ruling out the correlation between these parameters and the geocenter coordinates); the orbital arc length of 7 days (which is typically used in SLR analysis) contains more than 50 revolutions of the LAGEOS satellites as compared to about two revolutions of GNSS satellites for the daily arcs used in GNSS analysis; the orbit geometry is not as critical for LAGEOS as for GNSS satellites, because the elevation angle of the Sun w.r.t. the orbital plane is usually significantly changing over 7 days.

Improving a gas ion source for C-14 AMS

For more than 4 years, gaseous samples of 1-50 mu g carbon have been routinely measured with the gas ion source of the small AMS (Accelerator Mass Spectrometer) facility MICADAS (Mini CArbon DAting System) at ETH Zurich. The applied measurement technique offers a simple and fast way of C-14 measurements without the need of sample graphitization. A major drawback of gaseous C-14 measurements, however, is the relatively low negative ion current, which results in longer measurement times and lower precision compared to graphitized samples. In December 2009, a new, improved Cs sputter ion source was installed at MICADAS and we began to optimize conditions for the measurement of gaseous samples. C-12(-) currents from the new ion source were improved from initially 3 to 12-15 mu A for routine measurements and the negative ion yield was increased by a factor of 2, reaching 8 on average during routine operation. Moreover, the new measurement settings enable a doubled CO2 flow, thus substantially reducing measurement times. The achieved performance allows closing the sample size gap between gaseous and solid samples and makes the gas ion source a promising tool for dating with a measurement precision of 5 parts per thousand on samples as small as 50 mu g carbon. (C) 2012 Elsevier B.V. All rights reserved.