Archaeological dating of colluvial and lacustrine deposits in a GIS environment investigating the multi-period site Gortz 1 on Oberer Beetzsee, Brandenburg

From the mid-14th century CE onwards, extensive soil erosion, caused by intensive agricultural practices, has led to the destruction of landscape structures in Central Europe. In 2016, the University of Applied Sciences in Berlin investigated the colluvial deposits at the site of Gortz in western Brandenburg (Germany), which had accumulated on the lower slopes and were caused by the processes just mentioned. The mapping of each individual archaeological find made it possible to project all finds onto one profile running along the slope. Transformation of the finds' coordinates from profile view to plan view enabled the visualization in a Geographical Information System (GIS). The combination of adjacent strata into larger units using a pedological and sedimentological approach enabled an improved dating of colluvial deposits. In addition, the method facilitated the dating of historical water levels in the Beetzsee chain of lakes, which are part of the Havel river system. As a result, it could be demonstrated that substantial anthropogenic activity, such as clay quarrying and bank straightening, took place during the Late Slavic Period. An interlocking horizon of colluvial and lacustrine deposits indicates that the water level of the lake Oberer Beetzsee rose from a value under 29.4 m above sea level (a.s.l.) in the 11th/12th century CE to approximately 29.8 m a.s.l. in the 13th century CE. However, isolated flooding events during the 13th century CE can be recorded up to a height of 30.5 m a.s.l. A modern colluvial deposit of 1 m in thickness indicates an acute endangerment of the archaeological site by modern agriculture.Flächenhafte Bodenerosion, ausgelöst durch intensive landwirtschaftliche Nutzung, führte ab Mitte des 14. Jahrhunderts u.Z. zur Zerstörung von Landschaftsstrukturen und in Mitteleuropa. Kolluvien, welche durch diese Prozesse entstanden und am Unterhang akkumulierten, wurden auf dem Fundplatz Gortz (westliches Brandenburg, Deutschland) durch die Hochschule für Technik und Wirtschaft Berlin im Jahr 2016 untersucht. Konsequente Einzelfundeinmessung ermöglichte die Projizierung aller Funde auf eines der längs zum Hang verlaufenden Profile. Koordinatentransformation der Funde von der Profilansicht in die Draufsicht, ermöglichte die Visualisierung in einem GIS. Die Zusammenfassung benachbarter Schichten auf Basis der bodenkundlich-sedimentologischen Ansprache ermöglichte eine verbesserte Datierung der Kolluvien. Zusätzlich ermöglichte diese Methode die Datierung historischer Pegelstände der Beetzseekette, eines Teils des Flusssystems der Havel. Im Ergebnis ließen sich für die spätslawische Zeit starke anthropogene Aktivitäten wie Mergelabbau und eine Uferbegradigung nachweisen. Über einen Verzahnungshorizont limnischer und kolluvialer Sedimente. ließ sich ein Pegelanstieg des Oberen Beetzsees von einem Wert unterhalb von 29.4 m Normalhöhennull (NHN) im 11./12. Jahrhundert u.Z. auf etwa 29.8 m NHN im 13. Jahrhundert u.Z. feststellen. Es lassen sich für das 13. Jahrhundert u.Z. jedoch auch vereinzelte Überschwemmungsereignisse bis in eine Höhe von 30.5 m NHN fassen. Ein modernes Kolluvium von einem Meter Mächtigkeit zeigt die akute Gefährdung des Bodendenkmals durch die moderne Landwirtschaft

Spin self-rephasing and very long coherence times in a trapped atomic ensemble

We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and susceptible to appear in other physical systems.Comment: Revised version; improved description of the theoretical treatmen

An iterative method with error estimators

AbstractIterative methods for the solution of linear systems of equations produce a sequence of approximate solutions. In many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small. This paper presents a new iterative method based on the Lanczos process for the solution of linear systems of equations with a symmetric matrix. The method is designed to allow the computation of estimates of the Euclidean norm of the error in the computed approximate solutions. These estimates are determined by evaluating certain Gauss, anti-Gauss, or Gauss–Radau quadrature rules

Fractal time random walk and subrecoil laser cooling considered as renewal processes with infinite mean waiting times

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a concentration process, are two such processes that look qualitatively dissimilar. Yet, a unifying treatment of these two processes, which is the topic of this pedagogic paper, can be developed by combining renewal theory with the generalized central limit theorem. This approach enables to derive without technical difficulties the key physical properties and it emphasizes the role of the behaviour of sums with infinite means.Comment: 9 pages, 7 figures, to appear in the Proceedings of Cargese Summer School on "Chaotic dynamics and transport in classical and quantum systems

A comparison of parameter choice rules for ℓp - ℓq minimization

Images that have been contaminated by various kinds of blur and noise can be restored by the minimization of an ℓp-ℓq functional. The quality of the reconstruction depends on the choice of a regularization parameter. Several approaches to determine this parameter have been described in the literature. This work presents a numerical comparison of known approaches as well as of a new one

An Efficient Implementation of the Gauss-Newton Method Via Generalized Krylov Subspaces

The solution of nonlinear inverse problems is a challenging task in numerical analysis. In most cases, this kind of problems is solved by iterative procedures that, at each iteration, linearize the problem in a neighborhood of the currently available approximation of the solution. The linearized problem is then solved by a direct or iterative method. Among this class of solution methods, the Gauss-Newton method is one of the most popular ones. We propose an efficient implementation of this method for large-scale problems. Our implementation is based on projecting the nonlinear problem into a sequence of nested subspaces, referred to as Generalized Krylov Subspaces, whose dimension increases with the number of iterations, except for when restarts are carried out. When the computation of the Jacobian matrix is expensive, we combine our iterative method with secant (Broyden) updates to further reduce the computational cost. We show convergence of the proposed solution methods and provide a few numerical examples that illustrate their performance

Estimation of the Required Amount of Hydrological Exploration in Lignite Mining Areas on the Basis of Hypothetical Hydrogeological Models

Mine drainage is a necessary but very costly precaution for open-pit lignite mining in sandy aquifers. Consequently, the minimization of the number of drainage wells and their optimal operation become important tasks in designing mine drainage systems. Comprehensive groundwater flow models have to be used, both, for the design of drainage wells, and for the analysis of water management strategies in mining areas . The accuracy of computations with such models depends on the precision of the underlying hydrogeological informations. In order to get these informations detailed and costly hydrogeological explorations have to be done in the mining regions. The basic informations are obtained using exploration drilling. The cost for hydrogeological exploration are approximately a linear function of the number of exploration bore holes. Therefore the reduction of drilling gets a key role in reducing costs of exploration. This might be done by: increased use of geophysical exploration methods; complex analysis of exploration results using mathematical statistical methods; precise estimation of the required amount of hydrogeological informations. The paper describes a mathematical approach to support the complex decision making procedure of estimating the optimal amount of hydrogeological exploration with respect to a given mine drainage goal