An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Biographien und Netzwerke im Kaffeehandel zwischen Deutschland und Zentralamerika, 1920-1959

Kaffee ist nicht nur ein beliebtes Getränk, sondern vernetzte auch unterschiedliche Welten: Der Kaffeehandel band Hamburg und Bremen in transnationale Netzwerke ein, die sich zwischen Europa und Lateinamerika erstreckten. Zentralamerika war für den globalen Kaffeehandel wichtig, weil die Region als erste die „nasse“ Form der Aufbereitung einführte. Die hohe Qualität dieser „gewaschenen“ Kaffees machte sie auf dem Weltmarkt begehrt. Deutsche Einwanderer prägten die Handelsverbindungen zwischen den zentralamerikanischen Kaffee-Anbauregionen und den norddeutschen Hafenstädten: Sie gründeten Exportfirmen, erwarben Kaffeeplantagen und beteiligten sich an der Vorfinanzierung der Ernten. Christiane Berth analysiert Biografien und Netzwerke deutscher Kaffee-Akteure in Guatemala, Costa Rica und Chiapas. Dabei zeigt sie, wie deren Handelsnetzwerke durch wirtschaftliche Krisen und neue außenpolitische Konstellationen brüchig wurden, im Nationalsozialismus unter Druck gerieten und während des Zweiten Weltkrieges zerbrachen. Trotzdem blieben auch in der Nachkriegszeit Handelsbeziehungen zwischen Nationalstaaten, Netzwerke in der Kaffeebranche und Biografien der Kaffee-Akteure eng miteinander verknüpft.

Newton-Cartan supergravity with torsion and Schrödinger supergravity

We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The “superconformal” theory that we start with is Schrödinger supergravity which we obtain by gauging the Schrödinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call “old minimal” and “new minimal” Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.

Pollen and charcoal in lake sediments compared with historically documented forest fires in southern Switzerland since AD 1920

Charcoal in unlaminated sediments dated by 210Pb was analysed by the pollen-slide and thin-section methods. The results were compared with the number and area of forest fires on different spatial scales in the area around Lago di Origlio as listed in the wildfire database of southern Switzerland since AD 1920. The influx of the number of charcoal particles > 75 µm2 in pollen slides correlates well with the number of annual forest fires recorded within a distance of 20-50 km from the coring site. Hence a size-class distinction or an area measurement by image analysis may not be absolutely necessary for the reconstruction of regional fire history. A regression equation was computed and tested against an independent data set. Its use makes it possible to estimate the charcoal area influx (or concentration) from the particle number influx (or concentration). Local fires within a radius of 2 km around the coring site correlate well with the area influx of charcoal particles estimated by the thin-section method measuring the area of charcoal particles larger than 20 000 µm2 or longer than 50 µm. Pollen percentages and influx values suggest that intensive agriculture and Castanea sativa cultivation were reduced 30-40 years ago, followed by an increase of forest area and a development to more natural woodlands. The traditional Castanea sativa cultivation was characterized by a complete use of the biomass produced, so abandonment of chestnut led to an increasing accumulation of dead biomass, thereby raising the fire risk. On the other hand, the pollen record of the regional vegetation does not show any clear response to the increase of fire frequency during the last three decades in this area.