Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

Exact algorithms for p-adic fields and epsilon constant conjectures

We develop several algorithms for computations in Galois extensions of p-adic fields. Our algorithms are based on existing algorithms for number fields and are exact in the sense that we do not need to consider approximations to p-adic numbers. As an application we describe an algorithmic approach to prove or disprove various conjectures for local and global epsilon constants.

Organic inputs and farmers' management strategies in millet fields of western Niger

Research on soil fertility management in sub-Saharan Africa was criticized lately for largely ignoring farmers’ management strategies and the underlying principles. To fill this gap of knowledge, detailed interviews were conducted with 108 farm households about their rationale in managing the soil fertility of 307 individual fields in the agro-pastoral village territory of Chikal in western Niger. To amplify the farmers’ information on manuring and corralling practices, repeated measurements of applied amounts of manure were carried out within six 1-km^2 monitoring areas from February to October 1998. The interviews revealed that only 2% of the fields were completely fallowed for a period of 1–15 years, but 40% of the fields were at least partially fallowed. Mulching of crop residues was mainly practiced to fight wind erosion but was restricted to 36% of the surveyed fields given the alternative use of straw as livestock feed. Manure application and livestock corralling, as most effective tools to enhance soil fertility, were targeted to less than 30% of the surveyed fields. The application of complete fallow and manuring and corralling practices were strongly related to the households’ endowment with resources, especially with land and livestock. Within particular fields, measures were mainly applied to spots of poor soil fertility, while the restoration of the productivity of hard pans was of secondary importance. Given the limited spatial coverage of indigenous soil fertility measures and their strong dependence on farmers’ wealth, supplementary strategies to restrict the decline of soil fertility in the drought prone areas of Niger with their heavily weathered soils are needed.

Non-Born-Oppenheimer Dynamics of Hydrogen Molecules in Strong Laser-Fields

Die Arbeit behandelt die numerische Untersuchung von Wasserstoff-Moleküldynamik in starken Laserfeldern. Im Speziellen wird die Struktur von Ionisationsspektren bei Einfach-Photoionisation betrachtet. Korrelationen zwischen Elektron- und Kernbewegung werden identifiziert und mit Effekten in den Energiespektren in Verbindung gebracht. Dabei wird stets auf die Integration der zeitabhängigen Schrödingergleichung zurückgegriffen.

Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

Carbon and nitrogen emissions from stored manure and cropped fields in irrigated mountain oases of Oman

Little is known about gaseous carbon (C) and nitrogen (N) emissions from traditional terrace agriculture in irrigated high mountain agroecosystems of the subtropics. In an effort towards filling this knowledge gap measurements of carbon dioxide (CO_2), methane (CH_4), ammonia (NH_3) and dinitrous oxide (N_2O) were taken with a mobile photoacoustic infrared multi-gas monitor on manure-filled PE-fibre storage bags and on flood-irrigated untilled and tilled fields in three mountain oases of the northen Omani Al Jabal al Akhdar mountains. During typical 9-11 day irrigation cycles of March, August and September 2006 soil volumetric moisture contents of fields dominated by fodder wheat, barley, oats and pomegranate ranged from 46-23%. While manure incorporation after application effectively reduced gaseous N losses, prolonged storage of manure in heaps or in PE-fibre bags caused large losses of C and N. Given the large irrigation-related turnover of organic C, sustainable agricultural productivity of oasis agriculture in Oman seems to require the integration of livestock which allows for several applications of manure per year at individual rates of 20 t dry matter ha^−1.