Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Sustainable development in Darjeeling Hills, India : ecological and socio-economic aspects for small-scale farmers with supportive observations from Kanagawa, Japan

Organic farming means a holistic application of agricultural land-use, hence, this study aimed to assess ecological and socio-economic aspects that show benefits of the strategy and achievements of organic farming in comparison to conventional farming in Darjeeling District, State of West Bengal, India and Kanagawa Prefecture/Kanto in Central Japan. The objective of this study has been empirically analysed on aspects of crop diversity, yield, income and sales prices in the two study regions, where 50 households each, i.e. in total 100 households were interviewed at farm-level. Therefore, the small sample size does not necessarily reflect the broad-scale of the use and benefit of organic farming in both regions. The problems faced in mountainous regions in terms of agriculture and livelihoods for small-scale farmers, which are most affected and dependant on their immediate environment, such as low yields, income and illegal felling leading to soil erosion and landslides, are analyzed. Furthermore, factors such as climate, soils, vegetation and relief equally play an important role for these farmers, in terms of land-use. To supplement and improve the income of farmers, local NGOs have introduced organic farming and high value organic cash crops such as ginger, tea, orange and cardamom and small income generating means (floriculture, apiary etc.). For non-certified and certified organic products the volume is given for India, while for Japan only certified organic production figures are given, as there are several definitions for organic in Japan. Hence, prior to the implementation of organic laws and standards, even reduced chemical input was sold as non-certified organic. Furthermore, the distribution and certification system of both countries are explained in detail, including interviews with distribution companies and cooperatives. Supportive observations from Kanagawa Prefecture and the Kanto region are helpful and practical suggestions for organic farmers in Darjeeling District. Most of these are simple and applicable soil management measures, natural insect repelling applications and describe the direct marketing system practiced in Japan. The former two include compost, intercropping, Effective Microorganisms (EM), clover, rice husk charcoal and wood vinegar. More supportive observations have been made at organic and biodynamic tea estates in Darjeeling District, which use citronella, neem, marigold, leguminous and soil binding plants for soil management and natural insect control. Due to the close ties between farmers and consumers in Japan, certification is often neither necessary nor wanted by the producers. They have built a confidence relationship with their customers; thus, such measures are simply not required. Another option is group certification, instead of the expensive individual certification. The former aims at lower costs for farmers who have formed a cooperative or a farmers' group. Consumer awareness for organic goods is another crucial aspect to help improve the situation of organic farmers. Awareness is slightly more advanced in Kanto than in Darjeeling District, as it is improved due to the close (sales) ties between farmers and consumers in Kanto. Interviews conducted with several such cooperatives and companies underline the positive system of TEIKEI. The introduction of organic farming in the study regions has shown positive effects for those involved, even though it still in its beginning stages in Darjeeling District. This study was only partly able to assess the benefits of organic agriculture at its present level for Darjeeling District, while more positively for the organic farmers of Kanto. The organic farming practice needs further improvement, encouragement and monitoring for the Darjeeling District farmers by locals, consumers, NGOs and politicians. The supportive observations from Kanagawa Prefecture and the Kanto region are a small step in this direction, showing how, simple soil improvements and thus, yield and income increases, as well as direct sales options can enhance the livelihood of organic farmers without destroying their environment and natural resources.