Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

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.

Daily temperature trends in Trentino Alto Adige over the last century

Numerosi lavori apparsi sulla letteratura scientifica negli ultimi decenni hanno evidenziato come, dall’inizio del XX secolo, la temperatura media globale sia aumentata. Tale fenomeno si è fatto più evidente dagli anni ’80, infatti ognuno degli ultimi tre decenni risulta più caldo dei precedenti. L’Europa e l’area mediterranea sono fra le regioni in cui il riscaldamento risulta più marcato, soprattutto per le temperature massime (dal 1951 sono cresciute di +0.39 °C per decennio) che hanno mostrato trend maggiori delle minime. Questo comportamento è stato osservato anche a scala nazionale (+0.25°C/dec per le massime e +0.20°C/dec per le minime). Accanto all’aumento dei valori medi è stato osservato un aumento (diminuzione) degli eventi di caldo (freddo) estremo, studiati attraverso la definizione di alcuni indici basati sui percentili delle distribuzioni. Resta aperto il dibattito su quali siano le cause delle variazioni negli eventi estremi: se le variazioni siano da attribuire unicamente ad un cambiamento nei valori medi, quindi ad uno shift rigido della distribuzione, o se parte del segnale sia dovuto ad una variazione nella forma della stessa, con un conseguente cambiamento nella variabilità. In questo contesto si inserisce la presente tesi con l’obiettivo di studiare l’andamento delle temperature giornaliere sul Trentino-Alto-Adige a partire dal 1926, ricercando cambiamenti nella media e negli eventi estremi in due fasce altimetriche. I valori medi delle temperature massime e minime hanno mostrato un evidente riscaldamento sull’intero periodo specialmente per le massime a bassa quota (`0.13 ̆ 0.03 °C/dec), con valori più alti per la primavera (`0.22 ̆ 0.05 °C/dec) e l’estate (`0.17 ̆ 0.05 °C/dec). Questi trends sono maggiori dopo il 1980 e non significativi in precedenza. L’andamento del numero di giorni con temperature al di sopra e al di sotto delle soglie dei percentili più estremi (stimate sull’intero periodo) indica un chiaro aumento degli estremi caldi, con valori più alti per le massime ad alta quota ( fino a +26.8% per il 99-esimo percentile) e una diminuzione degli estremi freddi (fino a -8.5% per il primo percentile delle minime a bassa quota). Inoltre, stimando anno per anno le soglie di un set di percentili e confrontando i loro trend con quelli della mediana, si è osservato, unicamente per le massime, un trend non uniforme verso temperature più alte, con i percentili più bassi (alti) caratterizzati da trend inferiori (superiori) rispetto a quello della mediana, suggerendo un allargamento della PDF.