Hele-Shaw and Stokes flow with a source or sink : stability of spherical solutions

Qualitative aspects of mathematical models for the dynamics of liquids with a moving boundary are studied. These models describe for instance groundwater flow, extraction of oil, the growth of tumours and viscous sintering in the production of glass. Stability of radially symmetric solutions and decay properties of perturbations are studied for the case that in a single point fluid is injected or extracted. For the motion of the moving boundary a nonlinear non-local evolution equation is derived. The domain is rescaled in such a way that the spherical solution is represented by a stationary solution. Because of this rescaling, the evolution operator is time dependent. The nonlinear stability results are based on linearisation, energy estimates and the principle of linearised stability. The Hele-Shaw model is studied for several boundary conditions, describing various physical situations. In the case of zero pressure on the boundary, it is proved for the injection problem that balls around the injection point are asymptotically stable with respect to small star-shaped perturbations. If surface tension regularisation is included, then balls are stable even for the case of suction under additional assumptions on the initial geometry, suction speed and dimension. Moreover, perturbations turn out to decay algebraically fast. For two dimensional suction, the influence of surface tension dominates the influence of the sink for large time. As a consequence, no condition on the suction speed is necessary. In contrast to the two dimensional problem there is a bound on the suction speed for the 3D problem. In dimensions higher or equal to four the influence of the sink dominates the influence of surface tension. This leads to linear instability for the spherical solution for any suction speed. Making use of the autonomous character of the evolution equation, existence of nontrivial self-similarly vanishing solutions to the three dimensional suction problem with surface tension is proved. These solutions are found as bifurcation solutions from the trivial spherical solution. The suction speed plays the role of bifurcation parameter. Moreover, one branch of bifurcation solutions turns out to be stable with respect to a certain class of perturbations. For the closely related Stokes flow stability of the spherical solution in the case of injection has been proved for dimensions two and three. For the suction problem for these dimensions the spherical solution is linearly unstable

Why the Spanish State of Autonomies could be the right Example for the Bolivian State

The study’s aim is to analyze and investigate the characteristics of the regions demanding autonomy in Eastern Bolivia. Therefore the study takes a look at the Spanish political model, which could serve in a comparing and evaluating framework. The development of processes of autonomy has been part of Spanish history, especially in the regions of Catalonia and the Basque Country, which has contributed to the establishment of a stable democracy and a flourishing economy in Spain. Firstly, the study compares both autonomous regions in both countries out of a historical way. On the one hand, the reader will discover differences in the nationalist regions and on the other hand important similar developments in both countries. Finally, the study concludes that the Spanish State of Autonomies and its 1978 Constitution, established after Franco’s death, could serve as the right example for the Bolivian State. Essential in the article is the search for a consensus over the different characteristics which exist between the two ideologies which are the main reason why the Bolivian State could be described as a weak State.Regional Development; Economic Development

Stability of self-similar extinction solutions for a 3D Hele-Shaw suction problem

We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially symmetric. We show stability with respect to perturbations that preserve these properties

The Mediation of Emotive Scripts: A Cross-Cultural Study of Poetic Imagery, Gestures, and Emotion in Chrétien de Troyes’s Yvain and its Medieval Translations

This dissertation presents the results of a cross-cultural study of emotive representation in several European versions of one Arthurian story, that of the Knight with the Lion. It offers an intertextual comparison of the (re)drawing of emotionality in Chrétien de Troyes’s Yvain ou le chevalier au lion (1170–90) and its first generation translations that came about from the early thirteenth until the early fourteenth century. Methodologically, the study adopts the recently developed theoretical approach of analysing and comparing these medieval narratives by means of their underlying emotive script. Together with the emotional lexis of a text, an emotive script is made up of generically predetermined emotional codes that constitute ways of narrating emotion. These linguistic and literary means for displaying emotionality, i.e. the vocabulary and narrative strategies that make an emotional representation meaningful to an audience, have been shown to deviate between literary traditions, sometimes quite significantly. This meant that, along with the introduction of Yvain to other European textual traditions, came foreign linguistic and cultural codes that will very likely have included emotional signifying systems. This dissertation sheds light on this textual transferral (translatio) and explores what happens when emotive scripts of different literary traditions meet in the process of cross-cultural translation. How have the different textual traditions rendered any unfamiliar representations in the process of adapting the story to new literary contexts? What linguistic, (socio-)cultural and/or generic divergences regarding the literary representation of emotion does a comparative close reading of these narratives bring to light? More specifically, how did translators ‘mediate’ any incompatibilities between emotive scripts into meaningful renditions for their audiences? The questions posed are explored in the form of three case studies. In addition to discussing different vernacular literary traditions, each case study highlights varying narrative strategies for the staging of emotion. Chapter one examines poetic imagery and metaphorical representations of the heart in the Old French Yvain and the Old Norse-Icelandic Ívens saga, occasionally drawing on the Old Swedish Hærra Ivan as well. Chapter two foregrounds the emotional behaviour of characters as mediated through gesture and speech in Yvain and its Middle High German rendition Iwein. In addition to studying emotion as an individual phenomenon, chapter three explores the representation of collective emotions for Yvain, Ívens saga and the Middle English Ywain and Gawain. Together these case studies help us to gain insight into the adaptation process that emotive representation in the story of the Knight with the Lion underwent in order to make it speak to new cultural audiences.Í rannsókn þessari birtast niðurstöður þvermenningarlegrar rannsóknar um framsetningu tilfinninga í nokkrum evrópskum útgáfum einnar af Arthúrssögnunum, eða sögunni um riddarann og ljónið, þ.e. Yvain eða Ívens saga á íslensku. Í rannsókninni er notaður textasamanburður til að greina breytingar á framsetningu tilfinninga í sögu Chrétien de Troyes, Yvain ou le chevalier au lion (1170–90) og fyrstu þýðingum hennar sem birtust snemma á þrettándu öld og fram að byrjun fjórtándu aldar. Aðferðafræði rannsóknarinnar byggir á nýlegri hugmyndafræðilegri nálgun sem nýtir undirliggjandi tilfinningalegar forskriftir (e. emotive script) til greiningar og samanburðar á miðaldasögunum. Tilfinningalegar forskriftir byggja á ákveðnum hegðunarmynstrum sem eru notaðar til að miðla tilfinningum ásamt tilfinningalegum orðaforða innan textans. Málvísindalegar og bókmenntafræðilegar aðferðir sem bera á borð tilfinningasemi, þ.e. orðaforði og frásagnarháttur þar sem framsetning tilfinninga er þýðingamikil fyrir áheyrendur, virðist vera breytileg milli bókmenntahefða, í sumum tilfellum er mismunurinn verulegur. Þetta þýðir að þýðingin á Yvain bar með sér ýmis menningarbundin tákn, þar með talið forskriftir að tilfinningalegri hegðun. Þessi rannsókn varpar ljósi á þennan textaflutning (translatio) og kannar afleiðingar þess þegar tilfinningalegar forskriftir mismunandi bókmenntahefða mætast í gegnum þýðingaferla mismunandi menningarheima. Hvernig hafa mismunandi textahefðir veitt framandi framsetningu nýjan farveg í gegnum aðlögun sögunnar að nýju samhengi? Hvaða tungumálalegu, menningarlegu og tilfinningalegu frávik getur nákvæmur samanburður frásagnanna leitt í ljós? Ennfremur má spyrja hvernig þýðendur miðla ósamræmi milli tilfinningalegra forskrifta til nýrra áheyrenda? Framangreindum spurningum er hér svarað með rannsókn á þremur birtingarmyndum slíkrar miðlunar. Auk þess sem kaflarnir varpa ljósi á mismunandi bókmenntahefðir, þá draga þær einnig fram mismunandi frásagnarhátt þegar kemur að sviðsetningu tilfinninga. Í fyrsta kafla erljóðrænt myndmál tengt framsetningu hjartans í forn-frönsku sögunni Yvain og hinni fornnorsk-íslensku Ívens sögu kannað. Þá er einnig fornsænska þýðingin Hærra Ivan notuð til samanburðar. Í öðrum kafla er tilfinningatengd hegðun persóna í forgrunni, eins og henni er miðlað í gegnum látbragð og málfar í Yvain og í þýðingu hennar á mið-háþýsku í Iwein. Í þriðja kafla er ekki aðeins rýnt í tilfinningar sem einstaklingsfyrirbæri, heldur er jafnframt kannað hvernig hóptilfinningar birtist í sögunum Yvain, Ívens sögu og hinni miðensku Ywain and Gawain. Saman veita þessar sagnaútgáfur okkur innsýn í aðlögunarferlið sem tilfinningaleg framsetning sögunnar um Yvain undirgekkst til að ná til mismunandi menningarhópa og áheyrenda.University of Iceland Research Fund; Icelandic Research Fund (Rannís

Secondary lymphoid organ development

Mebius, R.E. [Promotor]Kraal, G. [Promotor