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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

none

Wu, Chih-hung 29 June 2009 (has links)
The aim of the paper is to investigate how the dual brand of firm decides its optimal allocation of advertising and fundamental strategy of marketing under taking account of markets with multi-consumption externalities. We assume that the market is multi-consumption externalities, and advertising may function as a device to coordinate consumer expectations of the purchasing decisions of other consumers, which is different from the past assumption that consumer type is single and role of advertising in market. Therefore, we reexamine the firm with optimal allocation of advertising. Finally, we show that the firm will adapt different pricing, allocation of advertising and strategy of marketing when facing the different consumer type of combination proportion. If market is dissimilar consumption externalities, above statement will be more significant; On the contrary, if firm facing similar consumption externalities, the optimal is single strategy. In other words, it is independent to consumer's type of combination proportion.
2

A re-assessment of the geochronology and geochemistry of the Postberg Ignimbrites, Saldanha, Western Cape, South Africa

Misrole, Matthew 13 March 2020 (has links)
>Magister Scientiae - MSc / The Saldania Belt in southern Africa, a product of the Pan-African Saldanian Orogeny, forms part of a system of Neoproterozoic mobile belts that border and weld older cratons on the African continent. It is a low-grade orogenic belt situated along the southwestern margin of the Kalahari Craton and is composed of several inliers of greenschist facies metasedimentary and metavolcanic rocks (Malmesbury Group), unroofed in megaanticlinal hinges of the Permo-Triassic Cape Fold Belt. The Malmesbury Group rocks were syn- and post-tectonically intruded in a pervasive transpressive regime between 555 Ma and 515 Ma by Neoproterozoic to early Cambrian S-, I- and A-type granites, monzodiorites, gabbros and quartz syenites, which collectively constitute the rocks of the Cape Granite Suite (CGS). Along the south-western coastline of South Africa, the Saldanha Bay Volcanic Complex (which forms part of the CGS) is divided into two eruption centres both of which have been identified as “intra-caldera pyroclastic ignimbrites”. The Postberg eruption centre is situated to the south of the Saldanha Bay entrance and the Saldanha eruption centre is situated to the north of the entrance. Both eruption centres display distinct geochemical signatures, the most apparent being the greater TiO2 concentrations (> 0.25 wt. %) of the Saldanha centre ignimbrites when compared to its Postberg centre counterparts. The Postberg eruption centre consists of S-type rhyolitic ignimbrites which are subdivided into the two geochemically distinct Plankiesbaai and Tsaarsbank Ignimbrites. Small amounts of the Jacobs Bay and Saldanha Ignimbrites (less felsic tephra from the Saldanha eruption centre) are also present in the Postberg eruption centre. A robust geochemical analysis of both the Plankiesbaai and Tsaarsbank magma groups display high SiO2 content (>76 wt. %), a lack of variation in TiO2 and Zr, high Al2O3 and ASI (aluminium saturation index) values (> 1.0 and generally >1.1 which, on average, is higher than the Saldanha eruption centre ignimbrites), low CaO and Na2O, and a highly ferroan character. The Plankiesbaai ignimbrite also display lower #Mg concentration compared to the Tsaarsbank ignimbrite. Typical geochemical trends in the Postberg eruption centre include the lack of variation in Zr content, higher Rb content and lower Sr, Ba, V and Zn concentrations when compared to the tephra of the Saldanha eruption centre found in the Postberg area. The study’s main aim is not only to assess the geochemistry of the ignimbrites relative to the previous phases of magmatism originally proposed by Scheepers (1995) for the magmatism of the Cape Granite Suite, but also their age distribution. Previously defined phases of magmatism include Phase I (S-type granites subdivided into Sb, Sa1 and Sa2 all of which are dated to 555 - 540 Ma), Phase II (I-type granites subdivided into Ia and Ib both dated to 540 – 520 Ma), Phase III (A-type granites subdivided into Aa and Ab dated to ~ 520 Ma) and Phase IV (S-type volcanic and subvolcanic rocks dated to 515 Ma). Re-examination of the geochronology displays a U-Pb age for Postberg Centre Jacobs Bay Ignimbrite (tephra from the Saldanha eruption centre) of 538 ± 2.2 Ma: and for the Postberg Centre Tsaarsbank Ignimbrite between 536 ± 2 Ma – 540 ± 3.4 Ma. These new dates, in combination with the geochronological work done in the Saldanha Centre (particularly in light of the Clemens and Stevens (2016) and Clemens et al. (2017) studies that reclassify these rocks differing from the original and previous studies), place all the ignimbrites of the Saldanha Bay Volcanic Complex securely within the age bracket for the initial S-type magmatism of the CGS. This thesis presents a revised order for the phases of magmatism of the Saldania Belt, and by extension, of the Cape Granite Suite. All S-type magmatism, including that of the Saldanha Bay Volcanic Complex (Sv), forms part of the Phase I magmatism of the Saldania Belt (Sa1, Sa2, and Sb) emplaced between 555 – 540 Ma.
3

Geochronology and geochemistry of the Postberg ignimbrites, Saldanha, Western Cape, South Africa

Misrole, Matthew January 2020 (has links)
>Magister Scientiae - MSc / The Saldania Belt in southern Africa, a product of the Pan-African Saldanian Orogeny, forms part of a system of Neoproterozoic mobile belts that border and weld older cratons on the African continent. It is a low-grade orogenic belt situated along the southwestern margin of the Kalahari Craton and is composed of several inliers of greenschist facies metasedimentary and metavolcanic rocks (Malmesbury Group), unroofed in megaanticlinal hinges of the Permo-Triassic Cape Fold Belt. The Malmesbury Group rocks were syn- and post-tectonically intruded in a pervasive transpressive regime between 555 Ma and 515 Ma by Neoproterozoic to early Cambrian S-, I- and A-type granites, monzodiorites, gabbros and quartz syenites, which collectively constitute the rocks of the Cape Granite Suite (CGS). Along the south-western coastline of South Africa, the Saldanha Bay Volcanic Complex (which forms part of the CGS) is divided into two eruption centres both of which have been identified as “intra-caldera pyroclastic ignimbrites”. The Postberg eruption centre is situated to the south of the Saldanha Bay entrance and the Saldanha eruption centre is situated to the north of the entrance. Both eruption centres display distinct geochemical signatures, the most apparent being the greater TiO2 concentrations (> 0.25 wt. %) of the Saldanha centre ignimbrites when compared to its Postberg centre counterparts. The Postberg eruption centre consists of S-type rhyolitic ignimbrites which are subdivided into the two geochemically distinct Plankiesbaai and Tsaarsbank Ignimbrites. Small amounts of the Jacobs Bay and Saldanha Ignimbrites (less felsic tephra from the Saldanha eruption centre) are also present in the Postberg eruption centre. A robust geochemical analysis of both the Plankiesbaai and Tsaarsbank magma groups display high SiO2 content (>76 wt. %), a lack of variation in TiO2 and Zr, high Al2O3 and ASI (aluminium saturation index) values (> 1.0 and generally >1.1 which, on average, is higher than the Saldanha eruption centre ignimbrites), low CaO and Na2O, and a highly ferroan character. The Plankiesbaai ignimbrite also display lower #Mg concentration compared to the Tsaarsbank ignimbrite. Typical geochemical trends in the Postberg eruption centre include the lack of variation in Zr content, higher Rb content and lower Sr, Ba, V and Zn concentrations when compared to the tephra of the Saldanha eruption centre found in the Postberg area.
4

Garnetites of the Cardigan Pluton - Evidence for Restite and Implications for Source Rock Compositions.

Pett, Teresa K. 17 November 2006 (has links) (PDF)
The Cardigan pluton, located in the southern half of New Hampshire, is a strongly peraluminous, S-type granite which is granodioritic in composition. It is inferred to have been emplaced rapidly, thrust up along west-verging nappes during the Acadian orogeny. Distinctive pods, consisting of 50 to 70 percent modal garnet, are found throughout the pluton in assemblages of garnet + sillimanite + biotite + plagioclase + quartz. These garnetite rocks present an intriguing case for restite. Textural features of the garnetite rocks, such as fibrolitic sillimanite mats and flat, unzoned major and trace-element garnet grain profiles, provide evidence for biotite dehydration melting with single-stage garnet growth from the reaction: bio + plag + qtz + kspar = gar + sill + liq. Temperatures calculated using garnet-biotite (GB) thermometry and garnet-aluminum silicate-quartz-plagioclase (GASP) barometry yield estimates between 662-714ºC and 3.8 kbars. These low calculated temperatures are most likely the result of biotite compositions which have been altered by retrograde exchange reactions. The dominant source rock for the Cardigan magmas was likely calc-pelitic to greywacke in composition. Major element modeling suggests that ~70% melting of a calc-pelitic metasediment from the Central Maine trough could have generated a granodioritic melt similar to the average granodiorite of the Cardigan pluton. However, most of the Cardigan garnetite rocks appear to have been derived from pelites, as they are too poor in CaO and Na2O. Hence, though the majority of garnetite rocks cannot represent the dominant restite of the source rocks that produced the Cardigan pluton, they do appear to be the melt-depleted residue of an unidentified pelitic source. Comparison of Nd and Sr isotopic data from garnetite and Central Maine trough metasediments permit an interpretation that the Lower Rangeley Formation, from the Central Maine trough, could be the source rock of the Cardigan magmas. However, one feldspar Pb isotopic analysis in the literature (Moench and Allienikoff, 2002) and rare monazite chemical ages near 600 Ma suggest that the Cardigan pluton does not have a Laurentian source (i.e. Lower Rangeley Formation or other Central Maine trough metasediments), whereas an inferred peri-Gondwanan basement source is permissible.
5

POLUIÇÃO DO AR POR MATERIAL PARTICULADO NO BAIRRO CENTRO DE SANTA MARIA/RS: UMA ANÁLISE A PARTIR DE VARIÁVEIS GEOURBANAS E GEOCOLÓGICAS / AIR POLLUTION IN SANTA MARIA/RS CITY IN FACE OF URBAN AND GEOCOLOGICAL ASPECTS

Rocha, José Renato 27 November 2008 (has links)
The purpose of this research is verified the concentration of particulate matter in the principals streets and avenues of Centro district of Santa Maria city/RS, making an association between geoecological conditions and the local urban structure. The specifics purposes are (a) make a zoning of Centro district s principals streets and avenues with their deposition potential of particulate matter. (b) Estimate the quantity of particulate matter emitted and its temporal variation through the years studied. (c) Quantified the bus fluxes in the streets and avenues researched, and others streets that have a significance flux; therefore a mapping of the principals traffics rote in the Center neighborhood can be made. (d) Correlate the occurrence of the principals atmospheric weather s type with the particulate emissions index stocked in FEPAM/RS s data basis. The research methodology was characterized for the environmental zoning s elaboration in the Centro district with focus on the air's quality. Lately, an investigation of particulate matter was made, using field work and secondary data related to inhale particulate matter, consulted in FEPAM/RS. The third stage consists in an intersection between particulate matter s data and the zoning map, with the intention of establish possible correlations and test the environmental zoning s efficiencies. The last stage consists in analyses the datas intersectioned relative to particulate matter concentrations suitable with what was pre-establish in the environmental zoning. Was verified that if the depositions were very differenced accordant to local collection, therefore, it wasn t possible to establish one relation that evidences the depositions level with the year s period. The investigation of the relation between inhalable particulate matters and habitual succession of atmospheric weather s type, it demonstrated the existence of a big correlation of day s concentration number up to 50 μg/m³ with winter s mouths for Santa Maria city. For this case we can say that the vehicles fluxes consisted in the principal factor that collaborated to air s quality deterioration. / O objetivo dessa pesquisa é o de verificar a concentração de material particulado nas principais ruas e avenidas do bairro Centro de Santa Maria/RS, relacionando, como variáveis de influência, as condições geoecológicas e a estrutura urbana local. Os objetivos específicos buscam: (a) Realizar um zoneamento das principais ruas e avenidas do bairro Centro quanto ao potencial de deposição de material particulado; (b) Estimar a quantidade de material particulado emitido, e sua variação temporal ao longo do ano; (c) Quantificar o fluxo de ônibus nas ruas e avenidas pesquisadas e demais ruas de fluxo significativo, estabelecendo um mapeamento das principais rotas de tráfego (d) Correlacionar a ocorrência dos principais tipos de tempo atmosférico com os índices de emissões de particulados armazenados na base de dados da Fepam/RS; (e) Realizar um mapeamento da vegetação no bairro Centro, em escala de detalhe, buscando estabelecer a correlação entre a cobertura vegetal existente e a quantidade estimada de emissão de material particulado. A metodologia de pesquisa caracterizou-se pela elaboração de um zoneamento ambiental do bairro Centro com enfoque na qualidade do ar. Posteriormente realizou-se a busca das concentrações de material particulado, em trabalho de campo, e dados secundários referentes ao material particulado inalável extraídos da FEPAM/RS. A terceira etapa consistiu no cruzamento dos dados de material particulado com o mapa de zoneamento, com vistas a estabelecer possíveis correlações e, também, testar a eficácia do zoneamento ambiental no que se refere à qualidade do ar. A última etapa consistiu na análise e cruzamento dos dados referentes às concentrações de material particulado e a sucessão habitual dos tipos de tempo em Santa Maria/RS. Constatou-se que grande parte das ruas e avenidas demonstraram quantidades de particulados condizentes com o que foi pré-estabelecido no zoneamento ambiental. Verificou-se que as deposições foram bem diferenciadas conforme o local de coleta, não sendo possível estabelecer uma relação que evidencie nível de deposição com período do ano. A investigação da relação entre as concentrações de material particulado inalável com a sucessão habitual dos tipos de tempo, demonstrou a existência de uma grande correlação quanto ao número de dias de concentração acima de 50μg/m³ com os meses de inverno para a cidade de Santa Maria. De maneira geral, pode-se dizer para o caso da cidade de Santa Maria, o fluxo de veículos constitui-se no principal fator de contribuição na deteriorização da qualidade do ar.
6

Petrogenesis, U-Pb zircon geochronology and tectonic evolution of the Malaysian granite provinces in the Southeast Asian tin belt

Ng, Wai Pan January 2014 (has links)
The Malaysian granitoids form the backbone of the Malay Peninsula and have long been recognized as composed of two distinct granitic provinces separated by the Bentong-Raub suture zone: <table><ol><li>Early Permian to Late Triassic Eastern Province (Indochina – East Malaya) with mainly “I-type” hornblende-bearing granitoids, associated with Cu-Au deposits, and subordinate hornblende-free pluton roof-zones hosting limited Sn-W deposits; and</li> <li>Late Triassic Main Range Province, western Malaysia (Sibumasu) with mainly “S-type” hornblende-free granitoids, associated with Sn-W deposits, and subordinate hornblende-bearing granitoids.</li></ol></table> Field observations and new geochemical data suggested that the division of the Eastern Province and Main Range granitoids using Chappell and White’s (1974) I-S classification could be problematic, as there is a large degree of overlap between the two granitic provinces in terms of lithology, mineralogy and metallogenic affinity. The Main Range granitoids are more fractionated than the hornblende-bearing Eastern Province. Although the two granitic provinces were emplaced into different continental terranes, both granitic provinces exhibit common trace element geochemistry in the enrichment of high field strength elements (HFSE) and rare earth elements (REE) compared to typical Cordilleran I-S granites. Such enrichment is interpreted as an inheritance signature from the protoliths. The Kontum massif (an analogue of Indochina lower continental crust) comprises intraplate ortho-amphibolites and para-gneisses, which could serve as two hypothetical source end-members for the Malaysian granitoids. The model suggests that the geneses of the parental magmas of the Eastern Province and the Main Range Province were related to hybridization of melts derived from protoliths, geochemically and isotopically similar to these two source end-members, but in differing proportions. The fact that the granites from the two granitic provinces are so similar compositionally and metallogenically, suggests that similar protoliths were involved in their source. The incorporation of sedimentary-sourced melt makes the Main Range granitoids transitional I/S-type in nature, but this is unlikely to be true for the less evolved Eastern Province fractionated I-type granitoids. The hybridization of igneous- and sedimentary-sourced melts, and granite fractionation promotes Sn metallogenesis in the Main Range granitic province. Previous ages were obtained using whole rock Rb-Sr and biotite K-Ar geochronology in the 1970s and 1980s, dating methods that almost certainly do not accurately represent the crystallization age of granites. New ion microprobe U-Pb zircon ages are presented that provide new temporal constraints for the Malaysian granitic magmatism. Eastern Province granitoids have U-Pb zircon ages that range from 289 to 220 Ma, while Main Range Province magmatism is constrained between 227 and 201 Ma. A progressive westward younging trend is apparent across the Eastern Province, but becomes less obvious in the Main Range Province. In addition, the U-Pb zircon analysis of the Malaysian granitoids suggests that both granitic provinces have Cambro-Ordovician and Mesoproterozoic inheritance signatures, which match the ages of the Kontum intraplate ortho-amphibolites and para-gneisses, the two source end-members of the suspected Indochina basement. Two different tectonic models have been suggested to explain the formation and the emplacement of the Malaysian granitoids. Both models involve an east-dipping subduction zone during the Early and Mid-Triassic with Palaeo-Tethys lithosphere rolling back along the Bentong-Raub suture zone to produce westward younging ages in the Eastern Province granitoids. The first model (modified after Searle et al. 2012) suggests the younger Main Range granitoids were produced by another Late Triassic – Cretaceous east-dipping (Neo-Tethyan) subduction to the west of Sibumasu, after the Sibumasu – East Malaya collision. The transitional I/S-type geochemistry of the Main Range granitoids was caused by the partial melting of the more heterogeneous Sibumasu basement. The second model (Oliver et al. 2014) suggests the younger Main Range granitoids were produced by the westward underthrusting of Indochina crust of East Malaya beneath Sibumasu along the Bentong-Raub suture zone after the continental collision. In this model, the source of the Main Range granitoids was the pre-collision I-type Eastern Province granitoids. The second model is less likely, as no geological evidence for such underthrust is found in the Malay Peninsula.
7

Singularly perturbed problems with characteristic layers : Supercloseness and postprocessing

Franz, Sebastian 13 August 2008 (has links) (PDF)
In this thesis singularly perturbed convection-diffusion equations in the unit square are considered. Due to the presence of a small perturbation parameter the solutions of those problems exhibit an exponential layer near the outflow boundary and two parabolic layers near the characteristic boundaries. Discretisation of such problems on standard meshes and with standard methods leads to numerical solutions with unphysical oscillations, unless the mesh size is of order of the perturbation parameter which is impracticable. Instead we aim at uniformly convergent methods using layer-adapted meshes combined with standard methods. The meshes considered here are S-type meshes--generalisations of the standard Shishkin mesh. The domain is dissected in a non-layer part and layer parts. Inside the layer parts, the mesh might be anisotropic and non-uniform, depending on a mesh-generating function. We show, that the unstabilised Galerkin finite element method with bilinear elements on an S-type mesh is uniformly convergent in the energy norm of order (almost) one. Moreover, the numerical solution shows a supercloseness property, i.e. the numerical solution is closer to the nodal bilinear interpolant than to the exact solution in the given norm. Unfortunately, the Galerkin method lacks stability resulting in linear systems that are hard to solve. To overcome this drawback, stabilisation methods are used. We analyse different stabilisation techniques with respect to the supercloseness property. For the residual-based methods Streamline Diffusion FEM and Galerkin Least Squares FEM, the choice of parameters is addressed additionally. The modern stabilisation technique Continuous Interior Penalty FEM--penalisation of jumps of derivatives--is considered too. All those methods are proved to possess convergence and supercloseness properties similar to the standard Galerkin FEM. With a suitable postprocessing operator, the supercloseness property can be used to enhance the accuracy of the numerical solution and superconvergence of order (almost) two can be proved. We compare different postprocessing methods and prove superconvergence of above numerical methods on S-type meshes. To recover the exact solution, we apply continuous biquadratic interpolation on a macro mesh, a discontinuous biquadratic projection on a macro mesh and two methods to recover the gradient of the exact solution. Special attentions is payed to the effects of non-uniformity due to the S-type meshes. Numerical simulations illustrate the theoretical results.
8

The Neoproterozoic tectonic evolution of the western Jiagenen Orogenic Belt and its Early Paleozoic-Mesozoic tectonic reworking / Evolution tectonique Néoproterozoïque de la chaîne de Jiangnan Occidental et sa réactivation au Paléozoïque inférieur Mésozoïque

Yan, Chaolei 29 October 2018 (has links)
La chaîne de collision d'âge néoprotérozoïque de Jiangnan, orientée NE-SW, marque la limite entre les blocs duYangtze et de Cathaysia. Son évolution tectonique reste encore débattue. Une des questions les plus controversées est l'âge de la collision entre les deux blocs. Afin d'acquérir une meilleure compréhension de ce problème, nous avons collecté des échantillons dans les couches sédimentaires situées au-dessus et au-dessous de la discordance dans le but de comparer les spectres d'âge des zircons détritiques et aussi de les confronter à ceux décrits dans les séries néoprotérozoïques des régions du Yangtze, Jiangnan et Cathaysia. En outre, nous nous sommes intéressés aux plutons granitiques d'âge néoproterozoïque de Sanfang et Yuanbaoshan, de type-S, situés dans la partie occidentale de la chaîne de Jiangnan afin de tracer l'évolution tectonique de la région depuis 830 Ma par la mise en œuvre de méthodes pluridisciplinaires : géologie structurale, géochronologie U-Pb, AMS, modélisation gravimétrique et thermochronologie Argon.Notre étude montre les résultats suivants : (i) La chaîne de Jiangnan s'est formée par la collision des blocs de Yangtze et Cathaysia entre ca. 865 and 830 Ma ; (ii) Les intrusions granitiques de 830 Ma se sont mises en place dans des formations encaissantes du groupe Sibao plissées et faillées. Les plutons ont été construits par accumulation latérale E-W de filons N-S, avec un écoulement horizontal du magma du sud vers le nord ; (iii). Un cisaillement ductile du haut vers l'Ouest a été reconnu dans la partie supérieure des plutons. Des âges Ar/Ar vers 420 Ma obtenus sur plusieurs grains de muscovite et biotite déformés impliquent que le cisaillement ductile peut être : a) formé pendant l'orogenèse du Paléozoïque inférieur de Chine du Sud, ou b) pendant la mise en place des plutons au Néoprotérozoïque dans une croûte chaude, sous la température de fermeture du chronomètre argon, puis lors de l'orogenèse du Paléozoïque inférieur, ce domaine crustal de Chine du Sud est passé au-dessous de 350°C; (iv) Durant la période 420-240 Ma, la région de Sanfang-Yuanbaoshana connu un refroidissement lent qui pourrait correspondre au ré-équilibrage isostatique de la croûte. / The Jiangnan Orogenic Belt is a NE-SW trending Neoproterozoic collisional suture, marking the boundary between the Yangtze Block and the Cathaysia Block. Its tectonic evolution is still debated. One of the most controversial questions is the timing of the collision between the Yangtze and Cathaysia blocks. In order to have a better understanding of this problem, we have collected the sedimentary rocks from the strata both overlying and underlying the Neoproterozoic unconformities to compare the detrital zircon age spectra between them, as well as to compare the detrital zircon spectra of Neoproterozoic sequences among the Yangtze, Jiangnan and Cathaysia regions. Moreover, we paid attention to the Neoproterozoic S-type granite plutons located in the western Jiangnan region in order to trace the crustal evolution in the Sanfang-Yuanbaoshan area since 830 Ma by multidisciplinary methods, including structural geology, geochronology, AMS, gravity modelling and Argon isotopic dating.Our study shows that : (i) The Jiangnan Orogenic Belt was built up due to the assembly of the Yangtze and Cathaysia blocks between ca. 865 and 830 Ma ; (ii) The 830 Ma granitic magma intruded into the pre-existing folds and faults in the Sibao group, the tongue-and/orsill-shaped plutonswere constructed by anE-W lateral accumulation of N-S oriented dykeswith adominantly northward horizontal magma flow from south to north ; (iii)A top-to-the-W ductile shearband has been identified on the top of plutons, (iv) the coherent mica Ar-Ar age of ca. 420 Ma, obtained from the deformed muscovite, implies that this shearing may be formed either a)during the Early Paleozoicorogeny, or b) during the Neoproterozoic plutons emplacement, then the plutons were exhumed by the Paleozoic orogeny ; (iv) During the 420-240 Ma period, the Sanfang-Yuanbaoshan area has experienced a slow cool ingrate, which may correspond to the isostatic re-equilibration of the crust.
9

Singularly perturbed problems with characteristic layers : Supercloseness and postprocessing

Franz, Sebastian 14 July 2008 (has links)
In this thesis singularly perturbed convection-diffusion equations in the unit square are considered. Due to the presence of a small perturbation parameter the solutions of those problems exhibit an exponential layer near the outflow boundary and two parabolic layers near the characteristic boundaries. Discretisation of such problems on standard meshes and with standard methods leads to numerical solutions with unphysical oscillations, unless the mesh size is of order of the perturbation parameter which is impracticable. Instead we aim at uniformly convergent methods using layer-adapted meshes combined with standard methods. The meshes considered here are S-type meshes--generalisations of the standard Shishkin mesh. The domain is dissected in a non-layer part and layer parts. Inside the layer parts, the mesh might be anisotropic and non-uniform, depending on a mesh-generating function. We show, that the unstabilised Galerkin finite element method with bilinear elements on an S-type mesh is uniformly convergent in the energy norm of order (almost) one. Moreover, the numerical solution shows a supercloseness property, i.e. the numerical solution is closer to the nodal bilinear interpolant than to the exact solution in the given norm. Unfortunately, the Galerkin method lacks stability resulting in linear systems that are hard to solve. To overcome this drawback, stabilisation methods are used. We analyse different stabilisation techniques with respect to the supercloseness property. For the residual-based methods Streamline Diffusion FEM and Galerkin Least Squares FEM, the choice of parameters is addressed additionally. The modern stabilisation technique Continuous Interior Penalty FEM--penalisation of jumps of derivatives--is considered too. All those methods are proved to possess convergence and supercloseness properties similar to the standard Galerkin FEM. With a suitable postprocessing operator, the supercloseness property can be used to enhance the accuracy of the numerical solution and superconvergence of order (almost) two can be proved. We compare different postprocessing methods and prove superconvergence of above numerical methods on S-type meshes. To recover the exact solution, we apply continuous biquadratic interpolation on a macro mesh, a discontinuous biquadratic projection on a macro mesh and two methods to recover the gradient of the exact solution. Special attentions is payed to the effects of non-uniformity due to the S-type meshes. Numerical simulations illustrate the theoretical results.
10

Multiple Asteroid Retrieval Mission

Gargioni, Gustavo 11 May 2020 (has links)
In this thesis, the possibility of enabling space-mining for the upcoming decade is explored. Making use of recently-proven reusable rockets, we envision a fleet of spacecraft capable of reaching Near-Earth asteroids. To analyze this idea, the goal of this problem is to maximize the asteroid mass retrieved within a spacecraft max life span. Explicitly, the maximum lifetime of the spacecraft fleet is set at 30 years. A fuel supply-chain is proposed and designed so that each spacecraft is refueled before departing for each asteroid. To maximize access to the number of asteroids and retrievable mass for each mission, we propose launching each mission from an orbit with low escape velocity. The L2-Halo orbit at the libration point in the Earth-Moon system was selected due to its easy access from Low-Earth Orbit and for a cislunar synergy with NASA Gateway. Using data from NASA SmallBody and CNEOS databases, we investigated NEAs in the period between 2030 and 2060 could be captured in the ecliptic plane and returned to L2-Halo with two approaches, MARM-1 and MARM-2. Together, these databases provide all information for every asteroid's close approach known today. Returning the asteroid as a whole is explored in the MARM-1 method, while MARM-2 evaluates the possibility of reaching larger asteroids and returning a fragment of their masses, such that it optimizes the available cargo weight per time of flight of each mission. The following results are compared with previous work from the community. The results show a 96% reduction in the cost per kg, with an enormous increase in retrieved mass. With these results, this thesis shows that not solely energy or dynamic optimization will be responsible for proving space mining feasibility, but rather a combination of those and business best practices. Proving feasibility for space mining is a complex and immense problem. Although this thesis opens new possibilities for future work on the field and sparkes the interest of private endeavors, the final solution for this problem still requires additional exploration. / M.S. / In this thesis, the possibility of enabling space-mining for the upcoming decade is explored. Making use of recently-proven reusable rockets, we envision a fleet of spacecraft capable of reaching Near-Earth asteroids, NEAs. To analyze this idea, the goal of this problem is to maximize the asteroid mass retrieved within a spacecraft max life span. Explicitly, the maximum lifetime of the spacecraft fleet is set at 30 years. A fuel supply-chain is proposed and designed so that each spacecraft is refueled before departing for each asteroid. To maximize access to the number of asteroids and retrievable mass for each mission, we propose launching each mission from an orbit with low escape velocity. A location after the Moon, at the L2-Halo orbit, was selected due to its easy access from Low-Earth Orbit and for a synergy with the proposed new space station at the Moon orbit. Using data from NASA databases, we investigated the asteroids in the period between 2030 and 2060 that could be captured and returned with two approaches, MARM-1 and MARM-2. Together, these databases provide all information for every asteroid's close approach known today. Returning the asteroid as a whole is explored in the MARM-1 method, while MARM-2 evaluates the possibility of reaching larger asteroids and returning a fragment of their masses, such that it optimizes the available cargo weight per time of flight of each mission. The following results are compared with previous work from the community. The results show a 96% reduction in the cost per kg, with an enormous increase in retrieved mass. With these results, this thesis shows that not solely energy or dynamic optimization will be responsible for proving space mining feasibility, but rather a combination of those and business best practices. Proving feasibility for space mining is a complex and immense problem. Although this thesis opens new possibilities for future work on the field and sparkes the interest of private endeavors, the final solution for this problem still requires additional exploration.

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