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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.
21

Settling and sedimentation behavior of fine-grained materials

Nam, Soonkie 27 May 2005 (has links)
Channeling has already been an observed phenomenon that often occurs during settling and sedimentation processes of finer materials. However, it has been regarded as a minor factor affecting settling process, e.g. settling velocity or consolidation rate. In this study, settling behaviors of talcs, kaolins and attapulgite were reviewed by experiments with small and large settling columns with special focus on channel formation during sedimentation. The large settling column is equipped with twenty eight measuring points, which are connected to pressure transducers for measuring pore pressure changes during settling. Throughout the study, channel formation was observed and related to the experimental conditions affecting it. The excess pore pressure changes were measured during the large column tests. Channels occurred under flocculation in zone settling and also in consolidation zones; pressure drop was observed near channels in some cases. It was apparent that channels work as a facilitator to dissipate the excess pore water pressure. It is summarized that not only initial concentration but also the material properties, such as specific gravity and shape of particles, can affect the channel formation. / Master of Science
22

Secondary Clarifier Modeling: A Multi-Process Approach

Griborio, Alonso 08 May 2004 (has links)
The performance of settling tanks depends on several interrelated processes and factors that include: hydrodynamics, settling, turbulence, sludge rheology, flocculation, temperature changes and heat exchange, geometry, loading, the nature of the floc, the atmospheric conditions and the total dissolved solids concentration. A Quasi-3D (Q3D) clarifier model has been developed to include the following factors: axisymmetric hydrodynamics (including the swirl component), five types of settling (nonsettleable particles, unflocculated discrete settling, flocculated discrete settling, hindered settling and compression), turbulence, sludge rheology, flocculation with four classes of particles, temperature changes and surface heat exchange with the atmosphere, various external and internal geometry configurations, unsteady solids and hydraulic loading, the nature of the floc settling/interaction. The model includes: shear flocculation, differential settling flocculation and sweep flocculation. The Q3D model reproduces the major features of the hydrodynamic processes and solids distribution on secondary clarifiers. When the model is executed with the field derived settling characteristics, it can accurately predict the effluent and recirculation suspended solids concentrations. The model has been formulated to conserve fluid, tracer and solids mass. The model has been developed and tested using field data from the UNO Pilot Plant and the Jefferson Parish Waste Water Treatment Plant located at Marrero, Louisiana. A field testing procedure is presented that addressees all of the settling regimes that are encountered in a Secondary Settling Tank. Results obtained with the Q3D model indicate that the flocculation process plays a major role in the effluent suspended solids (ESS) on secondary clarifiers. The extent of actual flocculation depends on the design of the center well and on the concentration of the incoming mixed liquor suspended solids (MLSS). The center well promotes flocculation, but its most important benefit is the improvement on the tank hydrodynamics. The changes in temperature on secondary clarifiers play an important role on the performance of secondary settling tanks. The gravity induced radial velocities in the sludge blanket are higher than the radial velocities of the scraper in the region near the hopper, therefore the blades are not highly effective in conveying the solids in this region.
23

Relationship between the Sludge Settling Characteristics and the Parameters of the Activated Sludge System

Rojas, Jose Angel 17 December 2004 (has links)
The activated sludge process is one of the most commonly employed domestic and industrial waste treatment process. Different types of mathematical models have been proposed for design and operation of this process, most of which do not consider the relationship between the sludge settling characteristics and the aeration unit performance. This project studies the validity of a model developed by La Motta (2004b) which links the operating parameters of an activated sludge system and the classical limiting flux sludge settling theory. Favorable results were obtained demonstrating that the model predicts very similar values of the parameters of the system in comparison with the parameters observed in an activated sludge pilot plant that is located within installations of the Marrero Wastewater Treatment Plant, New Orleans, Louisiana. This research also demonstrated that the model is a helpful tool for the design and operation of an activated sludge system.
24

Partida de reator em bateladas sequenciais visando à  identificação das condições operacionais necessárias para a formação de lodo granular aeróbio. / Start up of a sequencing batch reactor aiming to identify the necessary operational conditions to develop aerobic granular sludge.

Sandoval, Marcel Zanetti 03 May 2019 (has links)
O presente estudo teve como objetivo principal identificar as condições necessárias para a formação de lodo granular aeróbio em um reator de bateladas sequenciais, desenvolvendo uma estratégia de partida para obter a granulação e também avaliando as propriedades morfológicas do lodo formado. Ao longo da pesquisa, também foram avaliados os resultados que podem ser alcançados mediante a aplicação deste tipo de tratamento para esgoto universitário, em termos de remoção de matéria orgânica, nitrogênio e fósforo. Dividiu-se a pesquisa em duas fases, onde na primeira, desenvolvida no Laboratório de Saneamento da Escola Politécnica, utilizou-se um reator em escala de bancada e na segunda, desenvolvida no Centro Tecnológico de Hidráulica, um reator em escala piloto, ambos operando em bateladas sequenciais e com uma mesma razão altura diâmetro (H/D) de aproximadamente 10. Ambas as fases foram divididas em cinco etapas, cujo critério de divisão foi a redução progressiva do tempo de sedimentação do ciclo da batelada, inicialmente em 30 minutos, na etapa 1, e 5 minutos na etapa 10. Primeiramente, foi operado o reator de bancada por 330 dias, onde alimentou-se o sistema com efluente sintético. Em seguida, o reator piloto foi operado também por aproximadamente 330 dias, o qual foi alimentado com esgoto universitário. A pesquisa pode ser caracterizada como um período de partida para ambas as fases, onde não se obteve uma operação estável dos reatores, não sendo possível atingir um regime estacionário, uma vez que não foi realizado descarte de lodo intencional, devido à alta perda de sólidos com o efluente tratado ao final de cada ciclo. Os resultados mostraram que é possível obter a granulação aeróbia, indicando que as condições essenciais são a hidrodinâmica do reator, ou seja, a forte aeração gerando uma alta força de cisalhamento sobre as partículas e a alimentação de efluente pelo fundo do reator, fazendo com que este escoe em contato com o lodo em um ambiente anaeróbio. A estratégia operacional que envolve redução progressiva do período disponibilizado para a sedimentação do lodo contribui para aumentar a porção de biomassa granular dentro do sistema e assim favorecendo o desenvolvimento e crescimento das partículas granulares maiores e mais pesadas. No final da Etapa I foi pela primeira vez observada à presença de partículas granulares. A morfologia dos grânulos foi avaliada em termos do diâmetro de Feret e circularidade das partículas presentes. Outras propriedades do lodo foram avaliadas, como os índices volumétricos de lodo, sólidos sedimentáveis, as propriedades de remoção de carga orgânica e nutrientes. Os valores de Índice Volumétrico de Lodos (IVL) observados ficaram na faixa tipicamente observada para lodo floculento de boa sedimentabilidade. Ocorreram boas remoções de carga orgânica (DBO solúvel de 87% e DQO solúvel de 82%), assim como a eficiência de remoção de amônia, cuja média na fase I foi de 68%. Também ocorreu desnitrificação, com valores de nitrito e nitrato no efluente tratado com médias de 2,62 e 3,26 mg/L respectivamente. A remoção de fósforo foi avaliada em termos de fósforo solúvel, onde a eficiência média obtida foi de 41%. Observaram-se grânulos cujos diâmetros médios ficaram em torno de 0,3 mm, sendo que a média dos valores máximos de cada Etapa da Fase I foi de 2,3 mm. Com aproximadamente 250 dias de operação surgiram organismos filamentosos aderidos às superfícies dos grânulos formados. O crescimento de tais organismos foi progressivo, primeiramente refletindo na queda do coeficiente de circularidade dos grânulos, conferindo forma mais irregular aos mesmos e depois levando à finalização da operação do reator de bancada aos 330 dias, quando a proliferação acentuada de filamentosos resultou na quebra dos grânulos e desaparecimento destes. Na fase II, operou-se o reator em escala piloto por aproximadamente 330 dias. Nesta fase da pesquisa aplicou-se um fator de carga volumétrica e uma relação alimento-microrganismos menor do que na Fase I, contudo também foi possível observar o início do processo de granulação ainda sob tempos de sedimentação elevados (25 minutos), sendo que a granulação evoluiu ao longo da operação do reator, onde realizou-se a redução progressiva do período de sedimentação do ciclo da batelada. Os diâmetros médios dos grânulos, durante todo esse período, foram de 0,8 mm, sendo que a média dos diâmetros máximos de cada Etapa da Fase II foi de 4,8 mm. Os valores de índice volumétrico de lodo foram baixos, mostrando evolução do processo de granulação, contudo ainda na faixa considerada para lodo floculento, evidenciando ainda a presença de uma parcela considerável da biomassa na forma de flocos. Os resultados obtidos para as velocidades de sedimentação por zona também levaram à mesma conclusão. As propriedades de tratamento do lodo foram monitoradas e os resultados mostraram uma remoção de carga de 91% para DBO solúvel e 88% para DQO solúvel. A remoção de amônia apresentou eficiência média para o período de 50% e a remoção de nitrogênio kjeldahl total foi de 52%. Observaram-se valores baixos de nitritos e nitratos ao longo de toda a segunda fase, indicando a ocorrência de desnitrificação. As remoções de fósforo total e solúvel apresentaram média para o período de 75% e 76%, respectivamente. Não ocorreu proliferação de organismos filamentosos durante a operação do reator piloto. / The present study\'s main objective was to identify the necessary conditions for the formation of aerobic granular sludge in a sequential batch reactor, developing a starting strategy to obtain granulation and also evaluating the morphological properties of the formed sludge. It was also evaluated the aerobic sludge\'s treatment properties in terms of organic matter, nitrogen and phosphorus removal, the main contaminants present in the low strength wastewater fed to the reactor. The research was divided into two phases, where the first one a bench scale reactor was operated and a second one where a pilot scale reactor was used, both in sequential batch mode and with the same height diameter ratio (H/D) ratio of approximately 10. Phase I, (bench scale reactor) lasted for 330 days, and the system was fed with synthetic effluent. Then the pilot reactor was also operated for about 330 days (Phase II), which was fed with low strength wastewater. The research can be characterized as a start-up period for both phases, where a steady state for the reactor was not obtained, once no intentional sludge discharge was performed and an increased suspended solids concentration was observed in the effluent withdrawn at the end of each cycle during all the survey. The results showed that the essential conditions to obtain aerobic granulation are the hydrodynamics/flow patterns inside the reactor, that is, the strong aeration generating a high shear force over the particles surface and the plug flow effluent feed from the bottom of the reactor, in an anaerobic environment. The operational strategy that involves progressive reduction of the batch settling period creates a selective pressure that increases the portion of granular biomass within the system and thus favoring the development and growth of larger and heavier granular particles. At the end of phase I the presence of granular particles was observed for the first time. The morphology of the granules was evaluated in terms of the Feret\'s diameter and the circularity coefficient from the particles present in the sludge. Other properties of the sludge were evaluated, such as the sludge volumetric index, settleable solids and organic load and nutrient removal capacities. The observed values of SVI remained within a range typically correlated for flocculent sludge with good settling properties. Satisfactory organic load removal (87% soluble BOD and 82% soluble COD) was observed, as well as ammonia removal, which average value was around 68%. Denitrification also occurred, once nitrite and nitrate values in the treated effluent were low throughout the bench reactor operation. The removal of phosphorus was evaluated in terms of soluble phosphorus, where the average removal efficiency obtained was 41%. The granules average Feret\'s diameter for all this period was 0.3 mm and the average maximum value for all the stages of the first phase was 2.3 mm. With approximately 250 days of operation, filamentous organisms appeared adhered to the formed granules surfaces. The growth of these organisms was progressive, firstly reflecting in the drop of the circularity coefficient, resulting in a more irregular shape of the granules surface and then leading to the reactor\'s failure at 330 days of operation, when the filamentous overgrowth resulted in the granules breaking and disappearance. In phase II a pilot scale reactor was operated for approximately 330 days. In this phase, a lower volumetric loading factor and food to microorganism feed ratio were applied, compared to Phase I. However, it was also possible to observe the beginning of the granulation process still under high settling periods (25 minutes), with development of the granulation process throughout Phase II, using the same strategy based on the progressive reduction of the batch settling interval. The average Feret\'s diameter during this whole period was 0.8 mm, and the average maximum value for all the stages of the second phase was 4.8 mm. The values of sludge volumetric index decreased indicating evolution of the granulation process, yet still in the range considered for flocculent sludge, evidencing also the presence of a considerable amount of flocculant biomass. The results obtained for settling velocities also led to the same conclusion. The sludge treatment properties were monitored, and the results showed a 91% removal efficiency for soluble BOD and 88% removal efficiency for soluble COD. The average ammonia removal efficiency for the period was 50% and the average total kjeldahl nitrogen removal of 52%. Low nitrite and nitrate values were observed throughout the second phase in the treated effluent, indicating the occurrence of denitrification. The average total and soluble phosphorus removal for the period was 75% and 76%, respectively. No filamentous overgrowth was observed during the pilot reactor operation.
25

Formação da macrossegregação de carbono no silício durante a solidificação direcional ou decantação de carbonetos. / Formation of carbon macrosegregation in silicon during directional solidification of carbide settling.

Ribeiro, Tiago Ramos 05 April 2013 (has links)
As energias renováveis têm ganhado destaque como possíveis soluções para a questão da matriz energética mundial. Dentre as diferentes alternativas está a energia solar. As células fotovoltaicas são produzidas majoritariamente com silício metálico de alta pureza que é produzido tradicionalmente por um processo químico de alta complexidade e custo. Alternativas vêm sendo desenvolvidas para produção deste material, sendo a rota metalúrgica uma delas. Nesta rota parte-se de um silício de menor pureza e removem-se as impurezas através de operações metalúrgicas. Um dos elementos a serem removidos é o carbono, que está majoritariamente presente precipitado na forma de carboneto de silício (SiC). Visando o estudo da formação da macrossegregação de partículas de SiC em Si, ensaios de solidificação em um forno do tipo Bridgman com diferentes velocidades de extração e diferentes diâmetros de molde foram realizados. Ensaios para verificar o efeito de decantação destas partículas na macrossegregação também foram conduzidos. Nos ensaios de solidificação, os resultados mostram que um aumento da velocidade de extração do molde para fora da região quente do forno resulta em uma estrutura de grãos menos alinhada na direção axial dos lingotes cilíndricos. Adicionalmente, o aumento do diâmetro do lingote também possui um efeito na macroestrutura, dependo da velocidade de extração. A macrossegregação de carbono para o topo do lingote é mais severa quanto menor for a velocidade de extração e maior for a direcionalidade dos grãos. Esta macrossegregação é causada pelo empurramento das partículas de SiC pela interface sólido/líquido. A decantação de partículas de SiC causou macrossegregação de C para a base dos lingotes de Si, porém menos acentuada que aquela observada nos ensaios de solidificação direcional. A alteração do período de tempo reservado no experimento para ocorrência da decantação de uma para seis horas não influenciou significativamente a macrossegregação. Para um mesmo tempo de processo, a solidificação direcional a uma velocidade de extração de 5 µm/s resultou em uma maior macrossegregação de carbono do que aquela observada após decantação, apresentando um maior potencial para a remoção do carbono contido no silício. / Renewable energies have been considered as possible solutions to the world energy matrix issue. Solar energy is one of the alternatives. Photovoltaic cells are mainly made of high purity silicon, which is produced by a complex and costly chemical process. New alternative processes are under development and one of them is the metallurgical route. In this route, a less pure silicon is refined and impurities are removed by metallurgical operations. One of the elements to be removed is carbon, which is mainly present as silicon carbide (SiC). Aiming at an investigation about the macrosegregation of carbon and SiC particles in Si, solidification experiments were conducted in a Bridgman type furnace using different extraction velocities and different mold diameters. Experiments to investigate the effects of settling of SiC particles were also carried out. The results show that the mold extraction velocity plays an important role in the grain macrostructure formation: higher velocities give rise to a less directional grain structure. Additionally, the change in the ingot diameter also has an effect on the macrostructure depending on the extraction velocity. Carbon macrosegregation to the ingot top is more severe for lower mold extraction velocities. This macrosegregation is a result of SiC particles being pushed by the solid/liquid interface to the ingot top. The settling of SiC particles causes carbon macrosegregation to the ingot bottom, but less intense than that observed in the directional solidification experiments at the ingot top. The change of settling times from one to six hours, have no significant effect on the degree of macrosegregation. For equal processing times, directional solidification at a mold extraction rate of 5 µm/s causes more carbon macrosegregation than settling, representing a higher potential alternative for carbon removal from silicon.
26

Formação da macrossegregação de carbono no silício durante a solidificação direcional ou decantação de carbonetos. / Formation of carbon macrosegregation in silicon during directional solidification of carbide settling.

Tiago Ramos Ribeiro 05 April 2013 (has links)
As energias renováveis têm ganhado destaque como possíveis soluções para a questão da matriz energética mundial. Dentre as diferentes alternativas está a energia solar. As células fotovoltaicas são produzidas majoritariamente com silício metálico de alta pureza que é produzido tradicionalmente por um processo químico de alta complexidade e custo. Alternativas vêm sendo desenvolvidas para produção deste material, sendo a rota metalúrgica uma delas. Nesta rota parte-se de um silício de menor pureza e removem-se as impurezas através de operações metalúrgicas. Um dos elementos a serem removidos é o carbono, que está majoritariamente presente precipitado na forma de carboneto de silício (SiC). Visando o estudo da formação da macrossegregação de partículas de SiC em Si, ensaios de solidificação em um forno do tipo Bridgman com diferentes velocidades de extração e diferentes diâmetros de molde foram realizados. Ensaios para verificar o efeito de decantação destas partículas na macrossegregação também foram conduzidos. Nos ensaios de solidificação, os resultados mostram que um aumento da velocidade de extração do molde para fora da região quente do forno resulta em uma estrutura de grãos menos alinhada na direção axial dos lingotes cilíndricos. Adicionalmente, o aumento do diâmetro do lingote também possui um efeito na macroestrutura, dependo da velocidade de extração. A macrossegregação de carbono para o topo do lingote é mais severa quanto menor for a velocidade de extração e maior for a direcionalidade dos grãos. Esta macrossegregação é causada pelo empurramento das partículas de SiC pela interface sólido/líquido. A decantação de partículas de SiC causou macrossegregação de C para a base dos lingotes de Si, porém menos acentuada que aquela observada nos ensaios de solidificação direcional. A alteração do período de tempo reservado no experimento para ocorrência da decantação de uma para seis horas não influenciou significativamente a macrossegregação. Para um mesmo tempo de processo, a solidificação direcional a uma velocidade de extração de 5 µm/s resultou em uma maior macrossegregação de carbono do que aquela observada após decantação, apresentando um maior potencial para a remoção do carbono contido no silício. / Renewable energies have been considered as possible solutions to the world energy matrix issue. Solar energy is one of the alternatives. Photovoltaic cells are mainly made of high purity silicon, which is produced by a complex and costly chemical process. New alternative processes are under development and one of them is the metallurgical route. In this route, a less pure silicon is refined and impurities are removed by metallurgical operations. One of the elements to be removed is carbon, which is mainly present as silicon carbide (SiC). Aiming at an investigation about the macrosegregation of carbon and SiC particles in Si, solidification experiments were conducted in a Bridgman type furnace using different extraction velocities and different mold diameters. Experiments to investigate the effects of settling of SiC particles were also carried out. The results show that the mold extraction velocity plays an important role in the grain macrostructure formation: higher velocities give rise to a less directional grain structure. Additionally, the change in the ingot diameter also has an effect on the macrostructure depending on the extraction velocity. Carbon macrosegregation to the ingot top is more severe for lower mold extraction velocities. This macrosegregation is a result of SiC particles being pushed by the solid/liquid interface to the ingot top. The settling of SiC particles causes carbon macrosegregation to the ingot bottom, but less intense than that observed in the directional solidification experiments at the ingot top. The change of settling times from one to six hours, have no significant effect on the degree of macrosegregation. For equal processing times, directional solidification at a mold extraction rate of 5 µm/s causes more carbon macrosegregation than settling, representing a higher potential alternative for carbon removal from silicon.
27

Sedimentation of Organic - Inorganic Composites by Optical Turbidity

Harrinauth, Reshma K 04 November 2008 (has links)
Sedimentation is one of many characterization tools used to test materials in nanotechnology. Characterization of settling behavior is complex as there are many variables which can affect sedimentation. In our research, we focused on sedimentation in colloidal systems with the aid of an optical turbidometer. Nanoparticles of CeO2 (Ceria Oxide) and TiO2 (Titanium Dioxide) are embedded onto a polymeric matrix of a thermally responsive microgel of poly(N-isopropylacrylamide) (PNIPAM) and interpenetrating chains of poly(acrylic acid) to create novel composites. The composites are loaded with the inorganic oxide nanoparticles at different weight percent from a low value of 10 weight % to 75 weight %. The loading of the colloidal particles affects the sedimentation rate. In this thesis a turbidomenter is used to characterize the settling rate, which is an important characteristic for application of these new composites. TiO2 is a key constituent in many industrial products; cosmetics, paints, ceramics and used in waste water remediation. It is a potent photocatalyst which breaks down almost any organic compound when exposed to ultraviolet light. By combining nanoparticles of TiO2 with microgels of a polymer, the composites can facilitate use and recovery of the catalyst. Gravity settling of these loaded composites provides an easy separation of TiO2 nanoparticles. In this context, characterization of settling plays an important role. CeO2 composites are used to polish oxide coatings in the semiconductor industry and sedimentation of the composite particles is important as it can affect the efficiency of the planarization process. Therefore, measuring sedimentation of these composites is necessary. In this study, the settling behavior is measured optically for a variety of conditions that differ in loading of inorganic nanoparticles within the microgels, temperature of the solution, and concentration of particles in solution. The overall goal is to understand the sedimentation behavior of these novel composites and facilitate their use in industrial processes.
28

Settling Particulates and Sediments in the Northern South China Sea: Study of Flux and Pb-210

Huang, Huei-chung 31 July 2007 (has links)
In this study, the sediment cores taken in the northern South China Sea (SCS) as well as the settling particulates collected from time-series sediment traps deployed in the same area have been analyzed for Pb-210 activities in order to estimate the sedimentation rate and mass flux from core data and to obtain temporal variations in mass flux and Pb-210 from the time-series sediment traps. The main purposes are to compare and to discuss the mass balance problem between the sediment trap and core results in terms of mass flux, Pb-210 activity and its fluxes. The time-averaged particulate fluxes measured from different depths at M3S and M1T sites in the northern SCS generally increase with depth, reflecting an increasing effect of the lateral transport. The upper and middle traps display a synchronous trend in mass flux variations. The mean particulate flux at S5 site near Luzon Strait is clearly higher than the two sites mentioned above probably because of the effect of topography and bottom current. Distributions of Pb-210 are influenced by particulate scavenging: the longer the settling particles stay in the water column the more the surrounding Pb-210 will be scavenged. The temporal variations of Pb-210 at M3S show a similar trend and an increase with depth. At M1T site, the temporal variations of Pb-210 show no clear trend due to insufficient samples. It has been commonly observed in the marginal sea that Pb-210 activity is inversely correlated with the associated mass flux, i.e. higher Pb-210 is associated with lower mass flux in terms of their temporal variations. This study is also in line with such observations. The mean water content of the core at I located near the shelf break in the northern SCS is about 28%, and its mean loss on ignition (L.O.I.) is 3.2%. These are similar to those observed previously in the northern SCS (water content: 25-37%; L.O.I.: 3%-8%). The sedimentation rate as determined from the excess Pb-210 profile at core I is 18cm/100yr which is at the lower end of the previous study (16-52 cm/100yr) (Wu, 2006). The sediment flux and sedimentation rate estimated from both the Pb-210 inventory (I) and the upper limit of sedimentation rate are identical, respectively, at 0.32 g/cm2/yr and 18cm/100yr. Thus the mixing effect could be neglected. The Pb-210 flux estimated from the deep sediment trap at 2163m (M3S, 77.4 dpm/m2/d) is much lower than that observed from the core sediment (F, 761.1 dpm/m2/d). Although the specific Pb-210 activity of the particles is much greater than that in the surface sediment, the particle flux is too small relative to the mass flux of the sediment, suggesting that additional sediment with Pb-210 has been transported laterally from elsewhere and deposited here. This results in a large imbalance between the sinking particulates and the underlying sediment in mass flux and Pb-210 flux.
29

Settling Time Reducibility Orderings

Loo, Clinton 26 April 2010 (has links)
It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation time domination as a relation on $n$-c.e. sets where $n \geq 3$. This will be extended to the case of $2$-c.e. sets, showing that no ordering can be derived from computation time domination on $n$-c.e. sets when $n\geq 2$. Additionally, we will observe properties of the orderings given by settling time domination and strong settling time domination on c.e. sets, respectively denoted as $\mathcal{E}_{st}$ and $\mathcal{E}_{sst}$. More specifically, it is already known that any countable partial ordering can be embedded into $\mathcal{E}_{st}$ and any linear ordering with no infinite ascending chains can be embedded into $\mathcal{E}_{sst}$. Continuing along this line, we will show that any finite partial ordering can be embedded into $\mathcal{E}_{sst}$.
30

Settling Time Reducibility Orderings

Loo, Clinton 26 April 2010 (has links)
It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation time domination as a relation on $n$-c.e. sets where $n \geq 3$. This will be extended to the case of $2$-c.e. sets, showing that no ordering can be derived from computation time domination on $n$-c.e. sets when $n\geq 2$. Additionally, we will observe properties of the orderings given by settling time domination and strong settling time domination on c.e. sets, respectively denoted as $\mathcal{E}_{st}$ and $\mathcal{E}_{sst}$. More specifically, it is already known that any countable partial ordering can be embedded into $\mathcal{E}_{st}$ and any linear ordering with no infinite ascending chains can be embedded into $\mathcal{E}_{sst}$. Continuing along this line, we will show that any finite partial ordering can be embedded into $\mathcal{E}_{sst}$.

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