923 resultados para Geometry of numbers


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Public Lightning is an important part of municipality’s nighttime landscape. Lighting can be used to enhance public safety and security while improving the aesthetic appeal of the surrounding properties but with the current global financial crisis, such lighting systems must also be sustainable. Most climate policy efforts focus on the state and international level, however national governments won’t be able to meet their international commitments without local action. In Portugal, the Public Lighting is responsible for 3% of energy consumption. The problem is that the trend is to increase (about 4-5% per year) which represents very high costs for the municipal authorities. In terms of numbers are analyzed in this thesis 45 of 278 existent in Continental Portugal what represents only 16,2 % of the counties. This where the local authorities in Portugal that had a Sustainable Energy Action Plan (SEAP) that had been accepted and made available in the Covenant of Mayors website until the end of year 2013. It is important that the Covenant of Mayors will increase the local authorities awareness for energy efficiency and especially to public lighting because there is still a long way to go in terms of energy consumption reduction. In future works it would be interesting to see the payback of the EolGreen post in a real scenario due to lack of energy consumption from the grid it would allow to have a pretty high initial investment even with the maintenance that those technologies need.

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Soil is a complex heterogeneous system comprising of highly variable and dynamic micro-habitats that have significant impacts on the growth and activity of resident microbiota. A question addressed in this research is how soil structure affects the temporal dynamics and spatial distribution of bacteria. Using repacked microcosms, the effect of bulk-density, aggregate sizes and water content on growth and distribution of introduced Pseudomonas fluorescens and Bacillus subtilis bacteria was determined. Soil bulk-density and aggregate sizes were altered to manipulate the characteristics of the pore volume where bacteria reside and through which distribution of solutes and nutrients is controlled. X-ray CT was used to characterise the pore geometry of repacked soil microcosms. Soil porosity, connectivity and soil-pore interface area declined with increasing bulk-density. In samples that differ in pore geometry, its effect on growth and extent of spread of introduced bacteria was investigated. The growth rate of bacteria reduced with increasing bulk-density, consistent with a significant difference in pore geometry. To measure the ability of bacteria to spread thorough soil, placement experiments were developed. Bacteria were capable of spreading several cm’s through soil. The extent of spread of bacteria was faster and further in soil with larger and better connected pore volumes. To study the spatial distribution in detail, a methodology was developed where a combination of X-ray microtopography, to characterize the soil structure, and fluorescence microscopy, to visualize and quantify bacteria in soil sections was used. The influence of pore characteristics on distribution of bacteria was analysed at macro- and microscales. Soil porosity, connectivity and soil-pore interface influenced bacterial distribution only at the macroscale. The method developed was applied to investigate the effect of soil pore characteristics on the extent of spread of bacteria introduced locally towards a C source in soil. Soil-pore interface influenced spread of bacteria and colonization, therefore higher bacterial densities were found in soil with higher pore volumes. Therefore the results in this showed that pore geometry affects the growth and spread of bacteria in soil. The method developed showed showed how thin sectioning technique can be combined with 3D X-ray CT to visualize bacterial colonization of a 3D pore volume. This novel combination of methods is a significant step towards a full mechanistic understanding of microbial dynamics in structured soils.

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The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.

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Following the development of non-Euclidean geometries from the mid-nineteenth century onwards, Euclid’s system had come to be re-conceived as a language for describing reality rather than a set of transcendental laws. As Henri Poincaré famously put it, ‘[i]f several geometries are possible, is it certain that our geometry [...] is true?’. By examining Joyce’s linguistic play and conceptual engagement with ground-breaking geometric constructs in Ulysses and Finnegans Wake, this thesis explores how his topographical writing of place encapsulates a common crisis between geometric and linguistic modes of representation within the context of modernity. More specifically, it investigates how Joyce presents Euclidean geometry and its topographical applications as languages, rather than ideally objective systems, for describing visual reality; and how, conversely, he employs language figuratively to emulate the systems by which the world is commonly visualised. With reference to his early readings of Giordano Bruno, Henri Poincaré and other critics of the Euclidean tradition, it investigates how Joyce’s obsession with measuring and mapping space throughout his works enters into his more developed reflections on the codification of visual signs in Finnegans Wake. In particular, this thesis sheds new light on Joyce’s developing fascination with the ‘geometry of language’ practised by Bruno, whose massive influence on Joyce is often assumed to exist in Joyce studies yet is rarely explored in any great detail.

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Open-cell metal foams show promise as an emerging novel material for heat exchanger applications. The high surface-area-to-volume ratio suggests increased compactness and decrease in weight of heat exchanger designs. However, the metal foam structure appears conducive to condensate retention, which would degenerate heat transfer performance. This research investigates the condensate retention behavior of aluminum open-cell metal foams through the use of static dip tests and geometrical classification via X-ray Micro-Computed Tomography. Aluminum open-cell metal foam samples of 5, 10, 20, and 40 pores per inch (PPI), all having a void fraction greater than 90%, were included in this investigation. In order to model the condensate retention behavior of metal foams, a clearer understanding of the geometry was required. After exploring the ideal geometries presented in the open literature, X-ray Micro-Computed Tomography was employed to classify the actual geometry of the metal foam samples. The images obtained were analyzed using specialized software from which geometric information including strut length and pore shapes were extracted. The results discerned a high variability in ligament length, as well as features supporting the ideal geometry known as the Weaire-Phelan unit cell. The static dip tests consisted of submerging the metal foam samples in a liquid, then allowing gravity-induced drainage until steady-state was reached and the liquid remaining in the metal foam sample was measured. Three different liquids, water, ethylene glycol, and 91% isopropyl alcohol, were employed. The behaviors of untreated samples were compared to samples subjected to a Beomite surface treatment process, and no significant differences in retention behavior were discovered. The dip test results revealed two distinct regions of condensate retention, each holding approximately half of the total liquid retained by the sample. As expected, condensate retention increased as the pores sizes decreased. A model based on surface tension was developed to predict the condensate retention in the metal foam samples and verified using a regular mesh. Applying the model to both the ideal and actual metal foam geometries showed good agreement with the dip test results in this study.

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A two-step etching technique for fine-grained calcite mylonites using 0.37% hydrochloric and 0.1% acetic acid produces a topographic relief which reflects the grain boundary geometry. With this technique, calcite grain boundaries become more intensely dissolved than their grain interiors but second phase minerals like dolomite, quartz, feldspars, apatite, hematite and pyrite are not affected by the acid and therefore form topographic peaks. Based on digital backscatter electron images and element distribution maps acquired on a scanning electron microscope, the geometry of calcite and the second phase minerals can be automatically quantified using image analysis software. For research on fine-grained carbonate rocks (e.g. dolomite calcite mixtures), this low-cost approach is an attractive alternative to the generation of manual grain boundary maps based on photographs from ultra-thin sections or orientation contrast images.

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The paper studies the influence of rail weld dip on wheel-rail contact dynamics, with particular reference to freight trains where it is important to increase the operating speed and also the load transported. This has produced a very precise model, albeit simple and cost-effective, which has enabled train-track dynamic interactions over rail welds to be studied to make it possible to quantify the influence on dynamic forces and displacements of the welding geometry; of the position of the weld relative to the sleeper; of the vehicle's speed; and of the axle load and wheelset unsprung mass. It is a vertical model on the spatial domain and is drawn up in a simple fashion from vertical track receptances. For the type of track and vehicle used, the results obtained enable the quantification of increases in wheel-rail contact forces due to the new speed and load conditions.

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The current study examined the frequency and quality of how 3- to 4-year-old children and their parents explore the relations between symbolic and non-symbolic quantities in the context of a playful math experience, as well as the role of both parent and child factors in this exploration. Preschool children’s numerical knowledge was assessed while parents completed a survey about the number-related experiences they share with their children at home, and their math-related beliefs. Parent-child dyads were then videotaped playing a modified version of the card game War. Results suggest that parents and children explored quantity explicitly on only half of the cards and card pairs played, and dyads of young children and those with lower number knowledge tended to be most explicit in their quantity exploration. Dyads with older children, on the other hand, often completed their turns without discussing the numbers at all, likely because they were knowledgeable enough about numbers that they could move through the game with ease. However, when dyads did explore the quantities explicitly, they focused on identifying numbers symbolically, used non-symbolic card information interchangeably with symbolic information to make the quantity comparison judgments, and in some instances, emphasized the connection between the symbolic and non-symbolic number representations on the cards. Parents reported that math experiences such as card game play and quantity comparison occurred relatively infrequently at home compared to activities geared towards more foundational practice of number, such as counting out loud and naming numbers. However, parental beliefs were important in predicting both the frequency of at-home math engagement as well as the quality of these experiences. In particular, parents’ specific beliefs about their children’s abilities and interests were associated with the frequency of home math activities, while parents’ math-related ability beliefs and values along with children’s engagement in the card game were associated with the quality of dyads’ number exploration during the card game. Taken together, these findings suggest that card games can be an engaging context for parent-preschooler exploration of numbers in multiple representations, and suggests that parents’ beliefs and children’s level of engagement are important predictors of this exploration.

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Bone is a dynamic, highly vascularized tissue with a unique capacity to heal and regenerate without scarring. However, drilling remains a concern in several clinical procedures due to thermal damage of the bone and surrounding tissue. The success of this surgeries is dependent of many factors and also in temperature generation during the drilling bone. When an excessive heat is produced during the drilling, thermal necrosis can occur and the bone suffers injuries. Studies have shown that the increased temperature is directly related with the drilling parameters, particularly, the drill speed, feed-rate, applied force, the depth of cut, the geometry of the drill bit, the use or not of a cooling system and also the type of bone.

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Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are “minimal” in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx ≳ 2Lz, Ly ≳ Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx ≳ 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ∼20S−1, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general.

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Photothermal imaging allows to inspect the structure of composite materials by means of nondestructive tests. The surface of a medium is heated at a number of locations. The resulting temperature field is recorded on the same surface. Thermal waves are strongly damped. Robust schemes are needed to reconstruct the structure of the medium from the decaying time dependent temperature field. The inverse problem is formulated as a weighted optimization problem with a time dependent constraint. The inclusions buried in the medium and their material constants are the design variables. We propose an approximation scheme in two steps. First, Laplace transforms are used to generate an approximate optimization problem with a small number of stationary constraints. Then, we implement a descent strategy alternating topological derivative techniques to reconstruct the geometry of inclusions with gradient methods to identify their material parameters. Numerical simulations assess the effectivity of the technique.

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Phyllotaxis patterns in plants, or the arrangement of leaves and flowers radially around the shoot, have fascinated both biologists and mathematicians for centuries. The current model of this process involves the lateral transport of the hormone auxin through the first layer of cells in the shoot apical meristem via the auxin efflux carrier protein PIN1. Locations around the meristem with high auxin concentration are sites of organ formation and differentiation. Many of the molecular players in this process are well known and characterized. Computer models composed of all these components are able to produce many of the observed phyllotaxis patterns. To understand which parts of this model have a large effect on the phenotype I automated parameter testing and tried many different parameter combinations. Results of this showed that cell size and meristem size should have the largest effect on phyllotaxis. This lead to three questions: (1) How is cell geometry regulated? (2) Does cell size affect auxin distribution? (3) Does meristem size affect phyllotaxis? To answer the first question I tracked cell divisions in live meristems and quantified the geometry of the cells and the division planes using advanced image processing techniques. The results show that cell shape is maintained by minimizing the length of the new wall and by minimizing the difference in area of the daughter cells. To answer the second question I observed auxin patterning in the meristem, shoot, leaves, and roots of Arabidopsis mutants with larger and smaller cell sizes. In the meristem and shoot, cell size plays an important role in determining the distribution of auxin. Observations of auxin in the root and leaves are less definitive. To answer the third question I measured meristem sizes and phyllotaxis patterns in mutants with altered meristem sizes. These results show that there is no correlation between meristem size and average divergence angle. But in an extreme case, making the meristem very small does lead to a switch on observed phyllotaxis in accordance with the model.

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Crosswell data set contains a range of angles limited only by the geometry of the source and receiver configuration, the separation of the boreholes and the depth to the target. However, the wide angles reflections present in crosswell imaging result in amplitude-versus-angle (AVA) features not usually observed in surface data. These features include reflections from angles that are near critical and beyond critical for many of the interfaces; some of these reflections are visible only for a small range of angles, presumably near their critical angle. High-resolution crosswell seismic surveys were conducted over a Silurian (Niagaran) reef at two fields in northern Michigan, Springdale and Coldspring. The Springdale wells extended to much greater depths than the reef, and imaging was conducted from above and from beneath the reef. Combining the results from images obtained from above with those from beneath provides additional information, by exhibiting ranges of angles that are different for the two images, especially for reflectors at shallow depths, and second, by providing additional constraints on the solutions for Zoeppritz equations. Inversion of seismic data for impedance has become a standard part of the workflow for quantitative reservoir characterization. Inversion of crosswell data using either deterministic or geostatistical methods can lead to poor results with phase change beyond the critical angle, however, the simultaneous pre-stack inversion of partial angle stacks may be best conducted with restrictions to angles less than critical. Deterministic inversion is designed to yield only a single model of elastic properties (best-fit), while the geostatistical inversion produces multiple models (realizations) of elastic properties, lithology and reservoir properties. Geostatistical inversion produces results with far more detail than deterministic inversion. The magnitude of difference in details between both types of inversion becomes increasingly pronounced for thinner reservoirs, particularly those beyond the vertical resolution of the seismic. For any interface imaged from above and from beneath, the results AVA characters must result from identical contrasts in elastic properties in the two sets of images, albeit in reverse order. An inversion approach to handle both datasets simultaneously, at pre-critical angles, is demonstrated in this work. The main exploration problem for carbonate reefs is determining the porosity distribution. Images of elastic properties, obtained from deterministic and geostatistical simultaneous inversion of a high-resolution crosswell seismic survey were used to obtain the internal structure and reservoir properties (porosity) of Niagaran Michigan reef. The images obtained are the best of any Niagaran pinnacle reef to date.

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In the presented thesis work, meshfree method with distance fields is applied to create a novel computational approach which enables inclusion of the realistic geometric models of the microstructure and liberates Finite Element Analysis(FEA) from thedependance on and limitations of meshing of fine microstructural feature such as splats and porosity.Manufacturing processes of ceramics produce materials with complex porosity microstructure.Geometry of pores, their size and location substantially affect macro scale physical properties of the material. Complex structure and geometry of the pores severely limit application of modern Finite Element Analysis methods because they require construction of spatial grids (meshes) that conform to the geometric shape of the structure. As a result, there are virtually no effective tools available for predicting overall mechanical and thermal properties of porous materials based on their microstructure. This thesis is a separate handling and controls of geometric and physical computational models that are seamlessly combined at solution run time. Using the proposedapproach we will determine the effective thermal conductivity tensor of real porous ceramic materials featuring both isotropic and anisotropic thermal properties. This work involved development and implementation of numerical algorithms, data structure, and software.

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This paper proposes a method to indicate potential problems when planning dye penetrant and x-ray inspection of welded components. Inspection has been found to be an important part of the manufacturability evaluation made in a large CAD-based parametric environment for making multidisciplinary design simulations in early stages of design at an aircraft component manufacturer. The paper explains how the proposed method is to be included in the design platform at the company. It predicts the expected probability of detection of cracks (POD) in situations where the geometry of the parts is unfavourable for inspection so that potential problems can be discovered and solved in early stages. It is based on automatically extracting information from CAD-models and making a rule-based evaluation. It also provides a scale for how favourable the geometry is for inspection. In the paper it is also shown that the manufacturability evaluation need to take into consideration the expected stresses in the structures, highlighting the importance of multi-disciplinary simulations.