A uniformidade de emissão ao longo de uma linha lateral de irrigação localizada em nível, está relacionada com a variação de pressão, ocasionada pela perda de carga durante o escoamento da água no tubo emissor e pela saída de água pelos emissores ao longo da linha lateral. Para calcular o comprimento máximo das linhas laterais, é necessário determinar de forma precisa essa variação de pressão para atender um critério pré-estabelecido de variação de vazão. O objetivo desse trabalho foi desenvolver metodologia para o cálculo da perda de carga em linhas laterais de gotejamento com emissores do tipo bóbi, para tal foram desenvolvidos dois modelos, um usando regressão linear múltipla e outro usando análise dimensional. Ambos tiveram como base equações de perdas de carga contínua no tubo e localizadas nos emissores disponíveis na literatura. As variáveis dessas equações ficaram definidas como variáveis de entrada para os modelos e foram determinadas em laboratório, usando 12 modelos de tubos emissores, com diferentes diâmetros, espaçamentos entre emissores e seções transversais médias dos emissores. Os dois modelos apresentaram ótimo ajuste aos dados observados, com coeficiente de determinação ajustado de 0,977 e 0,99 para os modelos obtidos a partir de regressão linear múltipla e a partir de análise dimensional, respectivamente. O modelo obtido a partir de análise dimensional considera a variação de diâmetro que o tubo sofre com a pressão da água. Ambos os modelos são de fácil uso. / The uniformity of emission along a lateral line of drip irrigation, is related of the pressure variation caused by head losses during the flow in dripline and the water outlet by emitters along the lateral line. To calculate the maximum length of lateral lines, we need to accurately determine the variation of pressure to meet a pre-established criterion of flow variation. The objective of this work was to develop methodology for calculating the head loss in driplines with emitters type \"bóbi\". For this we developed two models, one using multiple linear regression and one using dimensional analysis. Both were based on equations of continuos head losses in the tube and located in the emitters available in the literature. The equations of these variables were defined as input variables for the models and were determined in the laboratory, using 12 models driplines with different diameters, spacing between emitters and emitters of medium cross sections. Both models showed good fit to the data observados with a determination coefficient of 0.977 for the model obtained from multiple linear regression and to 0.99 obtained from dimensional analysis. The model obtained from the dimensional analysis considers the change in diameter than the tube suffers the water pressure. Both models are easy to use.

Compliant suspensions are often used in micromechanical devices and precision mechanisms as substitutes for kinematic joints. While their small-displacement behavior is easily captured in simple formulae, large-displacement behavior requires nonlinear finite element analysis. In this work, we present a method that helps capture the geometrically nonlinear behavior of compliant suspensions using parameterized non-dimensional maps. The maps are created by performing one nonlinear finite element analysis for any one loading condition for one instance of a suspension of a given topology and fixed proportions. These maps help retrieve behavioral information for any other instance of the same suspension with changed size, cross-section dimensions, material, and loading. Such quantities as multi-axial stiffness, maximum stress, natural frequency, etc. ,can be quickly and accurately estimated from the maps. These quantities are non-dimensionalized using suitable factors that include loading, size, cross-section, and material properties. The maps are useful in not only understanding the limits of performance of the topology of a given suspension with fixed proportions but also in design. We have created the maps for 20 different suspensions. Case studies are included to illustrate the effectiveness of the method in microsystem design as well as in precision mechanisms. In particular, the method and 2D plots of non-dimensional kinetoelastic maps provide a comprehensive view of sensitivity, cross-axis sensitivity, linearity, maximum stress, and bandwidth for microsensors and microactuators.

Orientadores: Inacio Maria Dal Fabbro, Adilson Machado Enes / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agrícola / Made available in DSpace on 2018-08-24T11:36:45Z (GMT). No. of bitstreams: 1 Fracarolli_JulianaAparecida_D.pdf: 5319280 bytes, checksum: 4488936faca98d4c091c7703b2fd0ca0 (MD5) Previous issue date: 2014 / Resumo: Técnicas ópticas vêm sendo utilizadas para diversas finalidades técnicas e científicas. Algumas técnicas ópticas se caracterizam como métodos robustos, de baixo custo, não invasivos e não destrutivos para avaliação de materiais diversos, como produtos agrícolas, havendo aplicações desde a engenharia até a área da saúde humana e animal. Neste trabalho propõem-se a avaliação de frutos através da combinação de duas técnicas ópticas cujos estudos vêm comprovando suas aplicabilidades como métodos alternativos e inovadores, os quais empregam equipamentos de baixo custo na aquisição dos dados, permitindo automação de processos de seleção e classificação de produtos. Uma dessas técnicas é conhecida como Biospeckle, a qual fornece informações referentes à qualidade do material biológico em nível de estruturas celulares e a outra é o escaneamento com linha laser, que permite a obtenção de geometria do objeto nos eixos Xi (i = 1,2,3). O objetivo é proceder a um levantamento topográfico digital de materiais biológicos combinando o posicionamento geométrico dos pontos da imagem com informações referentes à atividade biológica. Foi realizada ainda a diferenciação entre frutos de formato variado, a classificação de frutos por formato, classe, coloração e defeitos por meio de processamento de imagens. Dessa forma é possível observar frutos com irregularidades superficiais, maturidade, danos mecânicos e latentes, entre outros. Esta pode se tornar a base para a seleção automática de produtos agrícolas. Foram utilizados um emissor de linha laser de diodo com 632 nm de comprimento de onda, luz branca difusa, câmera CCD, computador, mesa óptica, mamões, peras, tomates e esferas de isopor, bem como softwares ImageJ, Octave, Matlab. Foram desenvolvidos cinco programas computacionais para processamento das imagens. Foram realizados cinco experimentos, a saber: (1) Avaliação da Maturidade de Frutos; (2) Reconstrução Tridimensional e Mapeamento da Bioatividade; (3) Detecção de Formato Variado; (4) Mapeamento por Formato, Classe e Coloração; (5) Detecção de Defeitos. Na Avaliação da Maturidade foram correlacionados índices de maturidade tradicionais (parâmetros de Hunter L a b, pH, Sólidos Solúveis Totais (SST), a relação Sólidos Solúveis Totais e Acidez Total Titulável (SST/ATT), Módulo de Elasticidade, massa e diâmetro) e a técnica óptica Biospeckle, pelo cálculo do Momento de Inércia (MI). Para a Reconstrução Tridimensional os frutos foram rotacionados através de um motor de passo. A cada passo do motor, o fruto foi iluminado pela linha laser projetada e fotografado para obtenção dos dados de geometria e Biospeckle pelo método LASCA (Laser Speckle Contrast Analysis). Foi analisada a correlação entre os índices de maturidade tradicionais e os valores de MI na avaliação da maturidade. Esta tese mostra que é possível avaliar a maturidade dos frutos através do Biospeckle. Obteve-se um mapa tridimensional que integra as informações de topografia e bioatividade do fruto. Obteve-se, ainda, a detecção de formato variado, a classificação de frutos por mapeamento por formato, classe e coloração e detecção de defeitos através de software / Abstract: Optical techniques have been used for both technical and scientific purposes. Optical techniques are usually characterized as being robust, inexpensive, non-invasive and non-destructive methods in to evaluate a diversity of materials which include agricultural derived products. It also shows applications ranging from engineering to human and animal health. In this doctoral dissertation, a new technique to evaluate some fruit properties is proposed. It combines two optical techniques (i.e. Biospeckle and Scan-line laser) whose applicability has been demonstrated as being alternative and innovative. The new proposed technique allows low-cost data acquisition, automation of the entire process, and a proper selection and classification method of vegetable bodies (e.g. fruits). Biospeckle allows obtaining information regarding the quality level of biological material into cellular structures. Scan-line laser enables the attainment of the object geometry on the axes Xi (i=1,2,3). The main purpose of this doctoral dissertation is to obtain a digital survey of biological materials (i.e. papaya, pear and tomato) integrating both geometric positioning and information concerning to its biological activity. The differentiation between different fruit shapes, fruit sorting by size, class, color and defects through image processing was also carried out. Thus it was also possible to observe fruits with surface irregularities, maturity, and mechanical damage, among others. This is the basis proposed for the automatic selection of agricultural products. The following materials were employed in the tests: a line-emitting diode laser with a wavelength of 632 nm, diffuse white light, CCD camera, computer, optical table, papaya, pear and tomato fruits and polystyrene spheres. The softwares utilized were: ImageJ, Octave, Matlab. A total of five computer programs were developed for the image processing procedures. Five experiments were performed: (1) Maturity Assessment of Fruits; (2) Three Dimensional Reconstruction and Mapping of Bioactivity; (3) Miscellaneous Format Detection; (4) Mapping Format, Class and Coloration; (5) Defect Detection. In Maturity Assessment there were correlated traditional methods to verify the maturity (the Hunter parameters L a b, pH, Total Soluble Solids (TSS), the relationship between Total Soluble Solids and Titratable Acidity (TSS/TA), Modulus of Elasticity, weight and diameter) and the optical technique Biospeckle by calculating the Moment of Inertia (MI). For the Three Dimensional Reconstruction the fruits were rotated by a stepper motor. At every step of the motor, the fruit was illuminated by the projected laser line and photographed in order to obtain both geometric and biospeckle data by the LASCA (Laser Speckle Contrast Analysis) method. The correlation between traditional methods for the maturity assessment and values of MI was analyzed. This doctoral dissertation shows that it is possible to evaluate the maturity of fruits through Biospeckle. A three-dimensional map that includes topographical information and bioactivity of the fruit was generated. Also a software can now detect variations in size, classify fruit shapes, color and class as well as defect detection efficiently. / Doutorado / Maquinas Agricolas / Doutora em Engenharia Agrícola

Reservoir releases for generating power need to be reconciled with efforts to maintain healthy ecosystems in regulated rivers having irregular channel topography. Fluctuating, complex flow patterns near river obstructions such as boulders and large woody debris provide unique habitat for many aquatic organisms. Numerical modeling of the flow structures surrounding these obstructions is challenging, yet it represents an important tool for aquatic habitat assessment. Moreover, efforts for modeling the morphologically and biologically important transient flows, as well as quantifying their impacts on physical fish habitat during the unsteady-flow period remain rare. In this dissertation, the ability of two- (2-D) and three-dimensional (3-D) hydraulic models to reproduce the localized complex flow features at steady base and peak flows is examined first. The performance of the two hydraulic models is evaluated by comparing the numerical results with measurements of flow around a laboratory hemisphere and boulders located at a reach of the Smith River in Virginia. Close agreement between measured values and the velocity profiles predicted by the two models is obtained outside the wakes behind these obstructions. However, results suggest that in the vicinity of theses obstructions the 3-D model is better suited for reproducing the circulation flow behavior favored by many aquatic species over a broad range of flows. Further, time-dependent flow features affecting channel morphology and aquatic physical habitat are investigated using the numerical models for the same reach in the Smith River. Temporal variation measurements of water surface elevation and velocity profile obtained in the field during a reservoir release are in good agreement with the numerical results. A hypothetical "staggering" flow release scenario simulated by the 3-D model leads to reduced erosional area and longer refugia availability for juvenile brown trout during hydropeaking. Finally, an unsteadiness parameter β is proposed for determining whether an unsteady flow regime can be either modeled using a truly dynamic flow approach or a quasi-steady flow method. / Ph. D.

Uppsatsen behandlar skillnader i lagstiftning om tredimensionell fastighetsbildning i Sverige och Finland. Först sker en generell beskrivning av olika sorters tredimensionell fastighetsindelning för att sedan gå över till bildandeprocessen i Sverige samt i Finland. Uppsatsen har utförts som fallstudie där en litteraturstudie gjorts genom att studera lagstiftning och propositioner i länderna. Tredimensionell fastighetsindelning infördes i Sverige 2004. Då infördes även specifik lagstiftning kring bildandeprocessen av tredimensionella fastigheter. Denna lagstiftning går att finna i 3 kap. fastighetsbildningslag (1970:998). Alla typer av fastigheter ska, enligt 3 kap 1 § bildas så att de är varaktigt lämpade för sitt ändamål, har en lämplig utformning, tillgång till vägar samt att det finns godtagbara anordningar för vatten och avlopp om fastigheten är avsedd för bebyggelse. Fastighetsbildning får endast ske om fastigheten kan anses ha varaktig användning för ändamålet inom överskådlig tid och om ändamålet inte kan tillgodoses på något annat sätt än fastighetsbildning. Specifikt för tredimensionella fastigheter gäller även att den åtgärden ska anses lämpligare än andra åtgärder för att tillgodose ändamålet. Krav på tredimensionell fastighetsbildning beskrivs vidare i 3 kap. 1 a § FBL. I Sverige finns också möjlighet att bilda tredimensionella fastigheter avsedda för bostadsändamål, så kallade ägarlägenheter. Dessa kan endast bildas i ny bebyggelse eller fastigheter som inte varit bostäder de senaste åtta åren samt endast bildas i enheter om minst tre lägenheter. Finland införde tredimensionell fastighetsbildning 2018. I Finland finns krav på att tredimensionell fastighetsbildning endast får ske inom detaljplanelagt område samt med en bindande tomtindelning. Tredimensionell fastighetsbildning sker i Finland främst genom avstyckning. I båda länderna krävs en fastighetsförrättning för att få bilda fastigheter av alla slag. Ägarlägenhetsfastigheter har inte införts som ett alternativ i Finland. Den största skillnaden mellan lagstiftningen om tredimensionella fastigheter i Sverige och Finland är möjligheten att bilda tredimensionella fastigheter inom detaljplaneområde. Finland har inte heller någon lagstiftning gällande ägarlägenheter. / The thesis discusses differences in legislation about three-dimensional property in Sweden and Finland. The structure of the thesis follows a more general description of different types of three-dimensional property rights to in the next chapter be narrowed down to three-dimensional property formation in Sweden and Finland. The thesis has been written by studying Swedish and Finnish legislation and propositions and by studying literature on the subject. Sweden introduced independent three-dimensional property in 2004 and with it came new legislation that can be found in the third chapter of the Real Property Formation Act (1970:998). According to the legislation, all property, two- and three-dimensional, should be formed so that their purpose is long-lasting, has an appropriate shape, access to road and has proper sewage and water systems if the property is to be settlements. Property formation can only happen if the purpose of the formation cannot be fulfilled any other way. For three-dimensional property there is, as mentioned, specific regulations. For a three-dimensional property to be formed the measure needs to be the most appropriate to fulfil the purpose. Other legislation is further described in the third chapter 1 a § FBL. Sweden also has special legislation regarding condominiums, they can only be formed in pairs of three and only in buildings that has not been used for living purposes the last eight years. Finland introduced independent three-dimensional property in 2018 which also brought new legislation. In Finland is it only possible to form independent three-dimensional property within a detailed development plan and with a binding site layout plan. The formation of three-dimensional property is often done with subdivision. Finland has not passed legislation regarding condominiums. In both countries one must carry out a property formation procedure that looks very much alike in both countries. The biggest difference between the legislation regarding forming three-dimensional property of Finland and Sweden is the possibility to form three-dimensional property within an area with a detailed development plan. Another big difference is that Sweden has condominiums and Finland do not. Despite some differences in the legislation both countries end up with the same results, forming independent three-dimensional property.

Nowadays due to large demand for clean and defect-free steels, several techniques based on different characteristics of particles are applied to investigate the steel cleanness. Outokumpu Stainless AB in Avesta has performed extensive work in this field by applying several methods, which all of them have specific advantages and limitations. However, it is necessary to find an accurate technique to investigate real properties of inclusions in duplex stainless steels. For routine analytical methods, calibration and parameters adjustment can be followed by help of these investigation results. The aim of present work is to apply automated INCA-Feature method for controlling cleanness of LDX 6112 duplex stainless steels after electrolytic extractions (EE) as a reference method. Three methods of investigations, INCA-Feature on polished samples as two-dimensional and on film-filter as three-dimensional and EE as three-dimensional analyses, were compared. The results of comparison between running INCA-Feature on polished samples and film filters show an acceptable agreement which proves the possibility of performing EE on this steel grade and using INCA-Feature for investigating this as a fast method. These methods are compared statistically and quantitative results are reported in details.

Developing nonparametric statistical methods and inference procedures for high-dimensional large data have been a challenging frontier problem of statistics. To attack this problem, in recent years, a clear rising trend has been observed with a radically different viewpoint--``Graph-based Nonparametrics," which is the main research focus of this dissertation. The basic idea consists of two steps: (i) representation step: code the given data using graphs, (ii) analysis step: apply statistical methods on the graph-transformed problem to systematically tackle various types of data structures. Under this general framework, this dissertation develops two major research directions. Chapter 2—based on Mukhopadhyay and Wang (2019a)—introduces a new nonparametric method for high-dimensional k-sample comparison problem that is distribution-free, robust, and continues to work even when the dimension of the data is larger than the sample size. The proposed theory is based on modern LP-nonparametrics tools and unexplored connections with spectral graph theory. The key is to construct a specially-designed weighted graph from the data and to reformulate the k-sample problem into a community detection problem. The procedure is shown to possess various desirable properties along with a characteristic exploratory flavor that has practical consequences. The numerical examples show surprisingly well performance of our method under a broad range of realistic situations. Chapter 3—based on Mukhopadhyay and Wang (2019b)—revisits some foundational questions about network modeling that are still unsolved. In particular, we present unified statistical theory of the fundamental spectral graph methods (e.g., Laplacian, Modularity, Diffusion map, regularized Laplacian, Google PageRank model), which are often viewed as spectral heuristic-based empirical mystery facts. Despite half a century of research, this question has been one of the most formidable open issues, if not the core problem in modern network science. Our approach integrates modern nonparametric statistics, mathematical approximation theory (of integral equations), and computational harmonic analysis in a novel way to develop a theory that unifies and generalizes the existing paradigm. From a practical standpoint, it is shown that this perspective can provide adequate guidance for designing next-generation computational tools for large-scale problems. As an example, we have described the high-dimensional change-point detection problem. Chapter 4 discusses some further extensions and application of our methodologies to regularized spectral clustering and spatial graph regression problems. The dissertation concludes with the a discussion of two important areas of future studies. / Statistics

Molecules adsorbed on two-dimensional (2D) materials can show interesting physical and chemical properties. This thesis presents scanning probe microscopy (SPM) investigation of emerging 2D materials, molecular nanostructures on 2D substrates at the nanometer scale, and biophysical processes on the biological membrane. Two main techniques of nano-probing are used: scanning tunneling microscopy (STM) and atomic force microscopy (AFM). The study particularly emphasizes on self-assembled molecules on flat 2D materials and quasi-1D wrinkles. First, we report the preparation of novel 1D C60 nanostructures on rippled graphene. Through careful control of the subtle balance between the linear periodic potential of rippled graphene and the C60 surface mobility, we demonstrate that C60 molecules can be arranged into a 1D C60 chain structure of two to three molecules in width. At a higher annealing temperature, the 1D chain structure transitions to a more closely packed, quasi-1D hexagonal stripe structure. The experimental realization of 1D C60 structures on graphene is, to our knowledge, the first in the field. It could pave the way for fabricating new C60/graphene hybrid structures for future applications in electronics, spintronic and quantum information. Second, we report a study on nano-morphology of potential operative donors (e.g., C60) and acceptors (e.g., perylenetetracarboxylic dianhydride, aka. PTCDA) on wrinkled graphene supported by copper foils. We realize sub-monolayer C60 and PTCDA on quasi-1D and quasi-2D real periodic wrinkled graphene, by carefully controlling the deposition parameters of both molecules. Our successful realization of acceptor-donor binary nanostructures on wrinkled graphene could have important implications in future development of organic solar cells. Third, we report an STM and spectroscopy study on atomically thin transition-metal dichalcogenides (TMDCs) material. TMDCs are emerging 2D materials recently due to their intriguing physical properties and potential applications. In particular, our study focuses on molybdenum disulfide (MoS2) mono- to few-layers and pyramid nanostructures synthesized through chemical vapor deposition. On the few-layered MoS2 nanoplatelets grown on gallium nitride (GaN) and pyramid nanostructures on highly oriented pyrolytic graphite (HOPG), we observe an intriguing curved region near the edge terminals. The measured band gap in these curved regions is consistent with the direct band gap in MoS2 monolayers. The curved features near the edge terminals and the associated electronic properties may contribute to understanding catalytic behaviors of MoS2 nanostructures and have potential applications in future electronic devices and catalysts based on MoS2 nanostructures. Finally, we report a liquid-cell AFM study on the endosomal protein sorting process on the biological lipid membrane. The sorting mechanism relies on complex forming between Tom1 and the cargo sorting protein, Toll interacting protein (Tollip). The induced conformational change in Tollip triggers its dissociation from the lipid membrane and commitment to cargo trafficking. This collaborative study aims at characterizing the dynamic interaction between Tollip and the lipid membrane. To study this process we develop the liquid mode of AFM. We successfully demonstrate that Tollip is localized to the lipid membrane via association with PtdIns3P (PI(3)P), a major phospholipid in the cell membrane involved in protein trafficking. / Ph. D. / Two-dimensional (2D) materials are layered materials with thickness of single atom or few atoms. The ultimate thickness leads to novel properties that are useful for a wide range of applications in photovoltaics, electronics and quantum information. In order to explore these properties at the nanometer scale, we used scanning probe techniques, i.e., scanning tunneling microscopy (STM) and atomic force microscopy (AFM), to perform comprehensive investigations on these emerging materials. 2D materials, such as graphene and atomically thin transition-metal dichalcogenides (TMDCs), are promising candidates for building economic, safe and mechanically flexible solar cells with desirable optical and electronic properties, e.g. tunable sunlight absorption. The first part of the thesis focuses on graphene, a single-atom-thick carbon sheet. We deposited key components in organic solar cells, such as perylenetetracarboxylic dianhydride (PTCDA) and C₆₀ molecules, on graphene. On these materials we observed various novel nanostructures, like quasi-1D C₆₀ nanochains. The second part of the thesis focuses on mono- to few-layered MoS₂, which can be used as an active layer in high-efficiency solar cells. Our study has important implications in improving efficiency of organic solar cells in the future. In the final part of the thesis, we extended our subject to the biological lipid membrane, a 2D material critical in biology, and biophysical processes occurring on the membrane. Using a liquid-cell AFM, we investigated the endosomal protein sorting process on the biological membranes. Our study contributes to understanding of the interactions between the adaptor proteins and cell membranes in the protein sorting process that guides proteins to their proper destinations.

This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems. Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry. In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique. Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally. In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states. The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.

A avaliação volumétrica da face é uma medida dimensional importante na avaliação pré-operatória, no planejamento e acompanhamento pós-operatório. Os sistemas de imagem tridimensional (3D) têm sido considerados uma ótima alternativa na mensuração linear, angular e volumétrica da face em comparação com as imagens bidimensionais (2D). Especificamente na área de atuação da Cirurgia Crânio-Maxilo-Facial, o uso da imagem em 3D na avaliação das malformações congênitas, sequelas de traumas, sequelas tumorais, planejamento de cirurgias ortognáticas, simulação de mudanças volumétricas, assimetrias faciais e outros, pode tornar o tratamento mais objetivo, rápido e potencializar os resultados. O objetivo deste projeto foi a avaliação da acurácia do cálculo volumétrico das partes moles da face a partir de malhas 3D de superfície, estudo em cadáver. Foram avaliados 09 cadáveres oriundos do Sistema de Verificação de Óbito da Capital - Universidade de São Paulo (SVO-USP). Foi incluído um expansor tecidual na região do terço médio de cada hemiface, que foi expandido progressivamente e, por meio de captação seriada de imagens tridimensionais da face com escâner de luz estruturada, foram obtidas malhas de superfície 3D a cada momento de expansão. As malhas 3D foram avaliadas quanto a variação volumétrica da região de inclusão do expansor com o uso de um software livre. O cálculo amostral supôs que as correlações encontradas apresentariam valores acima de 0,80. Para testes com poder de 80% e nível de significância de 5% seriam necessários, então, 18 hemifaces no estudo. Uma forte correlação foi observada entre todas as medições. Os gráficos de correlação linear evidenciaram um aumento linear positivo uniforme para os diferentes volumes virtuais avaliados em todas as 18 hemifaces estudadas. Todas as hemifaces não expandidas tiveram um delta significativamente menor em seções externas do cubo virtual medidas em comparação com seções externas do cubo virtual dos lados da face com expansor (P = 0,008). O grau excelente de correlação entre o volume expandido e o volume aferido virtualmente, evidenciou que obtenção de 144 malhas 3D (9 faces, 18 hemifaces, cada uma utilizada 2 vezes, uma com expansor e outra sem, totalizando 36 hemifaces estudadas com 4 malhas 3D para cada) foi uma amostra adequada para o estudo. O protocolo apresentado para o cálculo volumétrico da face com o processamento de imagem 3D assistido por computador e com a utilização de software livre em um estudo em cadáver, demonstrou versatilidade e acessibilidade, tendo sido comprovada a sua acurácia / The face volumetric evaluation is an important dimensional measure in the preoperative evaluation in planning and postoperative follow-up. 3D imaging systems have been considered a good alternative in linear and angular measurement of face compared to 2D images. Specifically, in Cranio-Maxillofacial Surgery area, the 3D imaging use in the evaluation of congenital malformations, trauma sequelae, tumor sequelae, orthognathic surgery planning, volumetric changes simulation, facial imbalances and others could turn the treatment more objective, faster and potentiate the results. This project objective was calculation volumetric accuracy evaluation of the soft face parts from 3D surface meshes cadaver study. We evaluated 9 cadavers from the Sistema de Verificação de Óbito da Capital - Universidade de São Paulo (SVO-USP). A tissue expander was included in each middle third hemiface region which was progressively expanded and by means of serial three-dimensional face images acquisition with light scanners surface 3D meshes structured were obtained at expansion each moment. The 3D meshes were evaluated for the expander inclusion region volumetric variation with free software use. The sample calculation assumed that the correlations found would have values above 0.80. Eighteen hemifaces would be necessary in the study for tests with a power of 80% and a level of significance of 5%. A strong correlation was observed between all measurements. The linear correlation graphs showed a positive consistent linear increase for different virtual volumes evaluated in all 18 hemifaces studied. All unexpanded hemifaces had a significantly lower delta in outer virtual cube measured sections compared to virtual cube on face sides with expander (P = 0.008) external sections. The excellent degree of correlation between the expanded volume and the virtually verified volume showed that obtaining 144 3D meshes (9 faces, 18 hemifaces, each one used 2 times, one with expander and one without, totaling 36 hemifaces studied with 4 3D meshes for each) was an adequate sample for the study. The protocol presented for face volumetric calculation with computer assisted 3D image processing and the free software use in a cadaver study demonstrated versatility and accessibility and its accuracy was proven