Hierarchical boundary elements

In this paper we show the possibility of applying adaptive procedures as an alternative to the well-known philosophy of standard Boundary Elements. The three characteristic steps of adaptive procedures, i.e. hierarchical shape functions families, indicator criteria, and a posteriori estimation, can be defined in order to govern an automatic refinement and stopping of the solution process. A computer program to treat potential problems, called QUEIMADA, has been developed to show the capabilities of the new idea.

A contribution to the optimal numbering of tree structures

This paper develops an automatic procedure for the optimal numbering of members and nodes in tree structures. With it the stiffness matrix is optimally conditioned either if a direct solution algorithm or a frontal one is used to solve the system of equations. In spite of its effectiveness, the procedure is strikingly simple and so is the computer program shown below.

Global research alliance modelling platform (GRAMP): an open web platform for modelling greenhouse gas emissions from agro-ecosystems

Carbon (C) and nitrogen (N) process-based models are important tools for estimating and reporting greenhouse gas emissions and changes in soil C stocks. There is a need for continuous evaluation, development and adaptation of these models to improve scientific understanding, national inventories and assessment of mitigation options across the world. To date, much of the information needed to describe different processes like transpiration, photosynthesis, plant growth and maintenance, above and below ground carbon dynamics, decomposition and nitrogen mineralization. In ecosystem models remains inaccessible to the wider community, being stored within model computer source code, or held internally by modelling teams. Here we describe the Global Research Alliance Modelling Platform (GRAMP), a web-based modelling platform to link researchers with appropriate datasets, models and training material. It will provide access to model source code and an interactive platform for researchers to form a consensus on existing methods, and to synthesize new ideas, which will help to advance progress in this area. The platform will eventually support a variety of models, but to trial the platform and test the architecture and functionality, it was piloted with variants of the DNDC model. The intention is to form a worldwide collaborative network (a virtual laboratory) via an interactive website with access to models and best practice guidelines; appropriate datasets for testing, calibrating and evaluating models; on-line tutorials and links to modelling and data provider research groups, and their associated publications. A graphical user interface has been designed to view the model development tree and access all of the above functions.

Análisis del comportamiento de uniones metálicas viga-soporte mediante modelo de elementos finitos y comparación de resultados con el modelo de nudos y barras

Para el proyecto y cálculo de estructuras metálicas, fundamentalmente pórticos y celosías de cubierta, la herramienta más comúnmente utilizada son los programas informáticos de nudos y barras. En estos programas se define la geometría y sección de las barras, cuyas características mecánicas son perfectamente conocidas, y sobre las cuales obtenemos unos resultados de cálculo concretos en cuanto a estados tensionales y de deformación. Sin embargo el otro componente del modelo, los nudos, presenta mucha mayor complejidad a la hora de establecer sus propiedades mecánicas, fundamentalmente su rigidez al giro, así como de obtener unos resultados de estados tensionales y de deformación en los mismos. Esta “ignorancia” sobre el comportamiento real de los nudos, se salva generalmente asimilando a los nudos del modelo la condición de rígidos o articulados. Si bien los programas de cálculo ofrecen la posibilidad de introducir nudos con una rigidez intermedia (nudos semirrígidos), la rigidez de cada nudo dependerá de la geometría real de la unión, lo cual, dada la gran variedad de geometrías de uniones que en cualquier proyecto se nos presentan, hace prácticamente inviable introducir los coeficientes correspondientes a cada nudo en los modelos de nudos y barras. Tanto el Eurocódigo como el CTE, establecen que cada unión tendrá asociada una curva momento-rotación característica, que deberá ser determinada por los proyectistas mediante herramientas de cálculo o procedimientos experimentales. No obstante, este es un planteamiento difícil de llevar a cabo para cada proyecto. La consecuencia de esto es, que en la práctica, se realizan extensas comprobaciones y justificaciones de cálculo para las barras de las estructuras, dejando en manos de la práctica común la solución y puesta en obra de las uniones, quedando sin justificar ni comprobar la seguridad y el comportamiento real de estas. Otro aspecto que conlleva la falta de caracterización de las uniones, es que desconocemos como afecta el comportamiento real de éstas en los estados tensionales y de deformación de las barras que acometen a ellas, dudas que con frecuencia nos asaltan, no sólo en la fase de proyecto, sino también a la hora de resolver los problemas de ejecución que inevitablemente se nos presentan en el desarrollo de las obras. El cálculo mediante el método de los elementos finitos, es una herramienta que nos permite introducir la geometría real de perfiles y uniones, y nos permite por tanto abordar el comportamiento real de las uniones, y que está condicionado por su geometría. Por ejemplo, un caso típico es el de la unión de una viga a una placa o a un soporte soldando sólo el alma. Es habitual asimilar esta unión a una articulación. Sin embargo, el modelo por elementos finitos nos ofrece su comportamiento real, que es intermedio entre articulado y empotrado, ya que se transmite un momento y el giro es menor que el del apoyo simple. No obstante, la aplicación del modelo de elementos finitos, introduciendo la geometría de todos los elementos estructurales de un entramado metálico, tampoco resulta en general viable desde un punto de vista práctico, dado que requiere invertir mucho tiempo en comparación con el aumento de precisión que obtenemos respecto a los programas de nudos y barras, mucho más rápidos en la fase de modelización de la estructura. En esta tesis se ha abordado, mediante la modelización por elementos finitos, la resolución de una serie de casos tipo representativos de las uniones más comúnmente ejecutadas en obras de edificación, como son las uniones viga-pilar, estableciendo el comportamiento de estas uniones en función de las variables que comúnmente se presentan, y que son: •Ejecución de uniones viga-pilar soldando solo por el alma (unión por el alma), o bien soldando la viga al pilar por todo su perímetro (unión total). •Disposición o no de rigidizadores en los pilares •Uso de pilares de sección 2UPN en cajón o de tipo HEB, que son los tipos de soporte utilizados en casi el 100% de los casos en edificación. Para establecer la influencia de estas variables en el comportamiento de las uniones, y su repercusión en las vigas, se ha realizado un análisis comparativo entre las variables de resultado de los casos estudiados:•Estados tensionales en vigas y uniones. •Momentos en extremo de vigas •Giros totales y relativos en nudos. •Flechas. Otro de los aspectos que nos permite analizar la casuística planteada, es la valoración, desde un punto de vista de costos de ejecución, de la realización de uniones por todo el perímetro frente a las uniones por el alma, o de la disposición o no de rigidizadores en las uniones por todo el perímetro. Los resultados a este respecto, son estrictamente desde un punto de vista económico, sin perjuicio de que la seguridad o las preferencias de los proyectistas aconsejen una solución determinada. Finalmente, un tercer aspecto que nos ha permitido abordar el estudio planteado, es la comparación de resultados que se obtienen por el método de los elementos finitos, más próximos a la realidad, ya que se tiene en cuenta los giros relativos en las uniones, frente a los resultados obtenidos con programas de nudos y barras. De esta forma, podemos seguir usando el modelo de nudos y barras, más versátil y rápido, pero conociendo cuáles son sus limitaciones, y en qué aspectos y en qué medida, debemos ponderar sus resultados. En el último apartado de la tesis se apuntan una serie de temas sobre los que sería interesante profundizar en posteriores estudios, mediante modelos de elementos finitos, con el objeto de conocer mejor el comportamiento de las uniones estructurales metálicas, en aspectos que no se pueden abordar con los programas de nudos y barras. For the project and calculation of steel structures, mainly building frames and cover lattices, the tool more commonly used are the node and bars model computer programs. In these programs we define the geometry and section of the bars, whose mechanical characteristics are perfectly known, and from which we obtain the all calculation results of stresses and displacements. Nevertheless, the other component of the model, the nodes, are much more difficulty for establishing their mechanical properties, mainly the rotation fixity coefficients, as well as the stresses and displacements. This "ignorance" about the real performance of the nodes, is commonly saved by assimilating to them the condition of fixed or articulated. Though the calculation programs offer the possibility to introducing nodes with an intermediate fixity (half-fixed nodes), the fixity of every node will depend on the real connection’s geometry, which, given the great variety of connections geometries that in a project exist, makes practically unviable to introduce the coefficients corresponding to every node in the models of nodes and bars. Both Eurocode and the CTE, establish that every connection will have a typical moment-rotation associated curve, which will have to be determined for the designers by calculation tools or experimental procedures. Nevertheless, this one is an exposition difficult to carry out for each project. The consequence of this, is that in the practice, in projects are extensive checking and calculation reports about the bars of the structures, trusting in hands of the common practice the solution and execution of the connections, resulting without justification and verification their safety and their real behaviour. Another aspect that carries the lack of the connections characterization, is that we don´t know how affects the connections real behaviour in the stresses and displacements of the bars that attack them, doubts that often assault us, not only in the project phase, but also at the moment of solving the execution problems that inevitably happen in the development of the construction works. The calculation by finite element model is a tool that allows us to introduce the real profiles and connections geometry, and allows us to know about the real behaviour of the connections, which is determined by their geometry. Typical example is a beam-plate or beam-support connection welding only by the web. It is usual to assimilate this connection to an articulation or simple support. Nevertheless, the finite element model determines its real performance, which is between articulated and fixed, since a moment is transmitted and the relative rotation is less than the articulation’s rotation. Nevertheless, the application of the finite element model, introducing the geometry of all the structural elements of a metallic structure, does not also turn out to be viable from a practical point of view, provided that it needs to invest a lot of time in comparison with the precision increase that we obtain opposite the node and bars programs, which are much more faster in the structure modelling phase. In this thesis it has been approached, by finite element modelling, the resolution of a representative type cases of the connections commonly used in works of building, since are the beam-support connections, establishing the performance of these connections depending on the variables that commonly are present, which are: •Execution of beam-support connections welding only the web, or welding the beam to the support for the whole perimeter. •Disposition of stiffeners in the supports •Use 2UPN in box section or HEB section, which are the support types used in almost 100% building cases. To establish the influence of these variables in the connections performance, and the repercussion in the beams, a comparative analyse has been made with the resulting variables of the studied cases: •Stresses states in beams and connections. •Bending moments in beam ends. •Total and relative rotations in nodes. •Deflections in beams. Another aspect that the study allows us to analyze, is the valuation, from a costs point of view, of the execution of connections for the whole perimeter opposite to the web connections, or the execution of stiffeners. The results of this analyse, are strictly from an economic point of view, without prejudice that the safety or the preferences of the designers advise a certain solution. Finally, the third aspect that the study has allowed us to approach, is the comparison of the results that are obtained by the finite element model, nearer to the real behaviour, since the relative rotations in the connections are known, opposite to the results obtained with nodes and bars programs. So that, we can use the nodes and bars models, more versatile and quick, but knowing which are its limitations, and in which aspects and measures, we must weight the results. In the last part of the tesis, are relationated some of the topics on which it would be interesting to approach in later studies, with finite elements models, in order to know better the behaviour of the structural steel connections, in aspects that cannot be approached by the nodes and bars programs.

Dynamic analysis of translational shells

In this paper a dynamic analysis of transnational shells is presented. The general linear shell theory is used in conjunction with additional shallow and curved plate approximations. In order to apply some type of extended Levy solution, the shell is assumed to be limited by a rectangular plan form, with two opposite edges simply supported (gable boundary conditions). First, the shells free vibrations are studied in the usual way, obtaining for each Fourier term the natural frequencies as solutions of a transcendental equation. However, solving these equations arises enormous computational difficulties. This paper deals specifically with this problem, trying to reduce its dimension by a discretization procedure. In the shell dynamic characteristics, namely the mass. The shell mass is lumped along a family of coordinate lines. Therefore, the natural frequencies for each harmonic term can be found from the solution of a typical matrix eigenvalues problem and standard numerical techniques can be applied. The shell response to forced vibrations, particularly to earthquake excitation, can be determined by using conventional procedure either in the time or in the frequency domain. Finally, extending the above procedure, any system of translational shells under dynamic loading can be studied. Then, by using matrix methods, a general computer program is written and applied to some illustrative examples. Numerical results has been obtained in two cases: circular cylindrical shell and box girder bridge.

Certificación energética mediante la herramienta CE3X y rehabilitación energética de una vivienda unifamiliar

El siguiente proyecto lleva a cabo un estudio sobre la eficiencia energética en una vivienda unifamiliar basándose en la legislación actual europea y española. Para empezar se obtendrá la calificación energética del inmueble mediante el programa informático de la opción simplificada CE3X. A continuación se proporcionará un estudio con las medidas de mejora más adecuadas para mejorar la eficiencia energética de la vivienda, las medidas que se llevarán a cabo serán: la mejora de la envolvente térmica, mejorando el aislamiento de la fachada y la sustitución de ventanas, la instalación de una caldera de biomasa y la instalación de un sistema de colectores solares para cubrir la demanda de calefacción y ACS. Para finalizar se realiza un presupuesto de las medidas de mejoras propuestas, así como un análisis económico y una planificación y programación temporal. ABSTRACT The object of this Project is to carry out a study on the energy efficiency of a single family home in accordance with the present European and Spanish legislation. The first step is to obtain the home energy efficiency by means of a CE3X computer program. The second step is a study with the most appropriate improvement measures is provided in order to improve the home energy efficiency. The measures to be carried out will be as follows: improving the heat insulation, as well as, the facade heat insulation and replacing the windows, installing a biomass heating system and a solar collector in order to satisfy the heating and domestic hot water (DHW) demands. Finally a budget with the proposed improvement measures is made as well as a financial analysis and a time planning and programming of the project.

DETERMINAÇÃO DAS FORMAS DO ARCO DENTÁRIO INFERIOR NA OCLUSÃO NORMAL NATURAL

Com a finalidade de determinar as formas do arco dentário inferior de maior incidência na oclusão normal natural, utilizou-se um método matemático associado ao emprego de uma função polinomial, o qual foi aplicado a 63 modelos de arcadas inferiores selecionados a partir de 6118 adolescentes. Todos os indivíduos eram portadores de dentição permanente, incluindo os segundos molares, e oclusão normal natural. Em cada dente foi fixada uma esfera de vidro, que teve a função de simular o acessório do aparelho ortodôntico, sendo utilizada na medição das distâncias entre o centro da imagem dessas esferas aos eixos x e y. Após a digitalização dos modelos de gesso, as imagens foram plotadas em um programa de computador, a fim de se obterem a função polinomial de sexto grau e o gráfico dessa função para os 126 segmentos de curva, originados das secções das imagens em lado direito e esquerdo. A seguir organizaram-se esses segmentos, de acordo com as características da curvatura anterior dos arcos dentários, em oito grupos diferentes de formas, que receberam as denominações de Forma A, Forma B, Forma C, Forma D, Forma E, Forma F, Forma G, Forma H. Cada grupo foi, então, dividido em três subgrupos, conforme os tamanhos pequeno, médio e grande. Os resultados indicaram 23 formas representativas do arco dentário inferior e uma forma média para a oclusão normal natural.

DETERMINAÇÃO DAS FORMAS DO ARCO DENTÁRIO INFERIOR NA OCLUSÃO NORMAL NATURAL

Com a finalidade de determinar as formas do arco dentário inferior de maior incidência na oclusão normal natural, utilizou-se um método matemático associado ao emprego de uma função polinomial, o qual foi aplicado a 63 modelos de arcadas inferiores selecionados a partir de 6118 adolescentes. Todos os indivíduos eram portadores de dentição permanente, incluindo os segundos molares, e oclusão normal natural. Em cada dente foi fixada uma esfera de vidro, que teve a função de simular o acessório do aparelho ortodôntico, sendo utilizada na medição das distâncias entre o centro da imagem dessas esferas aos eixos x e y. Após a digitalização dos modelos de gesso, as imagens foram plotadas em um programa de computador, a fim de se obterem a função polinomial de sexto grau e o gráfico dessa função para os 126 segmentos de curva, originados das secções das imagens em lado direito e esquerdo. A seguir organizaram-se esses segmentos, de acordo com as características da curvatura anterior dos arcos dentários, em oito grupos diferentes de formas, que receberam as denominações de Forma A, Forma B, Forma C, Forma D, Forma E, Forma F, Forma G, Forma H. Cada grupo foi, então, dividido em três subgrupos, conforme os tamanhos pequeno, médio e grande. Os resultados indicaram 23 formas representativas do arco dentário inferior e uma forma média para a oclusão normal natural.

AVALIAÇÃO DAS ALTERAÇÕES DO SORRISO EM INDIVÍDUOS SUBMETIDOS À EXPANSÃO RÁPIDA DA MAXILA

O objetivo deste estudo foi avaliar as possíveis alterações das características horizontais, verticais, de simetria e do arco do sorriso de pacientes com atresia maxilar submetidos à expansão rápida da maxila. A amostra consistiu de 81 fotografias extra-bucais do sorriso máximo de 27 pacientes com idade média de 10 anos e 3 meses. Foram realizadas fotografias do sorriso máximo nos períodos: inicial (antes da instalação do aparelho expansor); 3 meses após a fixação do parafuso expansor; 6 meses após a fixação do parafuso expansor. Para a calibragem e análise das fotografias foi utilizado o programa CEFX 2001 CDT. Os pontos fotométricos e as medidas a serem analisadas foram escolhidos após revisão da literatura do sorriso realizada. Para avaliar as alterações no sorriso durante as fases, foi utilizada a análise de variância ANOVA, com nível de significância de 5%. A expansão rápida da maxila promoveu aumento estatisticamente significante da dimensão transversal do sorriso; aumento da quantidade de exposição dos incisivos centrais e laterais superiores; manutenção da simetria entre os lados direito e esquerdo e da falta de paralelismo entre a curvatura das bordas dos incisivos superiores com a curvatura do lábio inferior (arco do sorriso).(AU)

AVALIAÇÃO DAS ALTERAÇÕES DO SORRISO EM INDIVÍDUOS SUBMETIDOS À EXPANSÃO RÁPIDA DA MAXILA

O objetivo deste estudo foi avaliar as possíveis alterações das características horizontais, verticais, de simetria e do arco do sorriso de pacientes com atresia maxilar submetidos à expansão rápida da maxila. A amostra consistiu de 81 fotografias extra-bucais do sorriso máximo de 27 pacientes com idade média de 10 anos e 3 meses. Foram realizadas fotografias do sorriso máximo nos períodos: inicial (antes da instalação do aparelho expansor); 3 meses após a fixação do parafuso expansor; 6 meses após a fixação do parafuso expansor. Para a calibragem e análise das fotografias foi utilizado o programa CEFX 2001 CDT. Os pontos fotométricos e as medidas a serem analisadas foram escolhidos após revisão da literatura do sorriso realizada. Para avaliar as alterações no sorriso durante as fases, foi utilizada a análise de variância ANOVA, com nível de significância de 5%. A expansão rápida da maxila promoveu aumento estatisticamente significante da dimensão transversal do sorriso; aumento da quantidade de exposição dos incisivos centrais e laterais superiores; manutenção da simetria entre os lados direito e esquerdo e da falta de paralelismo entre a curvatura das bordas dos incisivos superiores com a curvatura do lábio inferior (arco do sorriso).(AU)

Selection of Gβ Subunits with Point Mutations That Fail to Activate Specific Signaling Pathways In Vivo: Dissecting Cellular Responses Mediated by a Heterotrimeric G Protein in Dictyostelium discoideum

In Dictyostelium discoideum, a unique Gβ subunit is required for a G protein–coupled receptor system that mediates a variety of cellular responses. Binding of cAMP to cAR1, the receptor linked to the G protein G2, triggers a cascade of responses, including activation of adenylyl cyclase, gene induction, actin polymerization, and chemotaxis. Null mutations of the cAR1, Gα2, and Gβ genes completely impair all these responses. To dissect specificity in Gβγ signaling to downstream effectors in living cells, we screened a randomly mutagenized library of Gβ genes and isolated Gβ alleles that lacked the capacity to activate some effectors but retained the ability to regulate others. These mutant Gβ subunits were able to link cAR1 to G2, to support gene expression, and to mediate cAMP-induced actin polymerization, and some were able to mediate to chemotaxis toward cAMP. None was able to activate adenylyl cyclase, and some did not support chemotaxis. Thus, we separated in vivo functions of Gβγ by making point mutations on Gβ. Using the structure of the heterotrimeric G protein displayed in the computer program CHAIN, we examined the positions and the molecular interactions of the amino acids substituted in each of the mutant Gβs and analyzed the possible effects of each replacement. We identified several residues that are crucial for activation of the adenylyl cyclase. These residues formed an area that overlaps but is not identical to regions where bovine Gtβγ interacts with its regulators, Gα and phosducin.

Intron positions correlate with module boundaries in ancient proteins

We analyze the three-dimensional structure of proteins by a computer program that finds regions of sequence that contain module boundaries, defining a module as a segment of polypeptide chain bounded in space by a specific given distance. The program defines a set of “linker regions” that have the property that if an intron were to be placed into each linker region, the protein would be dissected into a set of modules all less than the specified diameter. We test a set of 32 proteins, all of ancient origin, and a corresponding set of 570 intron positions, to ask if there is a statistically significant excess of intron positions within the linker regions. For 28-Å modules, a standard size used historically, we find such an excess, with P < 0.003. This correlation is neither due to a compositional or sequence bias in the linker regions nor to a surface bias in intron positions. Furthermore, a subset of 20 introns, which can be putatively identified as old, lies even more explicitly within the linker regions, with P < 0.0003. Thus, there is a strong correlation between intron positions and three-dimensional structural elements of ancient proteins as expected by the introns-early approach. We then study a range of module diameters and show that, as the diameter varies, significant peaks of correlation appear for module diameters centered at 21.7, 27.6, and 32.9 Å. These preferred module diameters roughly correspond to predicted exon sizes of 15, 22, and 30 residues. Thus, there are significant correlations between introns, modules, and a quantized pattern of the lengths of polypeptide chains, which is the prediction of the “Exon Theory of Genes.”

GenEST, a powerful bidirectional link between cDNA sequence data and gene expression profiles generated by cDNA-AFLP

The release of vast quantities of DNA sequence data by large-scale genome and expressed sequence tag (EST) projects underlines the necessity for the development of efficient and inexpensive ways to link sequence databases with temporal and spatial expression profiles. Here we demonstrate the power of linking cDNA sequence data (including EST sequences) with transcript profiles revealed by cDNA-AFLP, a highly reproducible differential display method based on restriction enzyme digests and selective amplification under high stringency conditions. We have developed a computer program (GenEST) that predicts the sizes of virtual transcript-derived fragments (TDFs) of in silico-digested cDNA sequences retrieved from databases. The vast majority of the resulting virtual TDFs could be traced back among the thousands of TDFs displayed on cDNA-AFLP gels. Sequencing of the corresponding bands excised from cDNA-AFLP gels revealed no inconsistencies. As a consequence, cDNA sequence databases can be screened very efficiently to identify genes with relevant expression profiles. The other way round, it is possible to switch from cDNA-AFLP gels to sequences in the databases. Using the restriction enzyme recognition sites, the primer extensions and the estimated TDF size as identifiers, the DNA sequence(s) corresponding to a TDF with an interesting expression pattern can be identified. In this paper we show examples in both directions by analyzing the plant parasitic nematode Globodera rostochiensis. Various novel pathogenicity factors were identified by combining ESTs from the infective stage juveniles with expression profiles of ∼4000 genes in five developmental stages produced by cDNA-AFLP.

Highly specific protein sequence motifs for genome analysis

We present a method for discovering conserved sequence motifs from families of aligned protein sequences. The method has been implemented as a computer program called emotif (http://motif.stanford.edu/emotif). Given an aligned set of protein sequences, emotif generates a set of motifs with a wide range of specificities and sensitivities. emotif also can generate motifs that describe possible subfamilies of a protein superfamily. A disjunction of such motifs often can represent the entire superfamily with high specificity and sensitivity. We have used emotif to generate sets of motifs from all 7,000 protein alignments in the blocks and prints databases. The resulting database, called identify (http://motif.stanford.edu/identify), contains more than 50,000 motifs. For each alignment, the database contains several motifs having a probability of matching a false positive that range from 10−10 to 10−5. Highly specific motifs are well suited for searching entire proteomes, while generating very few false predictions. identify assigns biological functions to 25–30% of all proteins encoded by the Saccharomyces cerevisiae genome and by several bacterial genomes. In particular, identify assigned functions to 172 of proteins of unknown function in the yeast genome.

Emaranhamento de feixes de fótons por meio do campo magnético

Foi proposta uma experiência na qual seria possível produzir um emaranhamento quântico de feixes de fótons com diferentes frequências, movendo-se em uma mesma direção, controlado por meio de um campo magnético externo. Nessa experiência, a interação entre o campo magnético e fótons é realizada por intermédio de elétrons, que interagem tanto com os fótons quanto com o campo magnético externo. Foi desenvolvida uma teoria que descreve processos físicos. Derivamos medidas de emaranhamento de informação e de Schmidt para um sistema geral de dois qubits e a medida residual para um sistema geral de três qubits. Usando a informação obtida da análise dos sistemas de dois e de três quase-fótons, calculamos medidas de emaranhamento. Criamos um programa para cálculo numérico, nesses casos, através do qual construímos gráficos de dependência das medidas de emaranhamentos em feixes de dois e de três fótons. Os resultados obtidos nos permitem ver como a medida de emaranhamento depende dos parâmetros, que caracterizam o sistema em questão. Por exemplo, se ambas as polarizações dos fótons coincidem, então, nenhum emaranhamento ocorre. O emaranhamento acontece apenas se as polarizações do fóton forem opostas.