Ensino de Entropia: um enfoque histórico e epistemológico.

The rational construction necessary to systematize scientific knowledge in physics, introduces difficulties of understanding in some of its concepts. One of these concepts which exemplify properly this difficulty in learning or teaching is entropy. This thesis propose the construction of a didactic route which constitute itself a historical and epistemological course to entropy, intending to contribute for teaching this concept as well as other physics concepts. The basic assumption to build this route is that through the historical review of the development of this concept in the way suggested by Bachelard s (1884-1962) epistemology it is possible to make subjects, to be taught and learned, more meaningful. Initially I composed a brief biographical note to give the reader an idea about the issues, interests and reflections, related to science, and how I dealt with them in my private and professional life, as well as the role they played to lead me to write this thesis. The strategy to construct the route to entropy was to split the usual contents of basic thermodynamics in three moments in a way they can constitute epistemological units , which can be identified by the way of thinking in the corresponding moments of scientific knowledge production: a technical and empiricist moment, a rationalist and positivist moment and a post-positivist rationalist one. The transition between each moment is characterized by a rupture with the former way of thinking; however the progress in the construction of knowledge in the area is evident. As the final part of this work I present an analysis based on elements of Bachelard s epistemology that are present in each moment. This analysis is the basic component of the didactic route that I propose myself to build. The way I made this route guide to entropy could contribute to the construction of other didactic routes in physics and other sciences, in a way to unveil hidden meanings and as a tool to humanize scientific knowledge.

Otimização Topológica com Termo-elasticidade Utilizando Elementos Tri3

This work proposes a formulation for optimization of 2D-structure layouts submitted to mechanic and thermal shipments and applied an h-adaptive filter process which conduced to computational low spend and high definition structural layouts. The main goal of the formulation is to minimize the structure mass submitted to an effective state of stress of von Mises, with stability and lateral restriction variants. A criterion of global measurement was used for intents a parametric condition of stress fields. To avoid singularity problems was considerate a release on the stress restriction. On the optimization was used a material approach where the homogenized constructive equation was function of the material relative density. The intermediary density effective properties were represented for a SIMP-type artificial model. The problem was simplified by use of the method of finite elements of Galerkin using triangles with linear Lagrangian basis. On the solution of the optimization problem, was applied the augmented Lagrangian Method, that consists on minimum problem sequence solution with box-type restrictions, resolved by a 2nd orderprojection method which uses the method of the quasi-Newton without memory, during the problem process solution. This process reduces computational expends showing be more effective and solid. The results materialize more refined layouts with accurate topologic and shape of structure definitions. On the other hand formulation of mass minimization with global stress criterion provides to modeling ready structural layouts, with violation of the criterion of homogeneous distributed stress

Biomecânica e otimização topológica com H-adaptatividade em implantes dentários nitretados a plasma em cátodo oco

In recent years there has been a significant growth in technologies that modify implant surfaces, reducing healing time and allowing their successful use in areas with low bone density. One of the most widely used techniques is plasma nitration, applied with excellent results in titanium and its alloys, with greater frequency in the manufacture of hip, ankle and shoulder implants. However, its use in dental implants is very limited due to high process temperatures (between 700 C o and 800 C o ), resulting in distortions in these geometrically complex and highly precise components. The aim of the present study is to assess osseointegration and mechanical strength of grade II nitrided titanium samples, through configuration of hollow cathode discharge. Moreover, new formulations are proposed to determine the optimum structural topology of the dental implant under study, in order to perfect its shape, make it efficient, competitive and with high definition. In the nitriding process, the samples were treated at a temperature of 450 C o and pressure of 150 Pa , during 1 hour of treatment. This condition was selected because it obtains the best wettability results in previous studies, where different pressure, temperature and time conditions were systematized. The samples were characterized by X-ray diffraction, scanning electron microscope, roughness, microhardness and wettability. Biomechanical fatigue tests were then conducted. Finally, a formulation using the three dimensional structural topology optimization method was proposed, in conjunction with an hadaptive refinement process. The results showed that plasma nitriding, using the hollow cathode discharge technique, caused changes in the surface texture of test specimens, increases surface roughness, wettability and microhardness when compared to the untreated sample. In the biomechanical fatigue test, the treated implant showed no flaws, after five million cycles, at a maximum fatigue load of 84.46 N. The results of the topological optimization process showed well-defined optimized layouts of the dental implant, with a clear distribution of material and a defined edge

Otimização topológica de estruturas termoelásticas tridimensionais

This work presents an optimization technique based on structural topology optimization methods, TOM, designed to solve problems of thermoelasticity 3D. The presented approach is based on the adjoint method of sensitivity analysis unified design and is intended to loosely coupled thermomechanical problems. The technique makes use of analytical expressions of sensitivities, enabling a reduction in the computational cost through the use of a coupled field adjoint equation, defined in terms the of temperature and displacement fields. The TOM used is based on the material aproach. Thus, to make the domain is composed of a continuous distribution of material, enabling the use of classical models in nonlinear programming optimization problem, the microstructure is considered as a porous medium and its constitutive equation is a function only of the homogenized relative density of the material. In this approach, the actual properties of materials with intermediate densities are penalized based on an artificial microstructure model based on the SIMP (Solid Isotropic Material with Penalty). To circumvent problems chessboard and reduce dependence on layout in relation to the final optimal initial mesh, caused by problems of numerical instability, restrictions on components of the gradient of relative densities were applied. The optimization problem is solved by applying the augmented Lagrangian method, the solution being obtained by applying the finite element method of Galerkin, the process of approximation using the finite element Tetra4. This element has the ability to interpolate both the relative density and the displacement components and temperature. As for the definition of the problem, the heat load is assumed in steady state, i.e., the effects of conduction and convection of heat does not vary with time. The mechanical load is assumed static and distributed

Método de Otimização Topológica em Estruturas Tridimensionais

The topology optimization problem characterize and determine the optimum distribution of material into the domain. In other words, after the definition of the boundary conditions in a pre-established domain, the problem is how to distribute the material to solve the minimization problem. The objective of this work is to propose a competitive formulation for optimum structural topologies determination in 3D problems and able to provide high-resolution layouts. The procedure combines the Galerkin Finite Elements Method with the optimization method, looking for the best material distribution along the fixed domain of project. The layout topology optimization method is based on the material approach, proposed by Bendsoe & Kikuchi (1988), and considers a homogenized constitutive equation that depends only on the relative density of the material. The finite element used for the approach is a four nodes tetrahedron with a selective integration scheme, which interpolate not only the components of the displacement field but also the relative density field. The proposed procedure consists in the solution of a sequence of layout optimization problems applied to compliance minimization problems and mass minimization problems under local stress constraint. The microstructure used in this procedure was the SIMP (Solid Isotropic Material with Penalty). The approach reduces considerably the computational cost, showing to be efficient and robust. The results provided a well defined structural layout, with a sharpness distribution of the material and a boundary condition definition. The layout quality was proporcional to the medium size of the element and a considerable reduction of the project variables was observed due to the tetrahedrycal element

Análise topológica experimental por perfilometria cíclica indutiva de superficies de paredes estruturais

To enhance the maintenance practices, Oil and Gas Pipelines are inspected from the inside by automated systems called PIG (Pipeline Inspection Gauge). The inspection and mapping of defects, as dents and holes, in the internal wall of these pipelines are increasingly put into service toward an overall Structural Integrity Policy. The residual life of these structures must be determined such that minimize its probability of failure. For this reason, the investigation on the detection limits of some basic topological features constituted by peaks or valleys disposed along a smooth surface is of great value for determining the sensitivity of the measurements of defects from some combinations of circumferential, axial and radial extent. In this investigation, it was analyzed an inductive profilometric sensor to scan three races, radius r1, r2, r3, in a circular surface of low carbon steel, equipped with eight consecutive defects simulated by bulges and holes by orbit, equally spaced at p/4 rad. A test rig and a methodology for testing in laboratory were developed to evaluate the sensor response and identify their dead zones and jumps due to fluctuations as a function of topological features and scanning velocity, four speeds different. The results are presented, analyzed and suggestions are made toward a new conception of sensor topologies, more sensible to detect these type of damage morphologies

Estudo teórico QTAIM e DFT dos compostos de coordenação: efeito quelato, titanocenos e ligação química

This work is a study of coordination compounds by quantum theory of atoms in molecules (QTAIM), based on the topological analysis of the electron density of molecular systems, both theoretically and experimentally obtained. The coordination chemistry topics which were studied are the chelate effect, bent titanocene and chemical bond in coordination complexes. The chelate effect was investigated according to topological and thermodynamic parameters. The exchange of monodentate ligands on polydentate ligands from same transition metal increases the stability of the complex both from entropy and enthalpy contributions. In some cases, the latter had a higher contribution to the stability of the complex in comparison with entropy. This enthalpic contribution is explained according to topological analysis of the M-ligand bonds where polidentate complex had higher values of electron density of bond critical point, Laplacian of electron density of bond critical point and delocalization index (number of shared electrons between two atoms). In the second chapter, was studied bent titanocenes with bulky cyclopentadienyl derivative π-ligand. The topological study showed the presence of secondary interactions between the atoms of π-ligands or between atoms of π-ligand and -ligand. It was found that, in the case of titanocenes with small difference in point group symmetry and with bulky ligands, there was an nearly linear relationship between stability and delocalization index involving the ring carbon atoms (Cp) and the titanium. However, the titanocene stability is not only related to the interaction between Ti and C atoms of Cp ring, but secondary interactions also play important role on the stability of voluminous titanocenes. The third chapter deals with the chemical bond in coordination compounds by means of QTAIM. The quantum theory of atoms in molecules so far classifies bonds and chemical interactions in two categories: closed shell interaction (ionic bond, hydrogen bond, van der Waals interaction, etc) and shared interaction (covalent bond). Based on topological parameters such as electron density, Laplacian of electron density, delocalization index, among others, was classified the chemical bond in coordination compounds as an intermediate between closed shell and shared interactions

Entropia de bloco no formalismo estatístico generalizado de Kaniadakis

A posição que a renomada estatí stica de Boltzmann-Gibbs (BG) ocupa no cenário cientifíco e incontestável, tendo um âmbito de aplicabilidade muito abrangente. Por em, muitos fenômenos físicos não podem ser descritos por esse formalismo. Isso se deve, em parte, ao fato de que a estatística de BG trata de fenômenos que se encontram no equilíbrio termodinâmico. Em regiões onde o equilíbrio térmico não prevalece, outros formalismos estatísticos devem ser utilizados. Dois desses formalismos emergiram nas duas ultimas décadas e são comumente denominados de q-estatística e k-estatística; o primeiro deles foi concebido por Constantino Tsallis no final da década de 80 e o ultimo por Giorgio Kaniadakis em 2001. Esses formalismos possuem caráter generalizador e, por isso, contem a estatística de BG como caso particular para uma escolha adequada de certos parâmetros. Esses dois formalismos, em particular o de Tsallis, nos conduzem também a refletir criticamente sobre conceitos tão fortemente enraizados na estat ística de BG como a aditividade e a extensividade de certas grandezas físicas. O escopo deste trabalho esta centrado no segundo desses formalismos. A k -estatstica constitui não só uma generalização da estatística de BG, mas, atraves da fundamentação do Princípio de Interação Cinético (KIP), engloba em seu âmago as celebradas estatísticas quânticas de Fermi- Dirac e Bose-Einstein; além da própria q-estatística. Neste trabalho, apresentamos alguns aspectos conceituais da q-estatística e, principalmente, da k-estatística. Utilizaremos esses conceitos junto com o conceito de informação de bloco para apresentar um funcional entrópico espelhado no formalismo de Kaniadakis que será utilizado posteriormente para descrever aspectos informacionais contidos em fractais tipo Cantor. Em particular, estamos interessados em conhecer as relações entre parâmetros fractais, como a dimensão fractal, e o parâmetro deformador. Apesar da simplicidade, isso nos proporcionará, em trabalho futuros, descrever estatisticamente estruturas mais complexas como o DNA, super-redes e sistema complexos

Desenvolvimento da célula base de microestruturas periódicas de compósitos sob otimização topológica

This thesis develops a new technique for composite microstructures projects by the Topology Optimization process, in order to maximize rigidity, making use of Deformation Energy Method and using a refining scheme h-adaptative to obtain a better defining the topological contours of the microstructure. This is done by distributing materials optimally in a region of pre-established project named as Cell Base. In this paper, the Finite Element Method is used to describe the field and for government equation solution. The mesh is refined iteratively refining so that the Finite Element Mesh is made on all the elements which represent solid materials, and all empty elements containing at least one node in a solid material region. The Finite Element Method chosen for the model is the linear triangular three nodes. As for the resolution of the nonlinear programming problem with constraints we were used Augmented Lagrangian method, and a minimization algorithm based on the direction of the Quasi-Newton type and Armijo-Wolfe conditions assisting in the lowering process. The Cell Base that represents the composite is found from the equivalence between a fictional material and a preescribe material, distributed optimally in the project area. The use of the strain energy method is justified for providing a lower computational cost due to a simpler formulation than traditional homogenization method. The results are presented prescription with change, in displacement with change, in volume restriction and from various initial values of relative densities.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

A forma do privilégio: renda, acessibilidade e densidade em Natal-RN

The aim of this work is to understand the morphological expression of ground occupation by the higher income population, by focusing on population distribution in accordance with income layers and demographical density, as well as topological accessibility (HILLIER and HANSON, 1984) resulting from the urban grid structure. It endeavors to identify a functional organizing principle regarding the intra-urban space of Natal capital city of the state of Rio Grande do Norte, the research focus. In order to achieve this, census data as well as syntactic data were utilized for mapping and spatial analysis of income patterns, topological accessibility and demographical density using Geographical Information System GIS. The organizing principle was named as the Form of Privilege, a pattern that concentrates or tends to concentrate wealth, topological accessibility and low demographical density. Attempting to assess its extent, beyond Natal, this principle was applied to other Brazilian northeastern capitals such as: Fortaleza, CE; Teresina, PI; Aracaju, SE; Recife, PE; and João Pessoa, PB. Findings point out that although the urban structures of these cities are not immune to the Form of Privilege, Natal is emblematic of this phenomenon, a fact that demonstrates the perverse character of its spatial process, which historically creates privileged areas within the city, by means of the appropriation of accessibility as well as of the many urban benesses that are related to it by higher income groups at the expense of the major part of the population, which though being the people mostly in need of the benefits originating from the urban form are excluded from them

Saudosa Maloca, Maloca querida: um estudo morfológico da relação forma/usos do espaço em moradias autoconstruídas e construídas pelo poder público após um ano de ocupação

This study intends to enhance the existing knowledge concerning the patterns of the uses of space for low cost housing in Parnamirim, Rio Grande do Norte, Brazil, by way of comparative morphological studies in spatial arrangements and articulations regarding three distinct, however inter-related, sets of social housing: (1) a development comprising 21 self-built houses erected on public routes and illegal plots within a tract of land originally designed to be an industrial development: (2) architect-designed houses built by the public authority in order to accommodate the previous 21 (plus a few additions) families occupying the self-built dwellings, and (3) modifications performed by dwellers on a total of those 24 houses built by the public authority after an occupation period of one year. The predominant uses of each room within the self-built and modified houses were represented in ground plan, based on empirical observation, surveys with dwellers and the use of analytical procedures of morphologic analysis of nature predominantly geometric (specific) and topology (space syntax analysis). A scale of priorities was identified in relation to the uses of each room, its geometrical arrangement (adjacency, front/back relations etc), and underlying structures (connectivity, depth and spatial integration) in order to establish congruencies and non-congruencies between a social-cultural order embedded in the self-built domestic space and the design logic contained in the houses offered by official agencies. The comparative analysis points towards the convivial existence of two tendencies: one that seems to reinforce a design logic inasmuch as the additions and modifications performed by the dwellers do not alter but even emphasize the original configuration of the designed houses, and another one in which those patterns are subverted in accordance with a logic which, to a lesser or greater degree, coincides with that of the self-built dwellings

Natal qual é a sua cara?: análise do perfil edilício da avenida Eng. Roberto Freire (Natal/RN) à luz da acessibilidade

This study focuses on the building ensemble of Avenida Roberto Freire, a main road in Natal, Brazil, as a material expression of the confluence of various factors among which the following may be emphasized: high level of accessibility due to urban spatial re-structuring and the growth of the real estate market, in view of the increasing number of consumers, who arrived in Natal within the last decades. The intense urban modification process that has been going on in Natal since at least the 1980s, has engendered the formation of long axial lines which express the expansion dynamics and some of the forces subjacent to it. Avenida Roberto Freire has been an iconic example of an urban thoroughfare where architecture becomes primarily a communication support that can be perceived by fast moving passers-by, what brings it close to the venturian concept of strip (Venturi at al, 1972). The building types that line the road not only respond to the dynamics in process but also contribute to intensify it, as they house a variety of uses which attract people and generate more movement. The dynamics is further strengthened by the action of the real estate business which benefits from the increase of highly accessible locations, and from the private and public investments and incentives to tourism that aim to insert this city into the globalized world. Although the intention of reconstituting part of the history of density increase on this avenue in a diachronical perspective was attempted within the limits of the available references and documentation, the central contribution of this study is to understand the relations between topological accessibility and the typological nature of the building ensemble. By observing the synchronic morphological frame resulting from the spatial configuration analysis pertinent to this avenue (cf. Hillier and Hanson,1984) and the inventory and classification of the building ensemble there existing, this study aims to understand how architecture responds to accessibility in view of the real estate pressure, boosted by a cosmopolitanizing process brought about by the continuous flow of foreign and Brazilian arrivals as visitors, temporary or permanent residents

Entre serras e sertões A(s) (trans)formaç(ões) de centralidade(s) da Região Metropolitana do Cariri/CE

This study reviews the spatial configuration from the road network of an urban compound formed by the cities of Crato, Juazeiro do Norte and Barbalha (the Crajubar - core of the Cariri metropolitan region, in the State of Ceará, Brazil), in order to establish nexus (or relations) between different levels of accessibility and the formation/ transformation and specialization of centralities in local and metropolitan scales. Stemming from the Social Logic of Space theoretical and operational apparatus, the study explores modeling possibilities (with axial lines, segments and lines of continuity) which is then confronted to empirical observations concerning movement flows and land use, within a Geographic Information System database. At different scales of analysis, the results suggest evidences of continuity were found in the permanence of intra-urban centres and sub-centres within each town, whereas evidences of change pointed out to the formation of a new centrality of metropolitan magnitude in the neighbourhood referred to as the Triângulo, in the municipality of Juazeiro, where high levels of topological accessibility coincides with the appearance of new business buildings as well as with the emergence of urban equipment of a scale more adequate to meet a regional demand