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Efeitos de hibridização correlacionada no modelo de Anderson de uma impureza / Effects of correlated hybridization in the single-impurity Anderson modelVeiga, Rodrigo Soares 31 May 2012 (has links)
O desenvolvimento de novos materiais tem tido papel fundamental nos recentes avanços tecnológicos. Esse progresso depende muito de fundamentos teóricos que abordem mecanismos microscópicos da matéria, ou seja, como átomos e moléculas interagem e geram configurações especiais, responsáveis pelo seu comportamento macroscópico. Dentre os materiais de interesse na atualidade estão os sistemas contendo impurezas magnéticas diluídas, isto é, átomos com camadas d ou f incompletas imersos, por exemplo, em metais não magnéticos, como átomos de ferro em uma matriz de cobre. Tradicionalmente, estes sistemas tem sido tratados através dos modelos de Kondo ou Anderson, os quais, desde os primeiros estudos na década de 1960, estão entre os mais importantes em física da matéria condensada. Neste trabalho, estudamos especificamente o modelo de Anderson de uma impureza. Ele se caracteriza por considerar uma correlação quando dois elétrons de spins opostos ocupam o nível localizado que representa a impureza. Além de, por outro termo no Hamiltoniano, contabilizar a hibridização eletrônica entre a banda de condução e a impureza, devido à superposição das funções de onda dos elétrons localizados e itinerantes. Em acréscimo ao modelo tradicional, incluímos um termo de hibridização adicional, que depende explicitamente do número de ocupação do nível localizado. Este termo de interação que acopla diretamente no Hamiltoniano o processo de hibridização e os efeitos de correlação é denominado de hibridização correlacionada. Através da estruturação e da consequente aplicação da técnica do Grupo de Renormalização Numérico - a qual estabelece uma transformação no Hamiltoniano, que a cada passo acrescenta uma escala de energia ao problema e constrói um método iterativo, no qual um Hamiltoniano é diagonalizado numericamente a cada iteração -, analisamos os efeitos de hibridização correlacionada sobre parte da física do modelo de Anderson de uma impureza. Em particular, isso é feito por meio de dados numéricos para a dependência da contribuição da impureza a três propriedades termodinâmicas - são elas: suscetibilidade magnética, calor específico e entropia - em função da temperatura, desde o topo da banda de condução até o nível de Fermi. / The development of new materials has been playing a fundamental role in the currently technological advances. This improvement is strongly dependent on the theoretical foundations which study the microscopic matter engine, i.e., the way atoms and molecules interact and create distinct configurations, responsible for their macroscopic behavior. Among the interesting materials, there are the dilute magnetic impurity systems. They are constituted by partially filled d or f orbital atoms immersed, for exemple, in nonmagnetic metals; like iron atoms in a copper background. Traditionally, such system has been described by the Kondo and Anderson models, which are, since the sixties, two of the most important models in condensed matter physics. In the present work, we specifically study the single-impurity Anderson model. It is characterized by taking correlation into account when two particles with opposite spins fill the impurity localized energy level. Beyond, by another term in the Hamiltonian, it considers the eletronic hybridization between impurity and conduction band, due their wave functions overlap. In addition to the usual model, we include a different hybridization term, which explicitly depends on localized level occupation number. This new interaction term, which couples hybridization process and correlation effects directy in the Hamiltonian, is named correlated hybridization. Through the exposition of Numerical Renormalization Group technique and its consequent enforcement - the procedure states a transformation in the Hamiltonian, where each step adds an energy scale to the problem and set up an iterative scheme, where a Hamiltonian is numerically diagonalized at each iteration - we analyse effects of correlated hybridization on part of the single-impurity Anderson model physics. In particular, this is done by numerical renormalization group data for the temperature dependence of the impurity contribution to three thermodynamical properties - they are: magnetic susceptibility, specific heat and entropy -, from the top of the conduction band until the Fermi level.
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Étude de la cinétique chimique et des propriétés de transport d'un plasma d'arc SF6-C2F4 en déséquilibre thermique : application à l'étude des disjoncteurs haute tension / Study of the chemical kinetic and transport properties of a sf6-c2f4 arc plasma in thermal non-equilibrium : application to the study of high voltage circuit breakerVanhulle, Gabriel 13 December 2018 (has links)
La modélisation d'un disjoncteur haute tension par un modèle MHD nécessite des banques de données de propriétés du plasma afin de simuler le comportement de l'arc électrique. L'hypothèse d'équilibre thermodynamique local est souvent utilisée afin de calculer ces propriétés. Cependant les conditions d'équilibre ne sont pas remplies près des parois ou des électrodes, ou lors du passage par zéro du courant. Les écarts à l'équilibre (thermique notamment) modifient alors considérablement la chimie et les propriétés du plasma. L'étude de ces propriétés dans ces conditions nécessite alors de supposer que le plasma est à deux températures (2T). Le calcul des propriétés du plasma à 2T fait l'objet de cette thèse. La première partie de cette thèse présente le contexte industriel à l'origine de cette étude. Les hypothèses de base qui sous-tendent l'hypothèse 2T sont ensuite rappelées. Dans cette partie une attention spéciale est portée aux températures caractéristiques de peuplement des modes d'énergies internes. Deux jeux d'hypothèses portant sur ces températures sont utilisés dans ces travaux, et le choix de ces hypothèses est discuté. La deuxième partie de ce travail est consacrée au calcul de composition d'un plasma de SF6-C2F4 à 2T. Ce calcul sera fait avec deux méthodes différentes : la première repose sur la loi d'action de masse étendue à 2T, et la seconde sur un calcul collisionnel-radiatif. Des exemples de composition obtenus avec ces deux méthodes sont présentés. Les hypothèses portant sur les températures de peuplement des niveaux d'énergies internes sont discutées au vu de ces résultats. Le troisième chapitre de cet ouvrage aborde le calcul des propriétés thermodynamiques à 2T du plasma. Les formulations théoriques de chacune de ces propriétés sont d'abord rappelés, et les résultats issus de ces expressions sont ensuite présentés et discutés, pour les deux méthodes de calcul de la composition. Le quatrième chapitre est dédié au calcul des coefficients de transports d'un plasma de SF6-C2F4 à 2T. Cette partie s'appuie sur une étude bibliographique des méthodes de calcul déjà existantes et des données indispensables à l'obtention de ces propriétés (intégrales de collision). Pour chaque propriété (viscosité, conductivité électrique et conductivité thermique) les différentes méthodes de calcul recensées dans la littérature sont comparées. Le choix de la technique de calcul la plus appropriée est réalisé par confrontation de résultats à l'ETL. Une attention toute particulière est portée au calcul de la partie réactive de la conductivité thermique, et une formulation adaptée aux besoins de ce travail est proposée. Les résultats issus de ces expressions sont présentés et discutés suivant la même logique quand dans le chapitre précédent. / Modelling a high voltage circuit breaker using a MHD model needs plasma properties databanks to simulate the electric arc behavior. The local thermodynamic equilibrium hypothesis is often used to calculate these properties. However, the equilibrium conditions are not satisfied near the walls or the electrodes, or during the zero crossing of the current. The thermal nonequilibrium considerably modify the chemistry and properties of the plasma. The study of these properties for a 2t plasma is the subject of this thesis. The first part of this thesis presents the industrial context at the origin of this study. Basics assumptions for the 2t hypothesis are then explained. In this section, special attention is given to the temperatures characteristic of the internal energy modes. Two sets of hypotheses concerning these temperatures are used in this work, and the choice of these hypotheses is discussed. The second part of this work is dedicated to the calculation of sf6-c2f4 plasma composition at 2t. This calculation will be done with two different methods: the first is based on the mass action law extended to 2t, and the second on a collisional-radiative calculation. Examples of compositions obtained with these two methods are presented. The hypotheses concerning the temperatures of populating of the internal energy levels are discussed in the light of these results. The third chapter of this thesis deals with the calculation of the thermodynamic properties at 2t of the plasma. The theoretical formulations of each of these properties are first recalled, and the results from these expressions are then presented and discussed, for the two methods of calculating the composition. The fourth chapter is dedicated to calculating the transport coefficients of a sf6-c2f4 plasma at 2t. This part is based on a bibliographic study of the already existing methods of calculation and the essential data to obtain these properties (collision integrals). For each property (viscosity, electrical conductivity and thermal conductivity) the various calculation methods identified in the literature are compared. The choice of the most appropriate calculation technique is made by comparing the results to the ETL. Particular attention is paid to the calculation of the reactive part of the thermal conductivity, and a formulation adapted to the needs of this work is proposed. The results from these expressions are presented and discussed following the same logic when in the previous chapter.
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Thermodynamic Database for Zirconium AlloysJerlerud Pérez, Rosa January 2006 (has links)
For many decades zirconium alloys have been commonly used in the nuclear power industry as fuel cladding material. Besides their good corrosion resistance and acceptable mechanical properties the main reason for using these alloys is the low neutron absorption. Zirconium alloys are exposed to a very severe environment during the nuclear fission process and there is a demand for better design of this material. To meet this requirement a thermodynamic database is useful to support material designers. In this thesis some aspects of the development of a thermodynamic database for zirconium alloys are presented. A thermodynamic database represents an important facility in applying thermodynamic equilibrium calculations for a given material providing: 1) relevant information about the thermodynamic properties of the alloys e.g. amount and composition of phases, oxygen activity, heat capacity etc, and 2) significant information for the manufacturing process e.g. heat treatment temperature. The basic information in the database is first the unary data, i.e. pure elements; those are taken from the compilation of the Scientific Group Thermodata Europe (SGTE) and then the binary and ternary systems. All phases present in those binary and ternary systems are described by means of the Gibbs energy as a function of composition and temperature. Many of those binary systems have been taken from published or unpublished works and others have been assessed in the present work. The elements included in the databse are: C, Fe, Cr, Nb, Ni, Mo, O, Si, Sn, and Zr + H, and the assessment performed under this thesis are: Cr-Sn, Mo-Zr, Sn-Zr, Fe-Nb-Zr and Nb-O-Zr. All the calculations have been made using Thermo-Calc software and the representation of the Gibbs energy obtained by applying Calphad technique with some use of ab initio calculations. / QC 20100902
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Mathcad-Bibliotheken für thermodynamische Stoffdaten und das E-Learning System Thermopr@cticeKretzschmar, Hans-Joachim, Stöcker, Ines, Kunick, Matthias, Jähne, Ines 27 May 2010 (has links) (PDF)
Das Lernsystem Thermopr@ctice stellt eine internetgestützte Lernumgebung für das Berechnen von
Übungsaufgaben mit dem Computer-Algebrasystem Mathcad dar. Die veränderte Arbeitsweise des
Lernenden besteht darin, das herkömmliche Arbeitsblatt durch den Mathcad-Arbeitsbildschirm zu
ersetzen und die Aufgabenlösung unmittelbar auf diesem zu erledigen. Dem Lernenden werden die
Übungsaufgaben – hier im Fach Technische Thermodynamik – in individuellen Varianten und mit
individuellen Zahlenwerten im Mathcad-Format über Internet bereitgestellt. Die Lösung erfolgt in
betreuten Übungen oder am heimischen PC. Für die Lösung benötigte Stoffwerte können der
Stoffwertsammlung im Internet entnommen bzw. mit Programmbibliotheken, die an Mathcad angeschlossen
sind, berechnet werden. Ergänzend wird eine Formelsammlung angeboten, aus der
wichtige Formeln auf den Arbeitsbildschirm gezogen werden können. Nach der Berechnung jeder
Teilaufgabe sendet der Lernende das Ergebnis an Thermopr@ctice. Im Fehlerfall werden
Zwischenergebnisse angefordert. Realisiert wird die Lernumgebung über PHP-Skripte in Verbindung
mit einer MySQL-Datenbank. Durch das Lernsystem werden die Studierenden an moderne
Arbeitsweisen unter Nutzung eines Computer-Algebrasystems und fachbezogener Programmbibliotheken
herangeführt. Da das System zum Selbststudium konzipiert ist, eignet es sich auch für die
Weiterbildung und das Fernstudium. Es kann auf alle Lehrfächer übertragen werden, in denen die
Aneignung oder Festigung von Wissen über das Berechnen von Übungsaufgaben erfolgt.
Thermopr@ctice wurde im Rahmen des Verbundprojektes „Bildungsportal Sachsen“ des
Sächsischen Staatsministeriums für Wissenschaft und Kunst entwickelt.
Neue Technologien in der Energietechnik, insbesondere Verfahren mit CO2-Abscheidung,
bedingen veränderte Arbeitsfluide. Neben reinen Stoffen kommen zunehmend fluide Stoffgemische
zum Einsatz, deren thermodynamische Eigenschaften berechnet werden müssen. Dies betrifft
feuchte Verbrennungsgasgemische einschließlich CO2/H2O-Gemische sowie feuchte Luft, auch bei
hohen Drücken. Daneben sind die Eigenschaften von gasförmigen, flüssigen und festem
Kohlendioxid und Mischungen mit verbliebenen Gasen zu berechnen. Auf Grund der Nutzung von
Abwärme sind Absorptionskältemaschinen mit Ammoniak-Wasser-Gemischen und Wasser-
Lithiumbromid-Gemischen nach wie vor von Interesse. Die Eigenschaften von Ammoniak/Wasser-
Gemischen werden auch für die Berechnung des Kalina-Prozesses benötigt. Zur Konzipierung von
ORC-Prozessen müssen die Eigenschaften von Silikonölen und Kohlenwasserstoffen berechenbar
sein. Für die Optimierung von fortschrittlichen Dampfkraftwerken sind extrem schnelle
Algorithmen für die Berechnung der thermodynamischen Eigenschaften von Wasser und
Wasserdampf Voraussetzung. Die weltweit an Bedeutung gewinnende Meerwasserentsalzung
bedingt eine immer genauere Modellierung der Verfahren, wofür die Eigenschaften von
Meerwasser berechenbar sein müssen. Für die Berechnung solcher Prozesse wurden
benutzerfreundliche Programmbibliotheken zur Ermittlung der thermodynamischen Zustandsgrößen
einschl. Umkehrfunktionen und Transporteigenschaften der Arbeitsfluide erarbeitet. Zur
komfortablen Nutzung der Stoffwert-Bibliotheken steht das Add-On FluidMAT für Mathcad® zur
Verfügung. Versionen für Studierende der wichtigsten Programme sind verfügbar.
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Μοριακή προσομοίωση διπλοστοιβάδων λιπαρών οξέων : η περίπτωση του παλμιτικού οξέος / Molecular simulations of bilipid layers : the case of palmitic acidΓεωργιλάς, Βασίλης, Λιόντα, Ευανθία 10 June 2013 (has links)
Στην παρούσα διπλωματική εργασία παρουσιάζονται Ατομιστικά Μοντέλα Διακριτών και Ενοποιημένων Ατόμων, τα οποία μπορούν να αποτελέσουν το πρώτο σημαντικό βήμα για τη μελέτη της βιολογικής μεμβράνης ή και ακόμα τη μελέτη συστημάτων μεμβρανών με πρωτεΐνες, σάκχαρα κ.α. Τέτοιες προσομοιώσεις θα μας δώσουν στοιχεία για μακροσκοπικές ιδιότητες της μεμβράνης (π.χ. διαχυτότητα) παρουσία συγκεκριμένων άλλων μακρομορίων.
Αρχικά μελετάται σε ατομιστικό επίπεδο, με τα μοντέλα Διακριτών και Ενοποιημένων Ατόμων, τήγμα παλμιτικού οξέος (383Κ). Η καταλληλόλητα του νέου μοντέλου που εισήχθη για την περίπτωση των Ενοποιημένων Ατόμων εξετάζεται με βάση τις ιδιότητες διαμόρφωσης (λ.χ. κατανομές γωνιών) που εξάγονται από το μοντέλο Διακριτών Ατόμων. Στο μοντέλο Διακριτών Ατόμων χρησιμοποιήθηκε το αναλυτικότερο δυνατό δυναμικό (COMPASS). Τα αποτελέσματα ήταν άκρως ικανοποιητικά. Έχοντας ένα αξιόπιστο μοντέλο Ενοποιημένων Ατόμων προχωρήσαμε στο επόμενο βήμα.
Επόμενο βήμα ήταν η μελέτη συστήματος παλμιτικού οξέος ανάμεσα από στρώμα νερού. Σημαντικό μειονέκτημα του μοντέλου Διακριτών Ατόμων για ένα τόσο μεγάλο σύστημα αποτελεί η περιορισμένη χρονική κλίμακα. Φαινόμενα σχηματισμού διπλοστοιβάδας παλμιτικού οξέος παρουσία νερού, είναι πολύ δύσκολο να μελετηθούν με χρήση μοντέλου Διακριτών Ατόμων λόγω των πολύ μικρών χρόνων που καλύπτουν. Επομένως, κρίνεται αναγκαία η χρήση μοντέλου Ενοποιημένων Ατόμων για το σύστημα PLM – νερό.
Χρησιμοποιήσαμε το μοντέλο Ενοποιημένων Ατόμων που οι ίδιοι αναπτύξαμε, όπως και για την περίπτωση του τήγματος, για την περιγραφή του παλμιτικού οξέος, και το μοντέλο SPCE για το νερό, το οποίο είναι ευρέως αποδεκτό από την επιστημονική κοινότητα.
Πέραν της σύγκρισης των μοντέλων Ενοποιημένων και Διακριτών Ατόμων που έγινε για το τήγμα του παλμιτικού οξέος, πραγματοποιήθηκαν και διάφοροι υπολογισμοί που αφορούν τη σταθεροποίηση του συστήματος (Autocorrelation faction of end-to-end distance vector), δομικές ιδιότητες (Radial Distribution Function), ιδιότητες διαμόρφωσης (angle distribution, radius of gyration, end-to-end distance vector) και θερμοδυναμικές ιδιότητες (density). Υπολογίστηκαν επίσης ο συντελεστής αυτοδιάχυσης (self diffusion coefficient) καθώς και το πλήθος δεσμών υδρογόνου. / This diploma thesis presents Atomistic Models of Discrete and Integrated atoms, which can be an important first step to study the biological membrane or even studying membrane systems with proteins, sugars, etc. Such simulations will give us data on macroscopic membrane properties (eg diffusivity) in the presence of certain other macromolecules.
Initially we study melt palmitic acid (383K)in atomistic level. The suitability of the new model, introduced for the case of the Consolidated Atoms is examined by checking the configuration properties (eg angles distributions) derived from the model of Discrete Atoms. In the model of discrete atoms the disaggregated possible dynamic (COMPASS)was used. The results were highly satisfactory. Having a reliable model for Unified atoms we move to the next step.
Next step was to study the system of palmitic acid between waterbed. Major drawback of the model of Discrete atoms for such a large system is the limited time scale. Phenomena of bilayer formation of palmitic acid in the presence of water is very difficult to be studied using discrete atoms model because of very short times covered. Therefore, it is necessary to use a model of integrated atoms for the system PLM - water.
We used the model of Unified atoms we ourselves have developed, as in the case of the melt, for the description of palmitic acid, and the SPCE model for water, which is widely accepted by the scientific community.
Beyond the comparison of models of integrated and discrete atoms made for the melt of palmitic acid, various calculations for the stabilisation the system (Autocorrelation faction of end-to-end distance vector), structural properties (Radial Distribution Function), properties configuration (angle distribution, radius of gyration, end-to-end distance vector) and thermodynamic properties (density)were made. The self-diffusion coefficient (self diffusion coefficient) and the number of hydrogen bonds were also calculated.
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Aplicações de secagem para o aproveitamento de resíduos da banana, visando sua aplicação na indústriaVilla Vélez, Harvey Alexander [UNESP] 21 February 2011 (has links) (PDF)
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villavelez_ha_me_sjrp.pdf: 807308 bytes, checksum: 262020576b600a66d35be63d82b014a7 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / A banana é a fruta com maior produção mundial, sendo plantada em quase todos os continentes. Devido à grande oferta de banana no mercado, é notável a existência de problemas com a geração de resíduos causados por desperdícios (fruta sobremadura) e material celulósico gerado no cultivar. O presente trabalho tem como objetivo principal a aplicação do processo de secagem para resíduos do cultivar da banana nanica (Mussa spp. Haploide AAB ), visando seu possível aproveitamento na indústria. Resíduos de banana tipo nanica (casca, pedicelo, pedúnculo) e polpa foram caracterizados quimicamente, encontrando valores de cinza, umidade, matéria seca, proteína, lipídeos e carboidratos totais muito próximos à literatura. A relação entre o conteúdo de umidade e a atividade de água proporciona informações uteis para a armazenagem e processamento destes resíduos. Na pesquisa foram determinadas isotermas de desorção para casca, pedicelo e polpa de banana a seis temperaturas (20, 30, 40, 50, 60 e 70°C), na faixa de conteúdo de umidade entre 0,001-6,360 kg·kg -1 e atividades de água entre 0,02-0,907. O modelo teórico de GAB foi empregado para a modelagem das isotermas de desorção. Foi proposta a segunda derivada da solução analítica da equação de Clausius-Clapeyron para calcular o calor isostérico de sorção, a entropia diferencial e, a energia livre de Gibbs, através do modelo de GAB quando o efeito da temperatura em equilíbrio higroscópico é considerado. Experimentos de secagem para casca de banana foram realizados em um secador de leito fixo, a três diferentes velocidades de ar (2.5, 1.5 e 1.0 m·s -1 ), e quatro temperaturas (40, 50, 60 e 70°C). Os modelos de Peleg, Lewis, Henderson-Pabis e difusivo, foram empregados na modelagem das curvas de secagem. Na análise gráfica, encontrou-se que a velocidade de ar não influência no tempo final secagem... / Banana is the most produced fruit in the world, being planted in every continent. Due to the large supply bananas in the market, the existence of problems with waste generation caused for overripe fruit and cellulosic material is noteworthy. The objective of this paper is the drying process implementation for banana waste, variety nanica (Mussa spp. Haploid AAB), for a possible application in the industry. Waste (peel, pedicel and peduncle) and pulp of banana nanica were characterized chemically, where values of ash, protein, fat, carbohydrates, and water were quantified, showing similar results with literature. The relationship between moisture content and water activity provides useful information for processing and storage of banana waste. The desorption isotherms of peel, pedicel and pulp of overripe bananas were determined at six different temperatures (20, 30, 40, 50, 60 and 70ºC) over wide ranges of moisture content (0,001–6,360 kg kg-1 d.b.) and water activity (0,02– 0,907). The theoretical model of GAB was used for modeling the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to compute the isosteric heat of sorption, the differential entropy, and the Gibbs’ free energy, by means of the GAB model when the effect of temperature on hygroscopic equilibrium is considered. Drying kinetics for peel banana in convective hot air forced equipment were determined, at three air velocities (2.5, 1.5 and 1.0 m·s -1 ), and four temperatures (40, 50, 60 and 70 ° C). The models of Peleg, Lewis, Henderson-Pabis, and diffusive were used to the modeling of drying curves. In the graphical analysis, for all experiments, air velocity does not influence in the final time of drying, showed a decreasing rate period of drying. Finally, acid hydrolysis of dry peel banana was performed by using a central composite design experimental with three... (Complete abstract click electronic access below)
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Analise dos mecanismos de degradacao de varetas combustiveis falhadas em reatores PWRCASTANHEIRA, MYRTHES 09 October 2014 (has links)
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09634.pdf: 20502766 bytes, checksum: d7ca137617708ba2e112264b734dcd6e (MD5) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Utilizacao da cinza da casca de arroz como carga em matriz de poliamida 6 submetida a radiacao ionizante / Utilization of rice husk ash as filler for polyamide 6 and ionizing radiation effect studies on this compositeFERRO, WALDIR P. 09 October 2014 (has links)
Made available in DSpace on 2014-10-09T12:26:24Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:09:59Z (GMT). No. of bitstreams: 0 / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP
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Desenvolvimento de fontes radioativas seladas imobilizadas em resina epóxi para verificação de detectores utilizados em medicina nuclear / Development of sealed radioactive sources immobilized in Epoxy resin for verification of detectors used in nuclear medicineTIEZZI, RODRIGO 22 June 2016 (has links)
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O grupo de renormalização numérico e o problema de duas impurezas / Numerical renormalization group and the two-impurity problemVivaldo Leiria Campo Júnior 10 May 2004 (has links)
Neste trabalho é calculada a contribuição de duas impurezas magnéticas ao calor específico e à entropia de um metal através do grupo de renormalização numérico. Tal sistema físico foi descrito pelo modelo Kondo de duas impurezas, onde cada impureza é simplesmente um momento magnético associado a um spin S=1/2, e representa um elétron ocupando um orbital de uma impureza magnética adicionada ao metal não magnético.Para tornar possível o cálculo com malhas de discretização grossas, foi introduzida uma correção no processo de discretização, levando a novas expressões para as energias da banda de condução discretizada e permitindo um melhor tratamento da assimetria partícula-buraco do modelo. Tal assimetria decorre da dependência com a energia do acoplamento entre as impurezas e os elétrons de condução do metal. A utilização de malhas grossas é extremamente desejável para a diminuição do esforço computacional envolvido. / In this work the contribution of two magnetic impurities to the specific heat and the entropy of a metal through the group of numerical renormalization is calculated. Such physical system was described for the Kondo model of two impurities, where each impurity is simply an associated magnetic moment to one spin S=1/2, and represents an electron occupying a orbital one of a magnetic impurity added to the magnetic metal. To not become possible the calculation with thick meshes of discretization, was introduced a correction in the discretization process, having led the new expressions for the energies of the band of discredited conduction and allowing to one better treatment of the asymmetry particle-hole of the model. Such asymmetry elapses of the dependence with the energy of the coupling between the impurities and electrons of conduction of the metal. The use of thick meshes is extremely desirable for the reduction of the involved computational effort.
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