A região de Gondola-Nhamatanda localiza-se na parte limítrofe entre as províncias de Manica e Sofala, centro de Moçambique. Ela está geologicamente inserida no complexo de Bárue (Grupo de Chimoio) e na cobertura fanerozoica. O Complexo de Bárue é composto pelos Grupos supracrustais de Macossa e Chimoio intrudidos por rochas plutônicas de várias composições. Enquanto que a cobertura fanerozoica consiste de sedimentos terrestres e rochas vulcânicas associadas pertencentes ao Supergrupo do Karoo e à sequências do rifte Este Africano. A área de trabalho foi estudada em termos de petrografia; geoquímica de elementos maiores, traço e de terras raras; geocronologia e geologia isotópica pelos métdos U -Pb em zircão, Rb-Sr e Sm-Nd em rocha total e Rb-Sr em minerais para o granito de Inchope, quartzo-sienito do monte Chissui e fonolito do monte Xiluvo. Este estudo permitíu determinar os litotipos que intrudiram o grupo supracrustal de Chimoio , suas idades de cristalização e de diferenciação dos magmas que formaram seus protólitos e ainda o enquadramento tectônico. As rochas estudadas são basicamente calci -alcalinas com variações de meta à peraluminoso para os granitoides e quartzo-sienito e peralcalino para o fonolito do monte Xiluvo. Os granitoides do grupo de Chimoio foram cristalizados no Mesoproterozoico (idades U-Pb e Rb-Sr) a partir de protólitos Paleoproterozoicos (\'T IND.DM\' = 1,7 - 2,3 Ga); por sua vez, as rochas vulcânicas (fonolitos) do monte Xiluvo cristalizaram rápidamente no Câmbrico (idade Rb-Sr) dum protólito do Neoproterozoico-Câmbrico (\'T IND.DM\' = 0,54 - 0,56 Ga). Os dados isotópicos obtidos no presente estudo sugerem que as rochas do cinturão de Moçambique foram geradas por fusão parcial que provavelmente envolveu mistura ( valores negativos de ?Nd ) da crosta arqueana / paleoproterozoica e magma mesoproterozoico a 1100 Ma e sofreram retrabalhamento marcado pela aglutinação do Gondwana (orogenia Pan-Africana) e tafrogênese marcada pela fraturação do Gondwana (Rifte Este Africano ). / The region of Gondola-Nhamatanda is located at the border between the provinces of Manica and Sofala, central part of Moçambique. It is geologically inserted in the Bárue complex and the Phanerozoic cover. The Bárue complex is composed of the Macossa and Chimoio supracrustal groups intruded by plutonic rocks of various compositions, whereas the Phanerozoic cover consists of terrestrial sediments and volcanic rocks belonging to the Karoo Super-group and East African Rift Sequences. The work area was studied in terms of petrography; geochemistry of major elements, trace and rare earth elements; geochronology and isotope geology by the methods U -Pb in zircon, Rb-Sr and Sm-Nd in whole rock and Rb-Sr in minerals for the Inchope granite, Chissui mountain Quartzo-sienito and Xiluvo mountain phonolite. This study allowed to determine the lithotypes that intruded the Chimoio supracrustal group, its crystallization ages and the differentiation ages of the magmas that formed the protoliths and the tectonic framework. The studied rocks are basically calc-alkaline varying from meta to peraluminous for the granitoids and quartz-sienite and peralkaline for the mount Xiluvo phonolite. The Chimoio Group granitoids had been crystallized in the Mesoproterozoic (U-Pb and Rb-Sr ages) from Paleoproterozoic protoliths (\'T IND.DM\' = 1.7 - 2.4Ga); on the other hand, the volcanic rocks (phonolites) of the Xiluvo mount had crystallized fast in the Cambrian (Rb-Sr age) from a Neoproterozoic-Cambrian protolith (\'T IND.DM\' = 0.54 - 0.56Ga). The isotopic data, in the present study , suggest that the rocks of the Mozambique belt had been generated by partial melting that probably involved the mixture of the archean/paleoproterozoic crust and the Mesoproterozoic magma at 1100Ma and had suffered reworking marked by the Gondwana amalgamation (Pan-African orogeny) and extensional processes marked by the Gondwana break up (East African Rift).

The D'Entrecasteaux Island (DEI) gneiss domes are fault-bounded domes with ~2.5 km of relief exposing ultrahigh-pressure (UHP) and high-pressure (HP) metamorphic gneisses and migmatites exhumed in an Oligocene-Miocene arc-continent collision and subduction zone subject to Late Miocene to Recent continental extension. To study the style of continental extension accompanying exhumation of the DEI gneiss domes, a grid of 1,518 km of 2-D multi-channel seismic (MCS) reflection data and well data is interpreted from the offshore areas surrounding the DEI, including the Trobriand basin and the Goodenough basin. The offshore study is combined with onshore geologic information to constrain the area's Oligocene to Recent basinal and tectonic evolution. MCS and well data show the Trobriand basin formed as a forearc basin caused by southward Miocene subduction at the Trobriand trench. Late Miocene basin inversion uplifted the southern and northern basin margins. Subduction slowed at ~8 Ma as the margin transitioned to an extensional tectonic environment. Since then, the Trobriand basin has subsided 1-2.5 km as a broad sag basin with few normal faults deforming the basin fill. South of the DEI, the Goodenough rift basin developed after extension began (~8 Ma) as the hanging-wall of the north-dipping Owen-Stanley normal fault bounding the southern margin of the basin. Rapid uplift of the adjacent footwall of the Owen-Stanley fault zone in the Papuan Peninsula accompanied the formation of the Goodenough submarine rift basin. The lack of upper crustal extension accompanying subsidence in the Trobriand and Goodenough basins suggests depth-dependent lithospheric extension from 8-0 Ma has accompanied uplift of the DEI gneiss domes. Structural reconstructions of seismic profiles show 2.3 to 13.4 km of basin extension in the upper crust, while syn-rift basin subsidence values indicate at least 20.7 to 23.6 km of extension occurred in the lower crust since ~8 Ma. Results indicating thinning is preferentially accommodated in the lower crust surrounding the DEI are used to constrain a schematic model of uplift of the DEI domes involving vertical exhumation of buoyant, post-orogenic lower crust, far-field extension from slab rollback, and an inverted two-layer crustal density structure. / text

Non-spherical particles are present all around us, in biological, industrial and environmental processes. Making predictions of their impact on us and systems in our vicinity can make life better for everyone here on earth. For example, the ash particles from a volcano eruption are non-spherical and their spreading in the atmosphere can hugely impact the air traffic, as was also proven in 2010. Furthermore, the orientation of the wood fibres in a paper sheet influences the final properties of the paper, and the cause of a specific fibre orientation can be traced back to the fluid flows during the manufacturing process of the paper. In this thesis, experimental and numerical work is presented with the goal to understand and utilize the behavior of elongated particles in fluid flows. Two different experimental setups are used. The first one, a turbulent half channel flow, aims at increasing the understanding of how particles with non-zero inertia behave in turbulence. The second setup is an attempt to design a flow field with the purpose to align nanofibrils and create high performance cellulose filaments. Experiments were performed in a turbulent half channel flow at different flow set- tings with dilute suspensions of cellulose acetate fibres having three different aspect ratios (length to width ratio). The two main results were firstly that the fibres agglom- erated in streamwise streaks, believed to be due to the turbulent velocity structures in the flow. Secondly, the orientation of the fibres was observed to be determined by the aspect ratio and the mean shear, not the turbulence. Short fibres were oriented in the spanwise direction while long fibres were oriented in the streamwise direction. In order to utilize the impressive properties (stiffness comparable to Kevlar) of the cellulose nanofibril in a macroscopic material, the alignment of the fibrils must be controlled. Here, a flow focusing device (resulting in an extensional flow), designed to align the fibrils, is used to create a cellulose filament with aligned fibrils. The principle is based on a separation of the alignment and the assembly of the fibrils, i.e. first align the fibrils and then lock the aligned structure. With this process, continuous filaments were created, with properties similar to that of the wood fibre at the same fibril alignment. However, the highest alignment (lowest angle) of the fibrils in a filament created was only 31o from the filament axis, and the next step is to increase the alignment. This thesis includes modeling of the alignment process with the Smoluchowski equation and a rotary diffusion. Finding a model that correctly describes the alignment process should in the end make it possible to create a filament with fully aligned fibrils. / <p>QC 20140908</p>

A região de Gondola-Nhamatanda localiza-se na parte limítrofe entre as províncias de Manica e Sofala, centro de Moçambique. Ela está geologicamente inserida no complexo de Bárue (Grupo de Chimoio) e na cobertura fanerozoica. O Complexo de Bárue é composto pelos Grupos supracrustais de Macossa e Chimoio intrudidos por rochas plutônicas de várias composições. Enquanto que a cobertura fanerozoica consiste de sedimentos terrestres e rochas vulcânicas associadas pertencentes ao Supergrupo do Karoo e à sequências do rifte Este Africano. A área de trabalho foi estudada em termos de petrografia; geoquímica de elementos maiores, traço e de terras raras; geocronologia e geologia isotópica pelos métdos U -Pb em zircão, Rb-Sr e Sm-Nd em rocha total e Rb-Sr em minerais para o granito de Inchope, quartzo-sienito do monte Chissui e fonolito do monte Xiluvo. Este estudo permitíu determinar os litotipos que intrudiram o grupo supracrustal de Chimoio , suas idades de cristalização e de diferenciação dos magmas que formaram seus protólitos e ainda o enquadramento tectônico. As rochas estudadas são basicamente calci -alcalinas com variações de meta à peraluminoso para os granitoides e quartzo-sienito e peralcalino para o fonolito do monte Xiluvo. Os granitoides do grupo de Chimoio foram cristalizados no Mesoproterozoico (idades U-Pb e Rb-Sr) a partir de protólitos Paleoproterozoicos (\'T IND.DM\' = 1,7 - 2,3 Ga); por sua vez, as rochas vulcânicas (fonolitos) do monte Xiluvo cristalizaram rápidamente no Câmbrico (idade Rb-Sr) dum protólito do Neoproterozoico-Câmbrico (\'T IND.DM\' = 0,54 - 0,56 Ga). Os dados isotópicos obtidos no presente estudo sugerem que as rochas do cinturão de Moçambique foram geradas por fusão parcial que provavelmente envolveu mistura ( valores negativos de ?Nd ) da crosta arqueana / paleoproterozoica e magma mesoproterozoico a 1100 Ma e sofreram retrabalhamento marcado pela aglutinação do Gondwana (orogenia Pan-Africana) e tafrogênese marcada pela fraturação do Gondwana (Rifte Este Africano ). / The region of Gondola-Nhamatanda is located at the border between the provinces of Manica and Sofala, central part of Moçambique. It is geologically inserted in the Bárue complex and the Phanerozoic cover. The Bárue complex is composed of the Macossa and Chimoio supracrustal groups intruded by plutonic rocks of various compositions, whereas the Phanerozoic cover consists of terrestrial sediments and volcanic rocks belonging to the Karoo Super-group and East African Rift Sequences. The work area was studied in terms of petrography; geochemistry of major elements, trace and rare earth elements; geochronology and isotope geology by the methods U -Pb in zircon, Rb-Sr and Sm-Nd in whole rock and Rb-Sr in minerals for the Inchope granite, Chissui mountain Quartzo-sienito and Xiluvo mountain phonolite. This study allowed to determine the lithotypes that intruded the Chimoio supracrustal group, its crystallization ages and the differentiation ages of the magmas that formed the protoliths and the tectonic framework. The studied rocks are basically calc-alkaline varying from meta to peraluminous for the granitoids and quartz-sienite and peralkaline for the mount Xiluvo phonolite. The Chimoio Group granitoids had been crystallized in the Mesoproterozoic (U-Pb and Rb-Sr ages) from Paleoproterozoic protoliths (\'T IND.DM\' = 1.7 - 2.4Ga); on the other hand, the volcanic rocks (phonolites) of the Xiluvo mount had crystallized fast in the Cambrian (Rb-Sr age) from a Neoproterozoic-Cambrian protolith (\'T IND.DM\' = 0.54 - 0.56Ga). The isotopic data, in the present study , suggest that the rocks of the Mozambique belt had been generated by partial melting that probably involved the mixture of the archean/paleoproterozoic crust and the Mesoproterozoic magma at 1100Ma and had suffered reworking marked by the Gondwana amalgamation (Pan-African orogeny) and extensional processes marked by the Gondwana break up (East African Rift).

No description available.

No description available.

De las numerosas subvariedades de las álgebras de Ockham, aquella estrechamente relacionada con las álgebras de De Morgan es Km,0 con m > 1, la cual está formada por las álgebras de Ockham que satisfacen la identidad adicional f2m(x) = x. Como las álgebras de Lukasiewicz-Moisil de orden n (o Ln–álgebras) tienen un reducto que es un álgebra de De Morgan, T. Almada y J. Vaz de Carvalho ([1]) consideraron una generalización de las Ln–álgebras reemplazando dicho reducto por uno que pertenece a Km,0 y, de este modo, introdujeron la variedad de las álgebras de Lukasiewicz m−generalizadas de orden n (o Lmn–álgebras). En esta tesis, nosotros continuamos con el estudio de esta variedad. Al volumen lo hemos organizado en cinco capítulos. En el Capítulo I damos nociones básicas y hacemos un repaso de los resultados más importantes de álgebra universal. Además, hemos incluido una breve exposición sobre la teoría de los cálculos proposicionales extensionales implicativos standars. Por último, describimos la localización para retículos distributivos acotados. Todos estos temas los hemos incluido tanto para facilitar la lectura como para fijar los conceptos que utilizaremos en el desarrollo de este trabajo. En el Capítulo II, comenzamos nuestro estudio de las álgebras de Lukasiewicz m– generalizadas de orden n. En primer lugar, y motivados por el rol fundamental que desempeña la implicación débil en las álgebras de Lukasiewicz de orden n, introducimos una operación de implicación en las Lmn –álgebras. Esta implicación nos permitió considerar la noción de sistema deductivo a partir de la cual caracterizamos a las congruencias. Cabe señalar que este resultado fue fundamental para describir a las congruencias principales, de manera más simple que la obtenida en [1] a partir de la teoría de las álgebras de Ockham. Además, dicha implicación nos permitió definir un elemento fundamental para obtener una nueva caracterización de las álgebras simples y hallar el polinomio discriminador ternario para esta variedad. Algunos de los temas estudiados en este capítulo fueron expuestos en las comunicaciones: Sobre las m−álgebras de Lukasiewicz generalizadas de orden n, C. Gallardo y A. Ziliani, LVIII Reunión Anual de Comunicaciones Científicas de la UMA, U.N. de Cuyo, 2008. La variedad discriminadora de las m-álgebras de Lukasiewicz generalizadas de orden n, LVIII Reunión Anual de Comunicaciones Científicas de la UMA, U.N. de Mar del Plata, 2009. Además, se encuentran publicados en [32]: Weak implication on generalized Lukasiewicz algebras of order n, A.V. Figallo, C. A. Gallardo y A. Ziliani, Bulletin of the Section of Logic, 39, 4(2010), 187–198. En el Capítulo III, y con el propósito de hallar un cálculo proposicional para el cual las Lmn–álgebras sean su contrapartida algebraica, introducimos una nueva operación de implicación a la que denominamos implicación standard. Ella jugó un papel primordial en la resolución del problema planteado y nos permitió obtener otra caracterización de las congruencias. A continuación describimos el cálculo hallado, que denotamos `mn y probamos que pertenece a la clase de los sistemas proposicionales implicativos extensionales standards. Finalmente, demostramos el teorema de completitud para `mn. Además, cabe mencionar que los resultados obtenidos en este capítulo dan respuesta positiva a un problema planteado en [1]. Algunos de estos resulatdos fueron expuestos en la siguiente presentación: On the congruence m-generalized Lukasiewicz algebras of order n, C. Gallardo y A. Ziliani, XVI EBL and 16th Brazilian Logic Conference, Petrópolis, Brasil, 2011 y han sido publicados en [33]: The Lmn–propositional calculus, C. A. Gallardo y A. Ziliani. Mathematica Bohemica, 140,1(2015), 11–33. En el Capítulo IV, desarrollamos la teoría de localización para las álgebras de Lukasiewicz m–generalizadas de orden n. En particular, para cada Lmn–álgebra L determinamos el álgebra de fracciones L[C] asociada a un conjunto ^-cerrado C de L. A continuación, introducimos la noción de 1–ideal en las Lmn–álgebras lo que nos permitió definir una topología F para ellas y el concepto de F-multiplicador. Luego, a partir de estas nociones construimos el álgebra de localización LF de L con respecto a F. Además, mostramos que la Lmn–álgebra de fracciones L[C] es un álgebra de localización. Posteriormente, definimos la noción de Lmn-álgebra de cocientes y probamos la existencia de la Lmn-álgebra maximal de cocientes. En la última sección de este capítulo nos dedicamos a analizar los resultados antes descriptos para el caso de las Lmn–álgebras finitas. En la siguiente comunicación presentamos algunos de estos temas: F–multipliers and localization of Lmn –algebras, C. Gallardo y A. Ziliani, Workshop Philosophy and History of Science State University of Campinas, UNICAMP, Campinas, Brasil, 2012 Cabe mencionar que los mismos han sido aceptados para su publicación en Journal of Multiple-Valued Logic and Soft Computing (2016). ([34]) En el Capítulo V, nos abocamos al estudio de las propiedades de las L2 n–álgebras finitas y finitamente generadas, obteniendo importantes propiedades de los átomos en estas álgebras. A continuación, describimos detalladamente a las álgebras simples. Además, determinamos la estructura de las L2 n–álgebras libres con un conjunto finito de generadores lies. Finalmente, indicamos un método para calcular el cardinal del álgebra libre con un conjunto finito n de generadores libres. / Ockham algebras have a great number of subvarieties, but the ones which are more closely related to De Morgan algebras are Km,0 with m > 1. They are constituted by Ockham algebras that satisfy the additional identity f2m(x) = x. Since Lukasiewicz- Moisil algebras of order n have a reduct which is a De Morgan algebra, T. Almada y J. Vaz de Carvalho ([1]) introduced a generalization of them, by switching this reduct by one which belongs to Km,0. Hence, they introduced the variety of m−generalized Lukasiewicz algebras of order n (or Lmn–algebras). Our aim in this thesis is to study in depth this variety. More precisely, we have organized this work in five chapters. In Chapter I, basic definitions are provided and we also do a review of the most important results in universal algebra. Furthermore, we have included as well a brief discussion on the class of standard systems of implicative extensional propositional calculi. Finally, we describe the localization for bounded distributive lattices. These topics have been included not only to simplify the reading but also to fix the notations and the definitions that we will use in this volume. In Chapter II, we began our study of m−generalized Lukasiewicz algebras of order n. First, and bearing in mind the fundamental role that the weak implication played in the study of Lukasiewicz algebras of order n, we introduced an implication operation on Lmn –algebras which generalize the latter. This notion enabled us to consider the notion of deductive systems from which we have given a new characterization of the congruence lattice on these algebras. It is worth mentioning that this result turned out to be very useful for describing the principal congruences on Lmn –algebras in a simpler way than the one obtained in [1], where the theory of Ockham’s algebras was applied. In addition, the aforementioned implication allowed us to define a fundamental element for what follows and, in this case, to obtain a new characterization of simple algebras and to describe the ternary discriminator polynomial for this variety. Some of the above results were presented in the following meetings: Sobre las m−´algebras de Lukasiewicz generalizadas de orden n, C. Gallardo y A. Ziliani, LVIII Reuni´on Anual de Comunicaciones Cient´ıficas de la UMA, U.N. de Cuyo, 2008. La variedad discriminadora de las m-´algebras de Lukasiewicz generalizadas de orden n, LVIII Reuni´on Anual de Comunicaciones Cient´ıficas de la UMA, U.N. de Mar del Plata, 2009. Furthermore, they were published in [32]: Weak implication on generalized Lukasiewicz algebras of order n, A.V. Figallo, C. A. Gallardo y A. Ziliani, Bulletin of the Section of Logic, 39, 4(2010), 187–198. In Chapter III, and in order to obtain a propositional calculus which has Lmn –algebras as the algebraic counterpart, we introduced another implication operation on these algebras which we called standard implication. This provided us with a crucial tool not only to solve the formulated problem, but also to give a new characterization of the congruence and the principal congruence lattice of these algebras, simpler than all the above obtained descriptions. Next, we described the propositional calculus, denoted by `mn , and we proved that it belongs to the class of standard systems of implicative extensional propositional calculi. Finally, the completeness theorem for `mn is obtained. It is worth noting that in this chapter we have given a positive answer to the problem posed in [1]. Besides, some of the topics presented in this chapter were previously discussed in the following event On the congruence m-generalized Lukasiewicz algebras of order n, C. Gallardo y A. Ziliani, XVI EBL and 16th Brazilian Logic Conference, Petr´opolis, Brasil, 2011. and they have been published in [33]: The Lmn –propositional calculus, C. A. Gallardo y A. Ziliani. Mathematica Bohemica, 140,1(2015), 11–33. In Chapter IV, we have developed the theory of localization for m−generalized Lukasiewicz algebras of order n. In particular, for each Lmn –algebra L we have determined the Lmn– algebra of fractions L[C] relative to an ^-closed system C of L. Later on, we introduced the notion of 1–ideal on Lmn –algebras which allows us to consider a topology F for them and the concept of F-multiplier. Furthermore, we have proved that the Lmn –algebra of fractions L[C] is an Lmn –algebra of localization. Moreover, we have defined the notion of Lmn –algebra of quotients and we have proved the existence of the maximal Lmn –algebra of quotients. By the end of this chapter, our attention is focused on analyzing the aforementioned results for the case of finite Lmn –algebras. Some of these results were presented in this report: F–multipliers and localization of Lmn –algebras, C. Gallardo y A. Ziliani, Workshop Philosophy and History of Science State University of Campinas, UNICAMP, Campinas, Brasil, 2012. Besides, it is worth mentioning that these topics have been accepted for publication in the Journal of Multiple-Valued Logic and Soft Computing (2016). ([34]). In Chapter V, our main aim was to study the properties of finite and finitely generated L2 n–algebras. In particular, we have obtained important results on the atoms of them. Next, we have provided an exhaustive description of the simple L2 n–algebras. Finally, we have determined the structure of the free L2 n–algebras with a finite set of free generators and we have also indicated a method to calculate the cardinal number of them in terms of the number of the free generators.

Le travail présenté dans ce manuscrit concerne la modélisation du comportementthermomécanique de films thermoplastiques déformés à l’état caoutchoutique. Lamodélisation du comportement des films amorphes isotropes est réalisée sur la base desmodèles de Lodge ou MSF. L’amélioration des prédictions des modèles pour destempératures de déformations proches de la température de transition vitreuse est possible enconsidérant dans le spectre des temps de relaxation des temps courts provenant de la zone detransition vitreuse. La modélisation du comportement de films amorphes anisotropes a étéeffectuée en considérant que l’anisotropie est due à une pré-déformation équivalente lors duprocédé de fabrication.Au cours de cette étude, les relations entre l’orientation de la phase cristalline et les propriétésmécaniques à température ambiante des films semi-cristallins ont été démontrées Au cours dela déformation à l’état caoutchoutique de ces films, la phase cristalline tend à s’orienterparallèlement à la direction de sollicitation par fragmentation des cristaux initiaux. En sebasant sur ces observations expérimentales, la modélisation du comportement mécanique desfilms semi-cristallins est possible en découplant les contributions en contrainte de la phasecristalline et de la phase. La réorientation des cristaux génère un phénomène de durcissementstructural sous contrainte qui peut être prédit par le modèle. / The work presented in this manuscript is devoted to the modeling of the thermomechanicalbehavior of polymer films deformed at the rubbery state. The modeling of the isotropicamorphous films is realized using the Lodge and the MSF models. For deformations appliednear the glass transition temperature, the predictions of these models are improved byincluding relaxation times coming from the glass transition domain in the spectra. Forpre-oriented amorphous films, the anisotropy is modeled by considering that it is due to aprevious equivalent deformation during the fabrication process.The relationship between the crystalline phase and the mechanical behavior at roomtemperature for the semi-crystalline films is established. During the deformation at therubbery sate of the semi-crystalline films, a reorientation of the crystalline phase occurs alongthe stretching direction. Based on the experimental observations, a semi-empirical model isdeveloped in order to describe the mechanical behavior of the semi-crystalline films. In thismodel, the contributions of both phases, amorphous and crystalline are separated. Thereorientation of the crystalline phase leads to a strain hardening stage which could bepredicted by the model

We develop a two dimensional model that simulates the response of the crust to prolonged mantle-derived intrusions in arc environments. The domain includes the entire crustal section and upper mantle and focuses on the evolving thermal structure due to intrusions and external tectonic forcing. We monitor the thermal response, melt fraction and volume for different environments after a definite time by considering geologically relevant melt flux and extensional tectonic rates. The amount of crustal melt versus fractionated primary mantle melts present in the crustal column helps determine crustal structure and growth through time. We observe that with a geophysically estimated flux and tectonic rate, the mantle-derived magma bodies can melt the surrounding volume of crust. We express the amount of crustal melting in terms of an efficiency; therefore we define the melting efficiency as the ratio of the melted volume of crustal material to the volume of melt expected from a strict enthalpy balance as explained by Dufek and Bergantz (2005). Melting efficiencies are less than 1.0 in real systems because heat diffuses to sections of the crust that never melt. The maximum calculated efficiency is 0.05 in our model while most of our simulations show zero efficiency. Additionally, maximum total melt amount is observed in relatively greater extensional environments (0.02 m/yr) and high intrusion rates (10⁻² m³/m²/yr) and in long time periods (2 x 10⁶ years). However, maximum crustal melting in the same environment is reached in 1.2 x 10⁶ years. The relative amounts of mantle-derived and crustal melts in the total volume of magma suggest that the majority of magma composition in crustal column is derived from the mantle material.

Στόχος της παρούσας Διατριβής είναι να ερευνήσει τη διαμόρφωση των αντιλήψεων γύρω από τα απειροστά και τις σχετικές μ’ αυτά επ’ άπειρον διαδικασίες σε δύο κατευθύνσεις: 1. Την ιστορική εξέλιξη και ερμηνεία της έννοιας του απειροστού και 2. Την ανάλυση των σχετικών αντιλήψεων των φοιτητών-αυριανών καθηγητών των μαθηματικών. Στο πρώτο μέρος της διατριβής γίνεται ανάλυση και ερμηνεία των αντιλήψεων για τα απειροστά που εκφράστηκαν από την Αρχαία μέχρι τη σύγχρονη εποχή. Η μελέτη αυτή οδηγεί στην κατασκευή ενός ερμηνευτικού πλαισίου που διακρίνει τα ιστορικά ερμηνευτικά πρότυπα (μοντέλα) των απειροστών σε τρία αντιθετικά ζεύγη ως εξής: Ι. Εντασιακά-Εκτασιακά πρότυπα απειροστών. ΙΙ. Ομογενή-Μη ομογενή πρότυπα απειροστών. ΙΙΙ. Μηδενοδύναμα-μη μηδενοδύναμα πρότυπα απειροστών. Το παραπάνω πλαίσιο χρησιμοποιείται στο δεύτερο μέρος της διατριβής ως μεθοδολογικό εργαλείο για το σχεδιασμό διδακτικών πειραμάτων και την ανάλυση των εμπειρικών δεδομένων. Ειδικότερα, έγιναν τρία διδακτικά πειράματα με φοιτητές του Τμήματος των Μαθηματικών. Στο πρώτο πείραμα ερευνήθηκε η έννοια της ταχύτητας σύγκλισης ακολουθίας ως μια διαισθητική προσέγγιση στα απειροστά. Στο δεύτερο πείραμα, ερευνήθηκε η δυνατότητα προσέγγισης στα απειροστά μέσα από κλασσικά θέματα των διακριτών Μαθηματικών, όπως ο υπολογισμός του αθροίσματος των δυνάμεων φυσικών αριθμών. Στο τρίτο πείραμα έγινε διδασκαλία ενός συγκεκριμένου μοντέλου των υπερ-πραγματικών αριθμών και αναλύθηκαν τα αποτελέσματα. Τα κυριότερα συμπεράσματα της διατριβής είναι: 1. Η σημασία της κατασκευής μαθηματικών οντοτήτων που ικανοποιούν τα αξιώματα της Πραγματικής Ανάλυσης, 2. Η σημασία της διαισθητικής προσέγγισης και τα όριά της και 3. Η καταλληλότητα των προτεινόμενων μοντέλων και θεμάτων, ως διδακτικού υλικού. / The aim of this Ph.D thesis is the conceptions regarding infinitesimals and infinitesimal processes in two directions: 1. The historical evolution and interpretation of the concept of infinitesimal and 2. The analysis of the conception of the students–prospective teachers of Mathematics. The first part of the thesis contains a study and an analysis of infinitesimals that appeared in History from Antiquity to our era. This study leads to the construction of a framework of interpretation which distinguishes the interpretative models into three pairs of opposites: I. Homogenous-Nonhomogenous, models of infinitesimals II. Intensional-Extensional, models of infinitesimals III. Nilpotent-Non nilpotent, models of infinitesimals The above framework is applied in the second part of the thesis, as a methodological tool for the design of didactical experiments with students of Mathematics. The first experiment concerns a research study on the notion of the rate of convergence, as an intuitive approach to infinitesimals. The second experiment is referred to the emergence of infinitesimals through classical themes (issues) of discrete mathematics, such as the computation of sums of powers of integers. The third experiment concerns the teaching of a specific model of Hyper-Real numbers and the analysis of its empirical outcomes. The main conclusions of this thesis are: 1. The significance of the construction of mathematical entities, which satisfy the axioms of Real Analysis. 2. The significance of the intuitive approach, as well with a focus on its foreseen limitations. 3. The relevance of the proposed models and themes as potential didactical material.