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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

The migration of the Galilean satellites in the circumjovian disk

Li, Wing-yi, 李泳誼 January 2014 (has links)
Various physical and orbital properties of the Galilean satellites, such as the decreasing density with distance and the Laplace resonance, imply an intriguing formation history of the system. With prograde orbits of low inclinations and eccentricities, the satellites are thought to be formed in a circumjovian disk composed of gas and solids. Satellites grew by accreting solids in the disk, and migrated due to disk-satellite interaction, both of which depend on disk properties. In this thesis, the migration of the Galilean satellites was studied, and how satellite migration can possibly help in assembling the satellites into their current Laplace configuration was also investigated. The gas-starved subnebula model by Canup & Ward (2002) and its modified version proposed by Turner et al. (2013) (TLS13) were adopted in this study. Supplied by inflowing materials from the ambient solar nebula, the disk profiles are determined by disk viscosity, disk opacity and the inflow timescale of the supply. Including a temperature-dependent opacity model, the TLS13 disk has non-smooth disk profiles, producing sharp changes in the profile gradients. The disk was assumed to deplete with the dissipation of the solar nebula. Non-isothermal type I regime was adopted in the migration of the satellites. Potential saturation of the corotation torque was also taken into account in the study. It was found that outward migration is possible in our disks, which contrasts with the solely inward migration in the isothermal regime, and that exist positions where the disk torque is zero and satellite migration is stalled. These zero-torque positions evolve with the disk. The non-smooth profile gradients of the TLS13 disk produce multiple zero-torque positions, resulting in interesting migration of the satellites. Using the SyMBA symplectic integrator, simulations for the migration of the satellites were conducted for various disk models and migration regimes. The effect of satellite growth and an inner cavity in the disk on satellite migration was included in this study. To begin with, single-satellite runs were conducted to study the migration behaviours of the individual satellites. Initial locations of the satellites were searched from the results of single-satellite runs, in which Europa has to cross Io’s orbit in most cases. Simulations with multiple satellites were then conducted to search for ways for the satellites to arrive at their current orbital configuration. Various satellite interactions were investigated, including the convergence of Europa and Ganymede into a 2:1 resonance and the effects of earlier-generation satellites. At last, the migration of multiple satellites in a disk with an inner cavity was explored, in which systems with similar orbital configuration as the real Galilean satellites could be reconstructed. Despite this, assembling the satellites into the Laplace resonance by migration due to interaction with a circumjovian disk was found to be difficult, probably due to the intrinsically faster migration of Io over Europa arising from differences in mass and location between the two satellites. / published_or_final_version / Earth Sciences / Master / Master of Philosophy
2

Symphony No. 1 “The Galilean Satellites”

Cortes, Michael 30 July 2010 (has links)
No description available.
3

Os aristotelismos da linguagem das variáveis em sociologia

Totaro, Paolo 09 October 2006 (has links)
Made available in DSpace on 2015-03-04T22:00:55Z (GMT). No. of bitstreams: 0 Previous issue date: 9 / Nenhuma / Esta dissertação é uma crítica epistemológica da linguagem das variáveis, a abordagem quantitativa em sociologia fundada por Paul Lazarsfeld. Ela se destaca das polêmicas anteriormente dirigidas contra a proposta de Lazarsfeld por desenvolver-se não a partir do ponto de vista histórico-interpretativo, mas de uma perspectiva interna à própria lógica dos procedimentos empírico-matemáticos. Seu encaixe analítico será o das condições epistemológicas apontadas pelo trabalho de Galileo Galilei, que permitiram, pela primeira vez na história do pensamento humano, o uso da matemática como linguagem descritiva dos fenômenos empíricos. A falta de tais condições é individuada como a origem de toda dificuldade da linguagem das variáveis e também de toda validade das argumentações contra ela dirigidas / This dissertation is an epistemological critic of the language of variables, the quantitative approach in sociology founded by Paul Lazarsfeld. It hilights itself from the previous controversies directed against Lazarsfeld’s proposal because it isn’t developed from the historical interpretative point of view, but from an internal perspective to the logical itself of the mathematical empirical procedures. Its analytical fitting will be that one of the epistemological conditions pointed by Galileo Galilei’s work, which allowed, for the first time in the history of human thinking, the use of mathematics as descriptive language of the empirical phenomena. The lack of such conditions is individualized as the origin of all difficulty of the language of variables as well as of the whole validity of the argumentations directed against it
4

Galilean moon tour using simplified trajectory computational techniques

Williams, Ryan. January 2006 (has links)
Thesis (M.S.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 23, 2007) Includes bibliographical references.
5

<b>Formation and evolution of outer solar system components</b>

Melissa Diane Cashion (18414999) 22 April 2024 (has links)
<p dir="ltr">We present a model describing an impact jetting origin for the formation of chondrules, the mm– scale, igneous components of chondritic meteorites which originated during the first few million years of solar system history. The ubiquity of chondrules in both non-carbonaceous and carbonaceous chondrites suggests their formation persisted throughout the protoplanetary disk, but their formation mechanism is debated and largely unexplored in the outer disk.<b> </b>Using the iSALE2D shock physics code, we generate models of the process of impact jetting during mixed material (dunite and water ice) impacts that mimic accretionary impacts that form giant planet cores. We show that the process of impact jetting provides the conditions necessary to satisfy critical first-order constraints on chondrule characteristics (size, shape, thermal history). We then explore the implications of chondrule formation by impact jetting during the formation of giant planet cores by combining the original results with simulations of giant planet core accretion generated using a Lagrangian Integrator for Planetary Accretion and Dynamics (LIPAD) code.</p><p dir="ltr">The second closest Galilean satellite to Jupiter is Europa, an ocean world with an outer ice shell and subsurface water ocean encapsulating its rocky core. The surface of Europa is covered in double ridges. These features are defined by two topographic highs about 100 meters tall, with a central trough between them, which extend for hundreds of kilometers over the surface of the moon. Accurate models for the formation of features as prominent as double ridges will help to further constrain the interior structure and dynamics of the interior of the body. We use analytical and numerical finite element models to show that the incremental growth of an ice wedge within the ice shell can cause deformation matching the observed size and shape of observed double ridges on Europa. These models indicate that the total height and width of the ridges correspond to the depth of the wedge, so that deeper wedges create shorter and broader ridges. We consider different sources for the wedge material and ultimately argue in favor of local sources of liquid water within the ice shell.</p>
6

Origin and formation of the regular satellites around planets / Etudes des conditions de formation des satellites glacés de Jupiter dans le cadre de la mission JUICE

Ronnet, Thomas 01 October 2018 (has links)
Les travaux réalisés au cours de cette thèse s'intéressent à l'origine et à la formation des satellites naturels réguliers de Mars et Jupiter qui sont les cibles de futures missions d'exploration spatiale dédiées à leur caractérisation. Le cas controversé de l'origine de Phobos et Deimos, les lunes de Mars, est adressé et il est montré que leur formation à la suite d'un impact géant permettrait de réconcilier leurs propriétés orbitales et physiques. Concernant les satellites galiléens orbitant Jupiter, il est montré que dans le contexte classiquement utilisé de leur formation, la croissance des lunes a certainement procédé par l'accrétion de grains de poussières, un processus appelé "pebble accretion", plutôt que par celle de corps plus grands comme il est typiquement considéré. Des propriétés intéressantes, ainsi que d'autres plus problématiques, de la croissance des lunes galiléennes par "pebble accretion" sont dérivées. Dans un second temps, le transport de solides nécessaires à l'assemblage des lunes galiléennes dans le disque circum-jovien est étudié dans le contexte des récentes théories de formation des planètes géantes. Nous montrons que la vision classique selon laquelle le gaz accrété par Jupiter transporte assez de solides pour former ses lunes est probablement erronée. Il est proposé que, aidée par la formation de Saturne, Jupiter a pu capturer dans son disque assez de planétésimaux pour assembler les satellites galiléens. Contrairement aux précédents scénarios, le cadre proposé prédit que des analogues aux satellites galiléens ne se forment pas autour de toutes les planètes géantes / This thesis aims at better understanding the origin and formation of the martian moons, Phobos and Deimos, and the major jovian satellites known as the galilean moons, each of these systems being the target of future space exploration missions dedicated to their characterization. We address the puzzling origin of Phobos and Deimos and show that their formation following a giant impact could allow to account for both their orbital and physical properties. As regards the galilean moons, we argue that their growth would likely proceed through the accretion of small dust grains, a process known as pebble accretion, rather than through the accretion of larger satellitesimals within the typical framework assumed for their formation. We derive some interesting properties as well as some drawbacks of pebble accretion in the galilean system. Then, the delivery of solid material from the protoplanetary disk to the circum-jovian disk is investigated in light of recent developments of the theory of giant planets' formation. It is shown that the classic view that the gas accreted by Jupiter transports enough solids to build many galilean-like satellites is likely to be erroneous and some other mechanism must have taken place to account for the presence of the massive galilean moons. It is proposed that, with the help of Saturn's formation, Jupiter could have captured within its disk enough planetesimals on initially heliocentric orbits to build the galilean moons. Unlike previous scenarios, the proposed framework predicts that the presence of galilean analogues would not be ubiquitous around extrasolar giant planets
7

Estudo de formação de satélites regulares de planetas gigantes usando integração numérica hidrodinâmica bidimensional com perturbação da estrela / Study of formation of the regular satellites of the giant planets using bidimensional hydrodynamical numerical integration with the perturbationof the star

Moraes, Ricardo Aparecido de 28 March 2018 (has links)
Submitted by Ricardo Aparecido de Moraes (ricardo.moraes07@gmail.com) on 2018-05-18T19:00:41Z No. of bitstreams: 1 diss.pdf: 66909549 bytes, checksum: 4760a79275fcbb266e054bab38611e16 (MD5) / Approved for entry into archive by Pamella Benevides Gonçalves null (pamella@feg.unesp.br) on 2018-05-18T19:16:15Z (GMT) No. of bitstreams: 1 moraes_ra_dr_guara.pdf: 66909549 bytes, checksum: 4760a79275fcbb266e054bab38611e16 (MD5) / Made available in DSpace on 2018-05-18T19:16:15Z (GMT). No. of bitstreams: 1 moraes_ra_dr_guara.pdf: 66909549 bytes, checksum: 4760a79275fcbb266e054bab38611e16 (MD5) Previous issue date: 2018-03-28 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / A formação de satélites em um disco circumplanetário é tida como sendo similar a formação de planetas em um disco protoplanetário, especialmente super Terras rochosas. Dessa forma, é possível utilizar sistemas com satélites massivos para se testar teorias de formação que podem ser aplicadas à planetas extrassolares. Um melhor entendimento sobre a origem dos satélite nos dará importantes informações sobre a vizinhança do planeta durante suas últimas fases de formação. Neste trabalho nós utilizamos simulações de N-corpos e hidrodinâmicas para investigar a formação e migração dos satélites galileanos. Nos modelos de N-corpos nós simulamos um disco circumplanetário estático (sem a entrada de material vindo de fontes externas), com baixa viscosidade, onde a ação do disco gasoso sobre os satélites foi aproximada a partir de prescrições analíticas para a migração do tipo I e o amortecimento da excentricidade e inclinação. O disco de gás é representado por um perfil de densidade superficial radial. Um estudo detalhado sobre os parâmetros do disco mostraram que o número final de satélites é muito influenciado pela distribuição inicial dos embriões e pelo perfil inicial da nébula gasosa. Para distribuições de gás com baixa dependência radial a formação de satélites massivos próximos da região dos satélites galileanos é favorecida. Ainda, mostramos que a formação de satélites tão massivos quanto Ganímedes e Calisto pode ser atingida apenas em discos mais quentes, onde a linha do gelo está inicialmente localizada em torno de 30 RJ . Em nossas simulações hidrodinâmicas foram testadas diferentes condições de contorno, distribuição superficial de gás e de temperatura para o disco circumplanetário. Nossos resultados indicam que Júpiter ainda acretava material durante a migração dos satélites galileanos, os satélites migraram em um regime do tipo I na maior parte de sua evolução e a probabilidade de formação de satélites massivos entre os satélites galileanos é baixíssima, nesse caso se mais satélites se formassem no disco joviano sua massa deveria ser menor do que a observada para os satélites galileanos / The formation of satellite systems in circumplanetary disks is believed to be similar to the formation of rocky planets in a protoplanetary disk, especially Super-Earths. In this way, it is possible to use massive satellite systems to test the theories of planetary formation. A better understanding of the satellites origin could give important informations about the environment near the forming planet during its late stages of formation. In this work we used N-body and hydrodynamic simulations to study the formation and migration of the Galilean satellites. With the N-body models with simulated a static, low viscous circumplanetary disk, where the actions of the gaseous disk was modeled using analytical prescriptions for the type I migration, eccentricity and inclination damping. A detailed study of the disk parameters showed that the final number of satellites is strongly influenced by the initial distribution of the embryos and by the initial gas density profile. For flatter gas distributions the formation of massive satellites close to the region of the Galilean satellites. Furthermore, we show that the formation of satellites as massive as Ganymede and Callisto can be achieved only in hotter disks, where the ice line is initially located around 30 RJ . In our hydrodynamic simulations we tested different boundary conditions, gas density distributions and temperature distribution for the circumplanetary disk. Our results indicate that Jupiter was still forming during the period of migration of the Galilean satellites, the satellites migrated in a type I regime for most part of their evolution and the probability of formation of massive satellites between the Galilean satellites is very low, in this case if more satellites were formed in the Jovian disk, the mass of these bodies should be smaller that what is observed for the Galilean satellites / 2013/24281-9
8

L'expérience MAJIS : développement d'un imageur spectral pour les lunes de Jupiter / The MAJIS experiment : development of a hyperspectral imager for the Galilean moons

Guiot, Pierre 28 October 2019 (has links)
La mission JUICE de l’ESA sera la troisième mission d’exploration entièrement dédiée au système de Jupiter, et la première à se concentrer sur les lunes Galiléennes glacées susceptibles d’abriter des océans d’eau liquide. Prévue pour un lancement en 2022 et une insertion en orbite jovienne fin 2029, la sonde emportera parmi ses 11 instruments le spectro-imageur MAJIS. Les données d’un tel instrument comprennent une image à haute résolution spatiale de la zone étudiée et un spectre pour chacun des pixels de cette image. Ce spectre, dans la gamme allant de 0.5 à 5.5 µm, permet d’obtenir des informations physico-chimiques sur le contenu du pixel concerné. Le laboratoire où j’ai effectué mon travail de thèse, l’IAS, s’est vu confier la responsabilité de la réalisation de MAJIS. Dans ce contexte, l’objectif de mon travail était de contribuer à la définition et à l’implémentation de l’étalonnage de l’instrument : j’ai pour cela dû comprendre d’abord ses objectifs scientifiques et les exigences instrumentales qui en découlent, et maîtriser les caractéristiques des sous-systèmes qui composent MAJIS. J’ai tout d’abord traité les données de l’imageur intégral de champ de SPHERE, un instrument du VLT, qui avait observé la lune Galiléenne volcanique Io en 2014. Bien que ce satellite soit un objectif mineur de la mission JUICE, j’ai dû me confronter au fonctionnement de l’instrument pour en réduire les données et le traitement des spectres a requis le développement d’un modèle photométrique d’observation de la surface que j’ai pu confronter à la réalité et à d’autres études. L’identification de nombreux biais systématiques dans ces données et la quantification de ses limites de détection spatiales et spectrales m’ont permis de souligner l’aspect critique de la phase d’étalonnage de MAJIS pour que ses données soient exploitables. Avant cette étape toutefois, la connaissance des sous-systèmes qui vont constituer l’instrument est elle aussi nécessaire car certains de leurs paramètres conditionneront le déroulement de cet étalonnage et ils ne pourront pas tous être mesurés à cette occasion. J’ai donc caractérisé, à l’aide des bancs optiques dédiés à l’IAS, le plan focal de l’instrument et surtout son détecteur CMOS infrarouge de type HgCdTe. J’ai pu mesurer ses caractéristiques les plus courantes, comme son courant d’obscurité, sa profondeur de puits, son efficacité quantique, son éventuelle persistance, son bruit de lecture et la linéarité de sa réponse. Dans le cas d’une mission vers Jupiter, un autre aspect des performances du détecteur doit être étudié en détail : sa résistance aux radiations, particulièrement intenses dans la magnétosphère jovienne. J’ai pu effectuer une série de tests sur des détecteurs témoins avec des sources d’électrons, de protons et de photons de hautes énergies, qui m’ont permis de montrer la très bonne résistance du plan focal aux dégâts permanents. Ces données ont aussi permis de caractériser expérimentalement le signal transient induit par un bombardement aux électrons, ce qui m’a permis de valider l’approche de filtrage de ce signal qui sera implémentée en vol. C’est enfin grâce aux résultats de ces trois approches et au développement d’un modèle photométrique complet de l’instrument et de son dispositif d’étalonnage, que j’ai pu discuter l’architecture de ce dernier et proposer des séquences de mesure pour la campagne d’étalonnage. J’ai donc travaillé avec les ingénieurs du laboratoire et des industriels pour réaliser ce dispositif d’étalonnage, sélectionner les sources de lumière qui permettront la mesure de la réponse spatiale, spectrale et radiométrique de l’instrument nécessaires à l’interprétation de ses données au cours de la mission. Au moment de la rédaction de ce manuscrit, le banc d’étalonnage était en cours d’assemblage et j’ai donc pu conclure ce travail par la confrontation de mon modèle aux résultats expérimentaux de validation de certaines voies optiques du dispositif d’étalonnage. / The ESA JUICE mission will only be the third mission fully dedicated to exploring the Jupiter system, and the first with a specific focus on the icy Galilean moons that may harbor oceans of liquid water. Planned for launch in 2022 for a Jovian orbit insertion in late 2029, the probe will carry MAJIS among its 11 instruments, an imaging spectrometer operating from the visible to medium infrared wavelengths. This type of instrument provides very comprehensive data of the observed surface or atmosphere/exosphere: its high spatial resolution capability provides geomorphological information, such as the presence of craters or faults that mark the age and activity of the terrain, while for each pixel a spectrum is acquired. This spectrum, ranging from 0.5 to 5.5 $mu$m, yields physical and chemical information on the region of interest, thus placed in its geomorphic context. The Institut d'Astrophysique Spatiale, my PhD host laboratory, has a legacy of development of such instruments, prominently OMEGA aboard the 2003 Mars Express probe, of which MAJIS is the latest and current project. In this context, my work’s aim was to contribute to the definition and implementation of the instrument’s calibration: to achieve that I first had to understand its scientific objectives and the resulting instrumental requirements, as well as mastering the characteristics of MAJIS subsystems. As part of that process, I analyzed recent data of Io acquired with SPHERE, an integral field spectrometer on the VLT, which possesses similarities with the expected data products of MAJIS. Though this satellite is a minor objective of the JUICE mission, I had to understand the instrument itself in order to reduce its data and the spectra analysis required the development of a photometric model of a surface observation which I confronted to the reality and to previous studies. The identification of many systematic biases in these data and the quantification of its spatial and spectral detection limits allowed me to highlight the critical aspect in the upcoming calibration phase of MAJIS in order to get interpretable in-flight data. To reach this goal the knowledge of the subsystems of the instrument is also necessary because their behavior will condition the calibration scenario and all their parameters will not be measured again on this occasion. I have therefore characterized, using dedicated optical benches, the focal plane of the instrument and especially its HgCdTe CMOS infrared detector. I was able to measure its most common characteristics, such as its dark current, full-well capacity, quantum efficiency, persistence and readout noise. The knowledge of QE and full-well depth was incorporated into an end-to-end radiometric model of MAJIS, which I fed with the spectral radiance of different scientific targets, including modeled ionian surface flows. In turn, this allowed me to select sources and optical solutions suitable for calibration. Due to the intense radiation levels in the Jovian magnetosphere, the detector’s resilience to radiations also needed to be studied. I was able to perform three test campaigns on control detectors with sources of electrons, protons and high energy photons, which allowed me to show the overall very good resilience of the focal plane to permanent damages and to validate the foreseen transient effects reduction algorithms. These three approaches required that I develop a complete photometric model of the instrument and of its calibration setup which I used to discuss its design and submit test sequences for the calibration campaign. I have worked with our laboratory engineers and industrials to design then build the calibration setup with the light sources that will allow measurement of the spatial, spectral and radiometric responses of the instrument, required to interpret its data during the mission.
9

A noção de referencial : uma interação cognitiva entre a mecânica newtoniana e a relativística

Dias, Lisete Funari January 2010 (has links)
Neste trabalho, propomos um conjunto de estratégias para enfrentar os obstáculos epistemológicos à aprendizagem da cinemática na Teoria da Relatividade Restrita. Tais estratégias são baseadas na proposta da noção de perfil conceitual de referencial (Ayala & Frezza, 2007) e visam promover uma interação cognitiva entre a Mecânica Newtoniana e Relativística. O perfil conceitual (Mortimer, 1995-2000) é um modelo para compreender a evolução conceitual em sala de aula. Para tais objetivos, foi desenvolvido um conjunto de ações em uma seqüência de aplicações de pré-testes e pós-testes com a finalidade de explicitar a concepção dos alunos sobre o aspecto a ser investigado e avaliar a evolução conceitual destes. A diferenciação entre as concepções dos alunos e aquelas cientificamente aceitas deu-se através da interpretação das concepções apresentadas, de discussões teóricas acerca do tema e da apresentação de animações construídas com o software Modellus. O público-alvo deste trabalho é formado por alunos de Licenciatura em Física, e o objetivo do mesmo é contribuir para a formação destes estudantes, futuros professores de Física. / In this work, we propose a set of strategies to face the epistemological obstacles to learning the kinematics in the Restricted Theory of Relativity. Such strategies are based on the proposal of the notion of conceptual profile of reference (Ayala & Frezza, 2007) and promote an interaction between cognitive Newtonian Mechanics and Relativistic Mechanics. The conceptual profile (Mortimer, 1995-2000) is a model for understanding the conceptual evolution of students in classroom. For these goals, we developed a set of actions in a sequence of applications of pre-tests and post-tests in order to explain the conception of students on the aspect to be investigated, and to assess your conceptual evolution. The differentiation between the students' conceptions and scientifically acceptable ones came through the interpretation of the concepts presented, theoretical discussions about the topic and the presentation of animations built with the software Modellus. The target of this work is formed by graduation students in Physics in order to contribute to your formation as future physics teachers.
10

A noção de referencial : uma interação cognitiva entre a mecânica newtoniana e a relativística

Dias, Lisete Funari January 2010 (has links)
Neste trabalho, propomos um conjunto de estratégias para enfrentar os obstáculos epistemológicos à aprendizagem da cinemática na Teoria da Relatividade Restrita. Tais estratégias são baseadas na proposta da noção de perfil conceitual de referencial (Ayala & Frezza, 2007) e visam promover uma interação cognitiva entre a Mecânica Newtoniana e Relativística. O perfil conceitual (Mortimer, 1995-2000) é um modelo para compreender a evolução conceitual em sala de aula. Para tais objetivos, foi desenvolvido um conjunto de ações em uma seqüência de aplicações de pré-testes e pós-testes com a finalidade de explicitar a concepção dos alunos sobre o aspecto a ser investigado e avaliar a evolução conceitual destes. A diferenciação entre as concepções dos alunos e aquelas cientificamente aceitas deu-se através da interpretação das concepções apresentadas, de discussões teóricas acerca do tema e da apresentação de animações construídas com o software Modellus. O público-alvo deste trabalho é formado por alunos de Licenciatura em Física, e o objetivo do mesmo é contribuir para a formação destes estudantes, futuros professores de Física. / In this work, we propose a set of strategies to face the epistemological obstacles to learning the kinematics in the Restricted Theory of Relativity. Such strategies are based on the proposal of the notion of conceptual profile of reference (Ayala & Frezza, 2007) and promote an interaction between cognitive Newtonian Mechanics and Relativistic Mechanics. The conceptual profile (Mortimer, 1995-2000) is a model for understanding the conceptual evolution of students in classroom. For these goals, we developed a set of actions in a sequence of applications of pre-tests and post-tests in order to explain the conception of students on the aspect to be investigated, and to assess your conceptual evolution. The differentiation between the students' conceptions and scientifically acceptable ones came through the interpretation of the concepts presented, theoretical discussions about the topic and the presentation of animations built with the software Modellus. The target of this work is formed by graduation students in Physics in order to contribute to your formation as future physics teachers.

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