Avaliação da estabilidade térmica e oxidativa do biodiesel de algodão e do efeito da adição de antioxidantes (α-tocoferol e BHT)

This work aims to study the effects of adding antioxidants, such as, α- tocopherol and BHT on the thermal and oxidative stability of biodiesel from cottonseed (B100). The Biodiesel was obtained through the methylical and ethylical routes. The main physical and chemical properties of cotton seed oil and the B100 were determined and characterized by FTIR and GC. The study of the efficiency of antioxidants, mentioned above, in concentrations of 200, 500, 1000, 1500, 2000ppm, to thermal and oxidative stability, was achieved by Thermogravimetry (TG), Differential Thermal Analysis (DTA), Differential Scanning Calorimetry (DSC), Differential Scanning Calorimetry - Hi-Pressure (P-DSC) and Rancimat. The Biodiesel obtained are within the specifications laid down by Resolution of ANP No7/2008. The results of TG curves show that the addition of both antioxidants, even in the lowest concentration, increases the thermal stability of Biodieseis. Through the DTA and DSC it was possible to study the physical and chemical transitions occurred in the process of volatilization and decomposition of the material under study. The initial time (OT) and temperature (Tp) of oxidation were determined through the P-DSC curve and they showed that the α-tocopherol has a pro-oxidant behavior for some high concentrations. The BHT showed better results than the α-tocopherol, with regard to the resistance to oxidation

Síntese e caracterização de compostos de coordenação homolépticos e heterolépticos com o ligante ácido kójico

The present work has as main objective to contribute to the coordination chemistry of the ligand kojic acid, with the synthesis and characterization of the homoleptic compounds [Al(kj)3], [Fe(kj)3], [Fe(kj)2], [Cu(kj)2] e [Ru(kj)3], and the new heteroleptic complexes, trans- K2[Fe(kj)2(CN)2] and trans-Na2[Ru(kj)2(CN)2]. The obtained compounds were characterized by vibrational spectroscopy in the infrared region (IV) and Electronic spectroscopy in the ultraviolet and visible region (Uv-Vis). The infrared results indicated the coordination of the bidentate ligand kojic acid, due to reductions in the values of the stretching frequencies of the carbonyl and double bonds, compared to the free ligand for all complexes obtained. The presence of new vibrational modes indicated the change of symmetry of the molecules in the new compounds synthesized. Additionally, the presence of vibrational modes assigned to metal-oxygen also contributed to confirm the ligand coordinating to the metal ions. Through this technique, was also possible to perform correlations of the numbers of vibrational modes, in the region 1400-900 cm-1 and the compounds geometry. The heteroleptic compounds exhibited υC≡N in 2065 and 2053 cm-1, respectively, for the trans-K2[Fe(kj)2(CN)2] and trans-Na2[Ru(kj)2(CN)2], indicating coordination of the cyano ligand to metal ions FeII e RuII. Comparing the obtained values with literature data was possible to identify the complex isomerism as trans. In relation to the results of electronic spectroscopy, studies of pH variation of kojic acid provided information on the distribution of electron density in the molecule, showing characteristic spectral profile of kojic ion and its protonated form (Hkj, kojic acid), with two bands at 215 and 269 nm, or deprotonated (kj-), with bands at 226 and 315 nm. The electronic spectra obtained for all complexes in aqueous medium, in the ultraviolet region, exhibited variations of the energies assigned to kojic acid intraligand transitions while in the visible region, only transitions assigned to charge transfer of iron and ruthenium complex have been identified

Joker: um realizador de desenhos animados para linguagens formais

Using formal methods, the developer can increase software s trustiness and correctness. Furthermore, the developer can concentrate in the functional requirements of the software. However, there are many resistance in adopting this software development approach. The main reason is the scarcity of adequate, easy to use, and useful tools. Developers typically write code and test it. These tests usually consist of executing the program and checking its output against its requirements. This, however, is not always an exhaustive discipline. On the other side, using formal methods one might be able to investigate the system s properties further. Unfortunately, specification languages do not always have tools like animators or simulators, and sometimes there are no friendly Graphical User Interfaces. On the other hand, specification languages usually have a compiler which normally generates a Labeled Transition System (LTS). This work proposes an application that provides graphical animation for formal specifications using the LTS as input. The application initially supports the languages B, CSP, and Z. However, using a LTS in a specified XML format, it is possible to animate further languages. Additionally, the tool provides traces visualization, the choices the user did, in a graphical tree. The intention is to improve the comprehension of a specification by providing information about errors and animating it, as the developers do for programming languages, such as Java and C++.

Reqsys-MDD: uma ferramenta para mapeamento entre modelos de features e requisitos em linhas de produto de software

The approach Software Product Line (SPL) has become very promising these days, since it allows the production of customized systems on large scale through product families. For the modeling of these families the Features Model is being widely used, however, it is a model that has low level of detail and not may be sufficient to guide the development team of LPS. Thus, it is recommended add the Features Model to other models representing the system from other perspectives. The goals model PL-AOVgraph can assume this role complementary to the Features Model, since it has a to context oriented language of LPS's, which allows the requirements modeling in detail and identification of crosscutting concerns that may arise as result of variability. In order to insert PL-AOVgraph in development of LPS's, this paper proposes a bi-directional mapping between PL-AOVgraph and Features Model, which will be automated by tool ReqSys-MDD. This tool uses the approach of Model-Driven Development (MDD), which allows the construction of systems from high level models through successive transformations. This enables the integration of ReqSys-MDD with other tools MDD that use their output models as input to other transformations. So it is possible keep consistency among the models involved, avoiding loss of informations on transitions between stages of development

Estimativa de expoentes críticos em Percolação

In Percolation Theory, functions like the probability that a given site belongs to the infinite cluster, average size of clusters, etc. are described through power laws and critical exponents. This dissertation uses a method called Finite Size Scaling to provide a estimative of those exponents. The dissertation is divided in four parts. The first one briefly presents the main results for Site Percolation Theory for d = 2 dimension. Besides, some important quantities for the determination of the critical exponents and for the phase transistions understanding are defined. The second shows an introduction to the fractal concept, dimension and classification. Concluded the base of our study, in the third part the Scale Theory is mentioned, wich relates critical exponents and the quantities described in Chapter 2. In the last part, through the Finite Size Scaling method, we determine the critical exponents fi and. Based on them, we used the previous Chapter scale relations in order to determine the remaining critical exponents

Dinâmica da paisagem no litoral oriental do Rio Grande do Norte: geocartografia e padrões espaciais dos campos de dunas móveis

This study shows the results of a research developed in the coastal regions of the Maxaranguape and Touros municipalities, more specific in the mobile dune fields of the Rio Grande do Norte's eastern coast. Although the coastal zones, represent a small percentage of the earth's surface it concentrates a great part of the world's population. The Rio Grande do Norte's state coastal landscape mosaic composed by the dune fields suggest a dynamic scene of changes in the spatial and temporal arranges, with significant changes in the geometry of the sedimentary cover. Following this perspective this research has the objective to map the emerged coastal zone of the Rio Grande do Norte's eastern coast under the perspective of the time-space evolution of the mobile dune fields using geoprocessing techniques, which includes remote sensing, digital images processing and geographic information system (GIS). The results imply the issue of thematic maps: Geologic map; multitemporal evolution map of the mobile dune fields; quantification of the mobile dune fields differences map; temporal evolution of the mobile dune fields surrounds map. The El Niño episodes have directly affected the atmospheric circulation, what have enhanced the sedimentary input in the sand dune, what can justify the relative area growth between the years of 1993 and 2001. The dynamic of the landscape transition were higher than the stability of the spatial pattern of the dune and it's surrounds, as a result the Rio Grande do Norte eastern coast dune fields, specially the mobile dunes from Touros, Zumbi and Maracajau have shown a decrease on the sedimentary cover without vegetation area from 1970 to 2007. Therefore, the data acquired and the techniques used, can be, eventually applied to the mobile dune fields monitoring in order to preserve the dune ecosystems in the Rio Grande do Norte coast

Concepções sobre os livros didáticos de geografia: narrativas autobiográficas de professores do ensino fundamental

O livro didático é um complexo objeto cultural, haja vista ser ao mesmo tempo elemento de intermediação nos processos de ensino e aprendizagem, produto comercializado que contém o conhecimento para a formação do aluno e objeto de compra, pelo Governo Federal, para ser distribuído para escolas em todo o Brasil. Configura-se, assim, como um produto cultural composto, híbrido, que se encontra no “cruzamento da cultura, da pedagogia, da produção editorial e da sociedade”. (STRAY,1993, p.77-78). Outrossim, o livro didático, tradicionalmente, é “um dos lugares formais do conhecimento escolar, pelo menos daquele saber julgado necessário à formação da sociedade e dos seus indivíduos” (MEDEIROS, 2006, p.34) e a materialização do seu uso pelo professor encontra-se interconectada pelas representações e conceitos construídos nas múltiplas transições na história de vida docente, tendo em vista que a práxis humana constrói-se numa perspectiva retroativa (do presente para o passado), numa hermenêutica social dos atos individuais. É nesse contexto que se situou a pesquisa, entendida como uma possibilidade de contribuição significativa ao debate da educação geográfica, ao propor a compreensão das concepções construídas nas múltiplas transições na narrativa de vida do docente com o livro didático de Geografia. A pesquisa se definiu como um estudo qualitativo, ancorado nas entrevistas narrativas, o qual abrangeu um levantamento de dados sobre as Histórias de vida de professores/professoras dos anos iniciais do Ensino Fundamental de uma escola da rede pública, no intuito de recorrermos às suas memórias escolares, acadêmica (formação inicial) e profissional para situarmos no espaço-tempo as suas concepções sobre o livro didático de Geografia. O livro didático de Geografia foi a área de interesse escolhida, sendo problematizada a partir do seguinte questionamento: quais as concepções atribuídas pelos professores do Ensino Fundamental aos livros didáticos de Geografia? As ideias dos professores expressas nas entrevistas narrativas da nossa pesquisa confirmam a conjuntura de indefinição e superficialidade teóricometodológica sobre o livro didático de Geografia, cujas concepções ficaram restritas aos seus aspectos descritivos, evidenciando a ausência de atribuições de significados pertinentes a uma reelaboração teórica do narrar produzido, como também, de questionamentos dos princípios organizadores das concepções sistematizadas. Desse modo, as ideias apontadas pelos professores em foco, restringiram-se à enumeração dos aspectos característicos do fenômeno em questão – o livro didático de Geografia – na sua superficialidade, isto é, não expressaram elementos que possibilitassem ver as concepções numa perspectiva macro, destacando-se mais as explicações das partes e das percepções isoladas, do que níveis mais abrangentes de generalidade do referido objeto de estudo. Enfatizamos, por fim, a necessária continuidade da pesquisa, e consequentemente, desse processo permanente de reflexão sobre as concepções do livro didático de Geografia, sendo mister explicitar, portanto, a razão histórica que as norteiam para que se possa buscar uma prática docente mais crítica e propositiva.

Estudo de complexos de ferro e de cobre com a base de Shiff 3-Meosalen e ligantes de relevância biológica

The goal set for this work was to synthesize and to characterize new iron and copper complexes with the Schiff base 3-MeOsalen and ligands of biological relevance, whose formulas are [Fe(3-MeOsalen)NO2], [Fe(3-MeOsalen)(etil2-dtc)], [Fe(3-MeOsalen)NO] and Na[Cu(3-MeOsalen)NO2]. The compounds were characterized by vibrational spectroscopy in the infrared region (IV) and Electronic spectroscopy in the ultraviolet and visible region (Uv-Vis). From the analysis of infrared spectra, they proved to formation of precursor complexes, as evidenced by changes in the vibrationals frequencies ν(C=N) e ν(C-O) and the emergence of vibrationals modes metal-oxygen and metal-nitrogen. For nitro complexes of iron and copper were observed ν(NO2)ass around 1300 cm-1 e ν(NO2)sim in 1271 cm-1 , indicating that the coordination is done via the nitrogen atom. The complex spectrum [Fe(3-MeOsalen)(etil2-dtc)] exhibited two bands, the ν(C-NR2) in 1508 cm-1 e ν(C-S) in 997 cm-1 , the relevant vibrational modes of coordinating ligand in the bidentate form. For the complex [Fe(3-MeOsalen)NO] was observed a new intense band in 1670 cm-1 related to the ν(NO). With the electronic spectra, the formation of complexes was evidenced by shifts of bands intraligands transitions and the emergence of new bands such as LMCT (p Cl-  d* Fe3+) in [Fe(3-MeOsalen)Cl] and the d-d in [Cu(3-MeOsalen)H2O]. As for the [Fe(3-MeOsalen)NO2] has highlighted the absence of LMCT band present in the precursor complex as for the [Cu(3-MeOsalen)NO2] found that the displacement of the band hipsocrômico d-d on 28 nm. The electronic spectrum of [Fe(3-MeOsalen)(etil2-dtc)] presented LMCT band shifts and changes in intraligantes transitions. With regard to [Fe(3-MeOsalen)NO], revealed a more energetic transitions intraligands regions from the strong character π receiver NO and MLCT band of transition dπFe(II)π*(NO).

Viver e esperar viver: corpo e identidade na transição de gênero de homens trans

This work seeks to understand how trans men build their identities and live the transsexual experience in the relationships they establish daily onto “man” category. It could be observed that for it they engenders a specific gender transition in the midst of male transsexuality. Despite being under a complex amalgam of relations of exploitation and disciplinary domination, ways of being man are brokered for a living and entry into spaces where they are expelled for not conform the bodies that gender norms require. It is understood that gender transition is a process at the same time of organic and prosthetic body management and the assumption of your own identity. Thus, they build a politic of identity that creatively fixes a person's category as rights holder. The "transition" is therefore to transact from nonexistence to a place of humanity. This dissertation describes how this process takes place in the experiences of the speakers, observing the practices that bring out the male, front of class positions on the labor market, access to health, hormonization and own identity. Thereby, theories that fix them as expressing female masculinities or marginal to the hegemony do not find exactitude in their lives. The research methodologically started performing "multilocated ethnographies" that gave possibilities to in-depth interviews with 15 stakeholders from the Northeast, Midwest, Southeast and South of Brazil. Between 2014 and 2015, from the applying of network technique to the first dialogues in research, it was possible to build a participant observation by the trans men’s everyday life. Wherewith I was capable to behold their own private activities, as well as their public agency amid a trans activism collective in northeast, and the follow-up actions in which they were involved during the XII Encontro Nacional em Universidades de Diversidade Sexual e de Gênero (ENUDSG) held in Mossoró/RN. Therefore, the thesis engages to describe and understand the different ways of constructing trans male gender transitions in access to transsexuality and therefore a way of explaining their own trajectories in terms of people that exist as such, even though in the midst of narratives marked by emotions linked to "not live", to suffering and dehumanization.

Behavioural profiles of captive capuchin monkeys (Sapajus spp.): analyses at group and individual levels

The use of behavioural indicators of suffering and welfare in captive animals has produced ambiguous results. In comparisons between groups, those in worse condition tend to exhibit increased overall rate of Behaviours Potentially Indicative of Stress (BPIS), but when comparing within groups, individuals differ in their stress coping strategies. This dissertation presents analyses to unravel the Behavioural Profile of a sample of 26 captive capuchin monkeys, of three different species (Sapajus libidinosus, S. flavius and S. xanthosternos), kept in different enclosure types. In total, 147,17 hours of data were collected. We explored four type of analysis: Activity Budgets, Diversity indexes, Markov chains and Sequence analyses, and Social Network Analyses, resulting in nine indexes of behavioural occurrence and organization. In chapter One we explore group differences. Results support predictions of minor sex and species differences and major differences in behavioural profile due to enclosure type: i. individuals in less enriched enclosures exhibited a more diverse BPIS repertoire and a decreased probability of a sequence with six Genus Normative Behaviour; ii. number of most probable behavioural transitions including at least one BPIS was higher in less enriched enclosures; iii. proeminence indexes indicate that BPIS function as dead ends of behavioural sequences, and proeminence of three BPIS (pacing, self-direct, active I) were higher in less enriched enclosures. Overall, these data are not supportive of BPIS as a repetitive pattern, with a mantra-like calming effect. Rather, the picture that emerges is more supportive of BPIS as activities that disrupt organization of behaviours, introducing “noise” that compromises optimal activity budget. In chapter Two we explored individual differences in stress coping strategies. We classified individuals along six axes of exploratory behaviour. These were only weakly correlated indicating low correlation among behavioural indicators of syndromes. Nevertheless, the results are suggestive of two broad stress coping strategies, similar to the bold/proactive and shy/reactive pattern: more exploratory capuchin monkeys exhibited increased values of proeminence in Pacing, aberrant sexual display and Active 1 BPIS, while less active animals exhibited increased probability in significant sequences involving at least one BPIS, and increased prominence in own stereotypy. Capuchin monkeys are known for their cognitive capacities and behavioural flexibility, therefore, the search for a consistent set of behavioural indictors of welfare and individual differences requires further studies and larger data sets. With this work we aim contributing to design scientifically grounded and statistically correct protocols for collection of behavioural data that permits comparability of results and meta-analyses, from whatever theoretical perspective interpretation it may receive.

Caracterização do ritmo circadiano de atividade e repouso em saguis idosos (Callithrix Jacchus)

Advanced age may become a limiting factor for the maintenance of rhythms in organisms, reducing the capacity of generation and synchronization of biological rhythms. In this study, the influence of aging on the expression of endogenous periodicity and synchronization (photic and social) of the circadian activity rhythm (CAR) was evaluated in a diurnal primate, the marmoset (Callithrix jacchus). This study had two approaches: one with longitudinal design, performed with a male marmoset in two different phases: adult (three years) and older (9 y.o.) (study 1) and the second, a transversal approach, with 6 old (♂: 9.7 ± 2.0 y.o.) and 11 adults animals (♂: 4.2 ± 0.8 y.o.) (study 2). The evaluation of the photic synchronization involved two conditions in LD (natural and artificial illuminations). In study 1, the animal was subjected to the following stages: LD (12:12 ~ 350: ~ 2 lx), LL (~ 350 lx) and LD resynchronization. In the second study, the animals were initially evaluated in natural LD, and then the same sequence stages of study 1. During the LL stage in study 2, the vocalizations of conspecifics kept in natural LD on the outside of the colony were considered temporal cue to the social synchronization. The record of the activity was performed automatically at intervals of five minutes through infrared sensor and actimeters, in studies 1 and 2, respectively. In general, the aged showed a more fragmented activity pattern (> IV < H and > PSD, ANOVA, p < 0.05), lower levels of activity (ANOVA, p < 0.05) and shorter duration of active phase (ANOVA, p < 0.05) in LD conditions, when compared to adults. In natural LD, the aged presented phase delay pronounced for onset and offset of active phase (ANOVA, p < 0.05), while the adults had the active phase more adjusted to light phase. Under artificial LD, there was phase advance and greater adjustment of onset and offset of activity in relation to the LD in the aged (ANOVA, p < 0.05). In LL, there was a positive correlation between age and the endogenous period () in the first 20 days (Spearman correlation, p < 0.05), with prolonged  held in two aged animals. In this condition, most adults showed free-running period of the circadian activity rhythm with  < 24 h for the first 30 days and later on relative coordination mediated by auditory cues. In study 2, the cross-correlation analysis between the activity profiles of the animals in LL with control animals kept under natural LD, found that there was less social synchronization in the aged. With the resubmission to the LD, the resynchronization rate was slower in the aged (t-test; p < 0.05) and in just one aged animal there was a loss of resynchronization capability. According to the data set, it is suggested that the aging in marmosets may be related to: 1) lower amplitude and greater fragmentation of the activity, accompanied to phase delay with extension of period, caused by changes in a photic input, in the generation and behavioral expression of the CAR; 2) lower capacity of the circadian activity rhythm to photic synchronization, that can become more robust in artificial lighting conditions, possibly due to the higher light intensities at the beginning of the active phase due to the abrupt transitions between the light and dark phases; and 3) smaller capacity of non-photic synchronization for auditory cues from conspecifics, possibly due to reducing sensory inputs and responsiveness of the circadian oscillators to auditory cues, what can make the aged marmoset most vulnerable, as these social cues may act as an important supporting factor for the photic synchronization.

Caracterização do ritmo circadiano de atividade e repouso em saguis idosos (Callithrix Jacchus)

Advanced age may become a limiting factor for the maintenance of rhythms in organisms, reducing the capacity of generation and synchronization of biological rhythms. In this study, the influence of aging on the expression of endogenous periodicity and synchronization (photic and social) of the circadian activity rhythm (CAR) was evaluated in a diurnal primate, the marmoset (Callithrix jacchus). This study had two approaches: one with longitudinal design, performed with a male marmoset in two different phases: adult (three years) and older (9 y.o.) (study 1) and the second, a transversal approach, with 6 old (♂: 9.7 ± 2.0 y.o.) and 11 adults animals (♂: 4.2 ± 0.8 y.o.) (study 2). The evaluation of the photic synchronization involved two conditions in LD (natural and artificial illuminations). In study 1, the animal was subjected to the following stages: LD (12:12 ~ 350: ~ 2 lx), LL (~ 350 lx) and LD resynchronization. In the second study, the animals were initially evaluated in natural LD, and then the same sequence stages of study 1. During the LL stage in study 2, the vocalizations of conspecifics kept in natural LD on the outside of the colony were considered temporal cue to the social synchronization. The record of the activity was performed automatically at intervals of five minutes through infrared sensor and actimeters, in studies 1 and 2, respectively. In general, the aged showed a more fragmented activity pattern (> IV < H and > PSD, ANOVA, p < 0.05), lower levels of activity (ANOVA, p < 0.05) and shorter duration of active phase (ANOVA, p < 0.05) in LD conditions, when compared to adults. In natural LD, the aged presented phase delay pronounced for onset and offset of active phase (ANOVA, p < 0.05), while the adults had the active phase more adjusted to light phase. Under artificial LD, there was phase advance and greater adjustment of onset and offset of activity in relation to the LD in the aged (ANOVA, p < 0.05). In LL, there was a positive correlation between age and the endogenous period () in the first 20 days (Spearman correlation, p < 0.05), with prolonged  held in two aged animals. In this condition, most adults showed free-running period of the circadian activity rhythm with  < 24 h for the first 30 days and later on relative coordination mediated by auditory cues. In study 2, the cross-correlation analysis between the activity profiles of the animals in LL with control animals kept under natural LD, found that there was less social synchronization in the aged. With the resubmission to the LD, the resynchronization rate was slower in the aged (t-test; p < 0.05) and in just one aged animal there was a loss of resynchronization capability. According to the data set, it is suggested that the aging in marmosets may be related to: 1) lower amplitude and greater fragmentation of the activity, accompanied to phase delay with extension of period, caused by changes in a photic input, in the generation and behavioral expression of the CAR; 2) lower capacity of the circadian activity rhythm to photic synchronization, that can become more robust in artificial lighting conditions, possibly due to the higher light intensities at the beginning of the active phase due to the abrupt transitions between the light and dark phases; and 3) smaller capacity of non-photic synchronization for auditory cues from conspecifics, possibly due to reducing sensory inputs and responsiveness of the circadian oscillators to auditory cues, what can make the aged marmoset most vulnerable, as these social cues may act as an important supporting factor for the photic synchronization.

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.

Frases magnéticas, polaritons magnéticos e modos magnetostáticos em filmes e cristais magnônicos de terras-raras

Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq