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ANA LICIA COSTA OLIVEIRA
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Problema da Difusão em Meio Poroso Via Cálculo Fracionário
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Orientador : FELIX SILVA COSTA
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Data: 06/11/2024
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Throughout history, renowned researchers have dedicated themselves and their studies to investigate, understand and describe nonlinear diffusion processes, using analytical, numerical and computational tools. In this work, we present a problem of nonlinear anomalous diffusion in porous media and aim to present Lie symmetry transformation groups as an alternative to solving the diffusion problem. Initially, a study was carried out on fractional calculus and its main operators, where we point out definitions, theorems, properties and applications. Fractional calculus allows us to describe natural characteristics more precisely, thus obtaining a greater amount of information linked to nonlocal operators, then called the memory effect. An analysis of anomalous fractional diffusion in porous media was carried out, where the problem of nonlinear fractional diffusion in time-space was addressed. Another important point presented here is the Lie point transformation groups, which we use as an alternative to the diffusion problem, since Lie symmetries prove to be a very important tool as it allows the transformation of a PDE into an ODE. We apply Lie symmetries to the discovery of diffusion in fractional porous media in terms of Riesz derivatives, including the Weyl derivative. And we demonstrate that the results can be understood for the fractional derivative in terms of the function ψ. We emphasize that the study of anomalous diffusion has been increasingly deepened and its concept applied in several fields such as diffusion in plasmas, diffusion in turbulent fluids, fluid transport in porous media, diffusion in fractals, anomalous diffusion on liquid surfaces and analysis of heartbeat histograms in healthy individuals, among other physical systems. Keywords: Anomalous Diffusion, Fractional Calculus, Fractional Diffusion in Porous Media, Lie Points.
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LUANA ROBERTA PACHECO BITTENCOURT
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MODELAGEM COMPUTACIONAL DAS PROPRIEDADES OPTOELETRÔNICAS E TERMODINÂMICAS DA NOVA MONOCAMADA HÍBRIDA 1T’ – RuOsSe2
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Orientador : EDVAN MOREIRA
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Data: 24/10/2024
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Transition metal dichalcogenides (TMDs) have a structural form XY2, where X is a transition metal and Y is a chalcogenide element, and are very promising for applications in the aerospace industry, transitors, sensor production and others. These materials are characterized by covalent bonds between the X and Y elements, with polarization caused by electronic transfer between the metallic and chalcogenide atoms. Therefore, the need to study new twodimensional structures in this sector was realized. Thus, a study and computational modeling of the optoelectronic and thermodynamic properties of the 1T’-RuOsSe2 monolayer was carried out from density functional theory (DFT) formalism using ab initio calculations, mainly considering the generalized gradient approximation (GGA) and adopting the HSE06 hybrid functional for bandgap estimation, based on nanostructures in the minimum energy state. The lattice parameters calculated for 1T’-RuOsSe2 are comparable with the known structures in the literature, 1T’-OsSe2 and 1T’-RuSe2. The electronic band structures show indirect bandgaps for the nanostructures 1T’-RuOsSe2, 1T’-OsSe2, and 1T’-RuSe2, with values of 1.0, 0.96, and 0.93 eV, respectively, with the upper energy limit in the valence band between the Γ-Y high symmetry points, and the lower energy limit in the conduction band at the Γ point, for the 1T’-RuOsSe2 hybrid monolayer (ΓY→Γ=1.0 eV). Investigation of optical absorption shows that the RuOsSe2 monolayer exhibits significant absorption in the ultraviolet and visible regions of the electromagnetic spectrum. Thermodynamic potentials and specific heat at constant volume have been calculated, the temperature dependence of which is discussed. We predict a new RuOsSe2 monolayer of the 1T’ phase that can potentially be synthesized for future electronic devices and bring potential technological applications.
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MARCUS VINICIUS DURANS PEREIRA
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EFEITOS TERMO-ELÉTRICOS E MAGNÉTICOS DAS MONOCAMADAS TMDs 1T’ − RuWTe2 E 1T’ − WTe2 VIA SIMULAÇÃO COMPUTACIONAL
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Orientador : EDVAN MOREIRA
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Data: 17/09/2024
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Transition metal dichalcogenides (TMDs) are chemical compounds consisting of two chalcogen atoms (Te, Se or S) connected by covalent bonds to a transition metal atom, having the structural form MX2. In this research, modeling and computer simulation were carried out, followed by an analysis of the physical properties of monoclinic monolayers (1T’) of tungsten ditelluride (W T e2) and tungsten-ruthenium ditelluride (RuW T e2) TMDs, the latter replacing a W atom with a Ru atom in the primitive cell, from density functional theory (DFT) formalism, mainly considering the generalized gradient approximation (GGA) and the HSE06 hybrid functional for bandgap estimation, from nanostructures in their minimum energy state. The lattice parameters of the proposed 1T’ − RuW T e2 TMD are compatible with the 1T’−W T e2 TMD already known in literature. The estimated bandgap for 1T’−RuW T e2 was 0.50 and 0.35 eV, for the spin up and down bands, respectively, characterizing it as a semiconductor, while 1T’−W T e2 showed conductor characteristics. As for their magnetic nature, these TMDs showed ferromagnetism, with 1T’ − RuW T e2 showing an apparent tendency towards ferrimagnetism. The density of partial states, thermodynamic potentials and thermal capacity were also analyzed, highlighting the potential for synthesis and estimation of new Technologies such as thermo-electric and magnetic nanodevices of the 1T’ − RuW T e2 TMD.
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