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Modelagem matemática e computacional do modelo de monod fracionário no estudo de biocombustíveis para possíveis aplicação em foguetes

2026-08-18T14:16:21Z

Título: Modelagem matemática e computacional do modelo de monod fracionário no estudo de biocombustíveis para possíveis aplicação em foguetes Abstact: This dissertation addresses the mathematical and computational modeling of bioprocesses oriented toward biofuel production, with potential applications to the study of rocket propellants. The work demonstrates the limitations of the classic Monod kinetic model and proposes an innovative approach using fractional calculus to describe the kinetics of reactions in biological systems. The introduction of fractional-order derivatives, within the Riemann-Liouville and Caputo formulations, allows the incorporation of memory effects and non-locality, which are inherent characteristics of complex bioprocesses. The general objective consists of the creation and computational application of a fractional Monod model for the analysis and optimization of biofuel production. The adopted methodology includes implementation in the Python language using the Modified Iterative Regularized Finite Difference Method (MIRDF), designed for the numerical resolution of non-linear fractional differential equations. Simulations were carried out in a batch reactor configuration, with parameters μmax = 0.009 h−1 and Ks = 4 × 10−8 mg/L. The results demonstrate that the fractional model, with order α < 1, describes microbial growth phases with greater fidelity compared to the classic model (α = 1.0), producing smoother transition curves between the lag and exponential phases and incorporating the historical dependence of the system. The numerical validation of the MIRDF, grounded on linear test problems for rigorous convergence analysis before application to the coupled nonlinear Monod system, yielded absolute errors on the order of 10−7, confirming the precision and robustness of the method under the conditions of Banach’s Fixed-Point Theorem. Comparative analysis with similar studies shows that the fractional parameter α acts as a calibration factor, expanding the predictive capacity of the model. It is concluded that fractional calculus constitutes an effective engineering tool for optimizing bioprocesses aimed at producing highperformance renewable propellants for aerospace applications, contributing to the development of clean energy sources in the space sector

Estudo teórico das propriedades eletrônicas, termodinâmicas e ópticas na estrutura de zeólita (rub-11) com as dopagens de metais de transição

2026-07-09T15:38:14Z

Título: Estudo teórico das propriedades eletrônicas, termodinâmicas e ópticas na estrutura de zeólita (rub-11) com as dopagens de metais de transição Abstact: The molecular selectivity of zeolites gives these materials the function of molecular sieves, a central property in research focused on the space sector. The ability to őlter molecules based on nanometric dimensions is what drives the development of new structural and chemical applications in this őeld. Furthermore, zeolitic material possesses speciőc requirements for environments in this segment, since the material has a certain resistance to extreme environments, thermal stability, and eiciency in adsorption and air puriőcation processes in enclosed environments, such as aircraft cabins or space stations, serving to control contaminants such as ��3, �2�, and ��4, given its already consolidated use. Therefore, this work aims to investigate possible enhancements of the properties of RUB-11 zeolite through metallic doping by silicon atom substitution and branching at points previously calculated by population analysis, using the DFT computational method with PBE-GGA functional. Initially, the structure of RUB-11 zeolite exhibited characteristics of an insulating material; however, the results of doping with transition metals show considerable alterations in the characteristics of the original structure, making the zeolitic material more reactive. Furthermore, the viability is conőrmed by the thermodynamic properties (Enthalpy, Heat Capacity at Constant Pressure, Entropy, and Gibbs Free Energy) and the reactivity through the band gap energy, agreeing with the optical results, with only an expected variation due to the methods used. Adsorption studies resulted in adsorption for all gases proposed in this research; however, ammonia and sulfur dioxide obtained the best results. Finally, the stability analysis of the materials demonstrated that the nature of the transition elements with oxygen atoms are determining factors for the stability of the variations in the doping process

Problema da difusão em meio poroso via cálculo fracionário

2025-10-07T18:28:52Z

Título: Problema da difusão em meio poroso via cálculo fracionário Abstact: 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 È. 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

Estudo teórico das propriedades termodinâmicas e cinéticas nas reações de combustão do diborano como combustível de foguete

2025-09-12T18:56:12Z

Título: Estudo teórico das propriedades termodinâmicas e cinéticas nas reações de combustão do diborano como combustível de foguete Abstact: A study was carried out on the thermodynamic and kinetic properties of the combustion reactions of diborane as rocket fuel. To this end, it aims to understand the characteristics and thermodynamic and kinetic properties of the thermal decomposition of high energy materials in order to develop a mechanism of chemical combustion reactions. From the methodological point of view, the geometrization of the molecules was modeled using the Gaussian9 software, considering the bonds of each molecule of interest B-B, B-H, B-О, О-О, Н-H, O-H, mentioned in the isodesmic reactions. It is evident that the optimizations of the equilibrium molecules in the ground state were performed using the functional B3LYP model of DFT for the geometries of the molecules. It is stated that the calculations of the reactions were computed at different temperatures of 100K, 298K, 500K, and 1000K, thus it was possible to extract from the Gaussian output file, the thermodynamic properties such as enthalpy variation, Gibbs free energy, and equilibrium constant. The equilibrium constants Keq were computed from the thermodynamic properties of the reactants and products as a function of temperature, and the enthalpy variation (AH) was calculated based on the difference between the enthalpies of the products and reactants. It reinforces that in the Density Functional Theory (B3LYP) the base set cc-pVTZ (Triple Zeta) was used to determine the enthalpy of formation of neutral and critical species in thermal decomposition. The presentation of the computational data of the molecular geometries was presented in the form of tables and graphs. It was concluded that the isodesmic reaction technique is very successful in determining the types of combustion reactions, and helped us to clarify which of the reactions are involved in the absorption of the heat produced during the process. It was observed that reactions I, II and III are reactions with a high value of the Gibbs energy variation (negative) and that release a high value of energy to the medium