I completed both my undergraduate and graduate studies at the Federal University of Minas Gerais (UFMG), earning a Master’s degree and a Ph.D. in Physical Chemistry. I have been a faculty member at the Federal University of Alfenas (UNIFAL) since 2009. At the undergraduate level, I teach General Chemistry to students across multiple programs, as well as elective courses such as Chemical Kinetics, Chemometrics, Mathematics for Chemists, and Practical Projects in Scientific Programming. Within the Graduate Program in Chemistry, I supervise Master’s and Ph.D. students and teach courses in Advanced Physical Chemistry, Quantum Mechanics, and other subjects closely related to my research expertise.
My research area is Mathematical Chemistry. Mathematical Chemistry is a field that employs non-standard mathematical methodologies to address chemically significant problems that require novel analytical approaches. In other words Mathematical Chemistry focuses on new mathematical ideas and concepts adapting and developing them for use within the context of Chemistry. My interests include film comics electronics (Arduino) programming (App Inventor and MATLAB) Mathematics (Fractional Calculus) and Chemistry (Solution Thermodynamics Chemical Kinetics and Statistical and Quantum Thermodynamics).
The equilibrium behaviors of two-phase liquid–liquid systems composed of poly(ethylene glycol) (PEG) 1500 or 4000 + sodium sulfite + water were experimentally determined at temperatures of (288.15, 298.15, 308.15, and 318.15) K. The effects of the molecular weight of PEG and the temperature on the phase separation were studied. The binodal curves were fitted to an empirical equation that correlates the concentrations of PEG 1500 or 4000 and sodium sulfite, and the coefficients for the different temperatures were estimated. The tie-line compositions were estimated and correlated using the Othmer–Tobias and Bancroft equations, and the parameters are reported. The liquid–liquid equilibrium (LLE) experimental data obtained were well-correlated to the activity coefficients of the non-random two-liquid (NRTL) and UNIversal QUAsiChemical (UNIQUAC) models, and the mean deviations were less than 0.36 % and 0.31%, respectively.
This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction number<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math>is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, when<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math>, is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations.
This paper focuses on the calculation of the quantum second virial coefficient, under a recently developed potential. This coefficient was determined to within 4-5 significant figures in the temperature range from 3 to 100 K. Our results are within experimental error. The three contributions to the overall value of the coefficient are the quantum scattering (continuum state contribution), the bound state (discrete state contribution) and the quantum ideal gas; we discuss these contributions separately. The most significant contribution is from the scattering states, whereas the smaller contributions are from the discrete states. A sensitivity analysis was performed as a function of temperature for one parameter in the short-range region of the potential and for three parameters in the long-range regions of the potential. For both temperatures considered, 10 and 100 K, the C6 dispersion coefficient was the most significant, and the C10 dispersion term was the least significant to the overall result. In general, the precision required to describe the potential decays as the temperature increases. The overall accuracy and the relationship of the parameters to the experimental errors are discussed.
Phase diagrams have been determined for aqueous two-phase systems containing (EO)11(PO)16(EO)11, notation L35 (50% EO), and sodium citrate, sodium tartrate, or sodium hydrogen sulfite at different temperatures. The influences of the temperature and anion on the behavior of these systems were also analyzed. The temperature effect on the position of the binodal curves for systems containing sodium citrate and tartrate was not relevant, indicating a small enthalpy contribution associated with the phase separation. However, an enthalpic contribution for the phase splitting of the systems formed by sodium hydrogen sulfite was observed. The ability of these three salts to induce the formation of a biphasic system with L35 followed the order sodium citrate > sodium tartrate > sodium hydrogen sulfite. In this work, the nonrandom two-liquid (NRTL) model was used to obtain new interaction energy parameters. The results were analyzed using root-mean-square deviations between experimental and calculated data in equilibrium phases and were considered satisfactory.
A general algorithm to solve linear and nonlinear inverse problems, based on recursive neural networks, is discussed in this work. The procedure will be applied to physical chemical problems modeled by integral, differential and eigenvalue equations. Representative applications discussed are in positron lifetime spectroscopy, chemical kinetics and vibrational spectroscopy. The method is robust with respect to errors in the initial condition or in the experimental data. The present approach is simple, numerically stable and has a broad range of applicability.
Abstract Important physical and chemical information can be extracted from scattering experiments data. This kind of problem is usually ill‐posed in the sense that one of the three conditions, existence, uniqueness, and continuity, is not satisfied. For example, the inversion of intermolecular potential functions from scattering data, such as experimental cross section, is an ill‐posed problem which can be modeled as a Fredholm integral equation. In this work, an inversion method based on recursive neural networks is proposed to solve this inverse quantum scattering problem within the Born approximation. As physical example, the repulsive component of the potential function for the interaction Ar–Ar is obtained from differential cross‐section data. The sensitivity of the potential energy function to be inverted, in relation to the differential cross‐section data, is also analyzed. The present approach is simple, general, and numerically stable. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008
This paper presents the derivation and applications of the variable phase equation for single channel quantum scattering. The approach was first presented in 1933 by Morse and Allis and is based on a modification of the Schrödinger equation to a first order differential equation, appropriate to the scattering problem. The dependence of phase shift on angular momentum and energy, together with Levinson's theorem, is discussed. Because the variable phase equation method is easy to program it can be further explored in an introductory quantum mechanics course.
(2020). Improving a Tikhonov regularization method with a fractional-order differential operator for the inverse black body radiation problem. Inverse Problems in Science and Engineering: Vol. 28, No. 11, pp. 1513-1527.
Phase behavior of new aqueous two-phase systems (ATPSs) composed by 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim]BF4) + copper sulfate (CuSO4) + water systems were determined experimentally at T = (283.15, 298.15, and 313.15) K. The phase diagrams obtained at the different study temperatures describe the liquid–liquid equilibrium (LLE) and, in some cases, the liquid–liquid–solid equilibrium for different mixture compositions. The effects of the temperature, composition, and ion exchange in the formation of this ATPS were available. The temperature had a remarkable effect on the position of phase diagrams. The decrease in temperature promoted phase separation indicating the exothermic character of formation of these ATPSs, and further, at temperatures of 283.15 and 298.15 K it was observed that there was phase inversion for some mixture compositions that occurred. The extent of the ionic exchange of the original ionic pairs between the phases in equilibrium was evaluated considering the electroneutrality of the phases. It was observed experimentally that, in the LLE condition established, there was no significant exchange of the ionic pairs. The ability of different cations, from different sulfate salts, to induce the formation of ATPSs in mixtures involving [Bmim]BF4 was evaluated. For this, thermodynamic data of hydration of different cations reported in the literature were used together with experimental data of saturation solubility to establish a scale. Thermodynamic parameters of transfer of components (cations, anions, and water) between the phases were also calculated from the experimental data and indicated that the material transfer of the bottom phase to the top is not spontaneous and tends to be less spontaneous as the length of the tie line value increases. Additionally, the equilibrium data and binodal curves were fitted to an empirical nonlinear expression (Merchuk equation), and the salting out effect was explored using the type-Setschenow equation.
In this paper, we study the well-posedness and the qualitative behavior of equilibria of a SEIR epidemic models with spatial diffusion for the spreading of COVID-19. The well-posedness of the model is proved using both the Semigroup Theory of sectorial operators and existence results for abstract parabolic differential equations. The asymptotical local stability of both disease-free and endemic equilibria are established using standard linearization theory, and confirmed by illustrative numerical simulations. The asymptotical global stability of both disease-free and endemic equilibria are established using a Lyapunov function.
Abstract All signals obtained as instrumental response of analytical apparatus are affected by noise, as in Raman spectroscopy. Whereas Raman scattering is an inherently weak process, the noise background may lead to misinterpretations. Although surface amplification of the Raman signal using metallic nanoparticles has been a strategy employed to partially solve the signal‐to‐noise problem, the preprocessing of Raman spectral data through the use of mathematical filters has become an integral part of Raman spectroscopy analysis. In this paper, a Tikhonov modified method to remove random noise in experimental data is presented. In order to refine and improve the Tikhonov method as a filter, the proposed method includes Euclidean norm of the fractional‐order derivative of the solution as an additional criterion in Tikhonov function. In the strategy used here, the solution depends on the regularization parameter, , and on the fractional derivative order, . As will be demonstrated, with the algorithm presented here, it is possible to obtain a noise‐free spectrum without affecting the fidelity of the molecular signal. In this alternative, the fractional derivative works as a fine control parameter for the usual Tikhonov method. The proposed method was applied to simulated data and to surface‐enhanced Raman scattering (SERS) spectra of crystal violet dye in Ag nanoparticles colloidal dispersion.
The liquid–liquid equilibrium for the mixtures of poly(ethylene glycol) (PEG) with mass-average molar of 4000, 6000, or 10 000 g mol–1 + sodium hydrogen sulfite (NaHSO3) + water systems has been determined experimentally at T = 288.15, 298.15, 308.15, and 318.15 K. The temperature, PEG mass molar, mixture composition, and nature of anion effects on phase equilibrium were studied. The binodal curves at different temperatures were fitted to an empirical equation that correlates the concentrations of polymers and salt. The consistence of experimental data of equilibrium was available through of the Othmer–Tobias and Bancroft equations, and the parameters were reported.
Retrieving the potential energy function from second virial data, and using the sensitivity analysis approach is discussed in this work. A potential energy function, with an initial average error of 92%, in temperature range of 100–500 K, with respect to a reference potential, was considered as an initial guess. Within the present framework it was possible to produce another potential with an average error of 0.7 and 2.7%, using two regularization methods. Analysis of the sensitivity matrix has shown to be an important step while inverting the data. This preliminary analysis provides important informations about the optimal temperature and coordinate range to be used in the inversion process.
Este trabalho concentra-se no cálculo do segundo coeficiente virial quântico, a partir de um potencial desenvolvido recentemente.Este coeficiente foi determinado com 4-5 algarismos significativos na faixa de temperatura de 3 a 100 K. Nossos resultados estão dentro do erro experimental.Três contribuições para o valor total deste coeficiente são o espalhamento quântico (contribuição de estados no contínuo), o estado ligado (contribuição de estados discretos) e o gás ideal quântico; discutimos estas contribuições separadamente.A contribuição mais importante é do espalhamento quântico, enquanto que as contribuições menores
This work propose a recursive neural network to solve inverse equilibrium problem. The acidity constants of 7-epiclusianone in ethanol-water binary mixtures were determined from multiwavelength spectrophotmetric data. A linear relationship between acidity constants and the %w/v of ethanol in the solvent mixture was observed. The proposed method efficiency is compared with the Simplex method, commonly used in nonlinear optimization techniques. The neural network method is simple, numerically stable and has a broad range of applicability.
RESUMOO presente trabalho tem como objetivo avaliar, em obra, a resistência superficial à tração (RST) de revestimentos de argamassa. O ensaio para avaliação dessa propriedade ainda não é normalizado no Brasil, merecendo, portanto, estudos visando a sua futura padronização, haja vista ser a resistência superficial de um revestimento de argamassa um dos aspectos relevantes no que tange ao seu desempenho. Neste sentido, foram realizadas avaliações em duas obras de diferentes construtoras na cidade de Goiânia (estado de Goiás, Brasil), onde foram analisadas a influência do operador do ensaio, as influências do traço, local de aplicação e idade do revestimento, e a influência da ergonomia durante a produção do revestimento. Os resultados obtidos foram analisados empregando procedimentos estatísticos, tendo sido calculado o tamanho da amostra e realizadas análises de variâncias, além de correlações entre a RST e outros ensaios realizados. Como resultado, obteve-se que o tamanho da amostra compatível com a variabilidade obtida no ensaio é de 10 a 15 corpos-de-prova por situação individual de análise. Também se verificou que as variáveis estudadas (traço da argamassa, idade do revestimento e ação de intempéries) exercem influência significativa nos resultados de RST. Foram observadas correlações satisfatórias entre a RST e os resultados de ensaios de resistência de aderência (r=0,87), permeabilidade (r=0,81) e índice esclerométrico (r=0,99).
What is an ill-posed inverse problem? The answer to this question is the main objective of the present paper and the pre-requisite to follow the material requires only elementary calculus. The first mathematical formulation of an inverse problem, due to N. H. Abel, together with the fundamental work by Jacques Hadamard, are explored at the beginning of the paper. A prototype system is used to consider the regularization concept. Three numerical methods, the Tikhonov regularization, the decomposition into singular values and the Hopfield neural networks, applied to remove the singularity are examined. General aspects of the ill-posed inverse problems in chemistry with emphasis in thermodynamics and a set of general rules for other areas of science are also analyzed.
In this work, a simple derivation of the variable amplitude method using the variation of parameters to solve a differential equation is presented. The variable amplitude method was originally devised by Tikochinsky in 1977, using the quantum theory of scattering. The method is applied to two model potentials, the rectangular potential barrier and the Eckart potential, both with analytical solutions for the reflection coefficient. Numerical results will be compared with the exact values for several energies. The problem of calculating the reflection coefficient, usually involving extensive algebra as described in several textbooks, is reduced to solving a first order differential equation with initial condition. The method is very simple to apply, representing an attractive tool for teaching introductory quantum mechanics. A simple computer code is available from which reflection coefficients for the Eckart potential can be calculated.
A hundred years ago, a twenty-eight year old Danish scientist published a series of three papers in which electron motion was quantized. The Bohr atomic model is surely known by every chemistry student. Nevertheless in this same 1913 trilogy, Bohr studied atoms with several electrons as well as molecules. Chemistry students, in general, are not aware of the Bohr molecule. The present paper aims at rescuing this important classical model. A review of the Bohr atomic model for both one and several electrons is discussed, together with a theoretical presentation of the Bohr molecule.
Abstract The Firsov inverse method was used to retrieve potential energy for helium–helium system from deflection function. Using a combination of accurate simulated data for large deflection function and a Lennard–Jones type potential for smaller values, it was possible to recover the short‐range potential in excellent agreement with the theoretical results. Errors in the deflection function ranged from 1 to 10% with a collision energy from 2 × 10 −3 to 2 eV. Inverted potential were obtained with a precision from 2 to 8%. This study explores the possibility to use Firsov approach for small collision energy, unlike the previous work on the subject. The method was proved to be robust, stable against experimental error, and very easy to be implemented numerically. © 2012 Wiley Periodicals, Inc.
Potential parameters sensitivity analysis for helium unlike molecules, HeNe, HeAr, HeKr and HeXe is the subject of this work. Number of bound states these rare gas dimers can support, for different angular momentum, will be presented and discussed. The variable phase method, together with the Levinson's theorem, is used to explore the quantum scattering process at very low collision energy using the Tang and Toennies potential. These diatomic dimers can support a bound state even for relative angular momentum equal to five, as in HeXe. Vibrational excited states, with zero angular momentum, are also possible for HeKr and HeXe. Results from sensitive analysis will give acceptable order of magnitude on potentials parameters.
<abstract language="eng">Analytical solutions of a cubic equation with real coefficients are established using the Cardano method. The method is first applied to simple third order equation. Calculation of volume in the van der Waals equation of state is afterwards established. These results are exemplified to calculate the volumes below and above critical temperatures. Analytical and numerical values for the compressibility factor are presented as a function of the pressure. As a final example, coexistence volumes in the liquid-vapor equilibrium are calculated. The Cardano approach is very simple to apply, requiring only elementary operations, indicating an attractive method to be used in teaching elementary thermodynamics.
Classical state-to-state Ar–CO2 rotational cross-sections are calculated using two potentials. Comparison with experimental data shows that there are discrepancies. The two-dimensional atom-ellipsoid model is used to analyse the cause of these discrepancies, and it is found that the cross-sections are sensitive to multiple collision effects. The results, considering only the contribution of the repulsive part of the two potentials, showed satisfactory agreement with the experimental measurements but, on taking into account the whole potentials, some deviations from the experimental state-to-state rotational cross-sections were observed. These deviations were attributed to the strong contribution from the long-range part of each potential.
In this study, the Van't Hoff differential equation is taken under consideration by making use of fractional derivative tools. In this context, the nonlinear Arrhenius behaviour can be obtained and some experimental values of reaction rate as function of temperature were fitted, with the proposed model. The new model showed better performance to fit rate constant data for different kinetics process, when compared with Arrhenius law. In these case, the Van't Hoff differential equation with noniteger order found relative percentage error less that 3% within experimental error. The fractional order plays an important role in modeling temperature dependence of these kinetic processes. Thus it provides a new perspective in the handling of many problems (e.g., as solubility as function of temperature; temperature dependency of the viscosity and conductivity, etc).
A simple analysis of glory and rainbow effects, together with the description of their trajectories is given by the geometric model.The energy dependence of glory and rainbow impact parameters and the energy dependence of the rainbow angle are determined analytically within the model.An universal function for glory and rainbow trajectories can be easily determined.
No processo de decaimento radioativo, a quantidade de espécies instáveis que permanecem no tempo t é dada por uma equação diferencial de primeira ordem, conhecida como lei de decaimento exponencial. Atualmente existem evidências de um decaimento não exponencial em longos tempos, quando o número de espécies presente decai suavemente, tal como $1/t^{n}$. O objetivo deste trabalho foi considerar a equação diferencial generalizada com ordem não inteira, da qual foi possível descrever os dados experimentais em ambas regiões: exponencial e não-exponencial região. Este comportamento, obtido do cálculo fracional, está de acordo com dados experimentais recentes da literatura.
Hoje em dia, as informacoes publicadas na internet e nas redes sociais se espalham de forma muito rapida e apresentam uma propagacao que e facil de serem obtidas com ferramentas como Google Trends por exemplo. O conhecimento dessa dinamica nos permite conhecer o interesse dos internautas, como tambem, definir formas de influencia-los. Alguns estudos, como feitos em [1–3], tem associado a propagacao de memes com a modelagem usada em problemas oriundos da epidemiologia, em geral, o modelo do tipo SIR. [...]
A energia total irradiada por um corpo negro em funcao da frequencia W (ν), com uma distribuicao de temperatura a(T ) ao longo de sua area superficial, e dado pela equacao integral de Fredholm de primeira ordem (1), onde h e a constante de Planck, k e a constante de Boltzmann e c a velocidade da luz no vacuo:[...]
The fractional calculus framework will be used to invert the potential energy function from the classical scattering angle, which will be related to Riemann-Liouville fractional integral. Numerical solution of this fractional order problem will be applied to the inverse Rutherford scattering and to the inverse scattering of Xe--Rn atoms, in which the potential is given by Lennard-Jones function. Proofs of existence will be presented for more clarity and completness of the present work. In the two cases considered, the potential energy function can be retrieved with a desired precision. The present method gives a clear understanding of the inverse fractional problem framework.
All signals obtained as instrumental response of analytical apparatus are affected by noise, as in Raman spectroscopy. Whereas Raman scattering is an inherently weak process, the noise background can lead to misinterpretations. Although surface amplification of the Raman signal using metallic nanoparticles has been a strategy employed to partially solve the signal-to-noise problem, the pre-processing of Raman spectral data through the use of mathematical filters has become an integral part of Raman spectroscopy analysis. In this paper, a Tikhonov modified method to remove random noise in experimental data is presented. In order to refine and improve the Tikhonov method as filter, the proposed method includes Euclidean norm of the fractional-order derivative of the solution as an additional criterion in Tikhonov function. In the strategy used here, the solution depends on the regularization parameter, $λ$, and on the fractional derivative order, $α$. As will be demonstrated, with the algorithm presented here, it is possible to obtain a noise free spectrum without affecting the fidelity of the molecular signal. In this alternative, the fractional derivative works as a fine control parameter for the usual Tikhonov method. The proposed method was applied to simulated data and to surface-enhanced Raman scattering (SERS) spectra of crystal violet dye in Ag nanoparticles colloidal dispersion.
The application of surface plasmon resonance (SPR) has transformed the field of study of interactions between a ligand immobilized on the surface of a sensor chip, designated as $L_S$, and an analyte in solution, referred to as $A$. This technique enables the real-time measurement of interactions with high sensitivity. The dynamics of adsorption-desorption process, $A+L_S \rightarrow AL_S$, can be expressed mathematically as a set of coupled integer-order differential equations. However, this approach has limited ability to acoount for temperature distribution, diffusion and transport effects involved in the reaction process. The fractional kinetic model provides a methodology for incorporating non-local effects into the problem. In this study, the proposed model was applied to analyze data to the interaction between Immobilized Baru Protein (IBP) and Congo Red dye (CR) at concentrations ranging from $7.5$ to $97.5$ $μM$, at pH $7.4$ and $16^o$ C. The variation in the kinetic constants was studied, and it was demonstrated that the integer-order model is unable to adequately represent the experimental data. This work has shown that the fractional-order model is capable of capturing the complexity of the adsorption-desorption process involved in the SPR data.
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to those used in image denoising, our approach minimizes a functional involving fractional derivatives to balance noise suppression with the preservation of essential chemical features of the signal, such as peak position, intensity, and area. The original problem is reformulated in the frequency domain through the Fourier transform, making the implementation simple and fast. In this work, we discuss the theoretical framework, practical implementation, and the advantages and limitations of this method in the context of {simulated} Raman data, as well as in image processing. The main contribution of this article is the combination of a variational approach in the frequency domain, the use of fractional derivatives, and the optimization of the {regularization parameter and} derivative order through the concept of Shannon entropy. This work explores how the fractional order, combined with the regularization parameter, affects noise removal and preserves the essential features of the spectrum {and image}. Finally, the study shows that the combination of the proposed strategies produces an efficient, robust, and easily implementable filter.
I am seeking collaborators to work on fractional-order modeling applied to chemical kinetics, nonlocal thermodynamics, and reaction–diffusi…