Ervin Kaminski Lenzi

Ervin Kaminski Lenzi
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Ervin verified their affiliation via an institutional email.
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Ervin verified their affiliation via an institutional email.
State University of Maringá | UEM

PhD

About

381
Publications
46,178
Reads
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5,963
Citations
Additional affiliations
September 2014 - present
State University of Ponta Grossa
Position
  • Professor (Associate)
Description
  • Research interest: anomalous diffusion, fractional diffusion equations, diffusion equation, electrical impedance, and liquid crystal boundary problems.
January 2015 - present
State University of Ponta Grossa
Position
  • Professor (Associate)
August 2002 - September 2014
State University of Maringá
Position
  • Professor (Associate)

Publications

Publications (381)
Article
Full-text available
From the analytical perspective, we investigate the diffusion processes that arise from a system composed of a surface with a backbone structure coupled to the bulk via the boundary conditions. The problem is formulated in terms of diffusion equations with nonlocal terms, which can be used to model different processes, such as sorption–desorption a...
Article
Full-text available
Here, we investigate a three-dimensional Schrödinger equation that generalizes the standard framework by incorporating geometric constraints. Specifically, the equation is adapted to account for a backbone structure exhibiting memory effects dependent on both time and spatial position. For this, we incorporate an additional term in the Schrödinger...
Article
This paper investigates the use of fractional-order PIλ (FO-PI) controllers and compares their performance with classical integer-order PID (IO-PID) and fractional-order PID (FO-PID) controllers for a two-input, two-output (TITO) distillation column. Additionally, a comparative study between FO-PI and model predictive control (MPC) is conducted on...
Article
Full-text available
We investigate the diffusion phenomenon of particles in the vicinity of a spherical colloidal particle where particles may be adsorbed/desorbed and react on the surface of the colloidal particle. The mathematical model comprises a generalized diffusion equation to govern bulk dynamics and kinetic equations which can describe non-Debye relaxations a...
Article
Helical twists exist in liquid crystals as a result of the addition of chiral dopants or boundary conditions and play a role in several liquid-crystal phenomena and devices. To date, various methodologies have been explored, albeit with varying degrees of precision and complexity, often resulting in the measurement of just one parameter, such as he...
Preprint
Full-text available
One way to study the spread of disease is through mathematical models. The most successful models compartmentalize the host population according to their infectious stage, e.g., susceptible (S), infected (I), exposed (E), and recovered (R). The composition of these compartments leads to the SI, SIS, SIR, and SEIR models. In this Chapter, we present...
Article
Full-text available
We investigate the H-theorem for a class of generalized kinetic equations with fractional time-derivative, hyperbolic term, and nonlinear diffusion. When the H-theorem is satisfied, we demonstrate that different entropic forms may emerge due to the equation’s nonlinearity. We obtain the entropy production related to these entropies and show that it...
Article
Full-text available
Many fundamental physical problems are modeled using differential equations, describing time- and space-dependent variables from conservation laws. Practical problems, such as surface morphology, particle interactions, and memory effects, reveal the limitations of traditional tools. Fractional calculus is a valuable tool for these issues, with appl...
Article
This paper investigates the Sundaresan technique for modeling fractional order systems. Sundaresan, Prasad, and Krishnaswamy published this method in 1978 for modeling oscillatory and non-oscillatory systems based on the second-order integer transfer function. This technique is based on the transient response parameters. A problem of convergence of...
Article
Full-text available
Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-near...
Article
Full-text available
In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers R0+. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topol...
Article
Full-text available
The interplay of diffusion with phenomena like stochastic adsorption–desorption, absorption, and reaction–diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dimensionality, and the interplay of diffusion across bulk and surfaces. To address this complexity, we investigate...
Preprint
Full-text available
Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-near...
Article
Full-text available
We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussian distribution as the initial condition. Measuring the spread of the Gaussian distribution by u(0,t)...
Article
Full-text available
The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behavior of neurons. One successful model used for this purpose is the Adaptive Exponential Integrate-and-Fire (Adex), which is composed of two ordinary differential equations. Usually, thi...
Article
Cancer is a group of diseases in which cells grow uncontrollably and can spread into other tissues. Various studies consider the interactions between cancer cells and the immune system as well as different types of treatment. Mathematical models have been used to study the growth of cancerous cells. We study a fractional order model that describes...
Article
Full-text available
In this study, we investigate a nonlinear diffusion process in which particles stochastically reset to their initial positions at a constant rate. The nonlinear diffusion process is modeled using the porous media equation and its extensions, which are nonlinear diffusion equations. We use analytical and numerical calculations to obtain and interpre...
Article
Full-text available
Objective: To propose a modeling for the flow in oil reservoirs using Caputo’s definition of fractional derivative applied to the spatial coordinate of the problem. Furthermore, delimit a region of numerical stability for the explicit method of solving the model equations. Methodology: Starting from the material balance in a differential control vo...
Article
Full-text available
We study the entropy production in a fractal system composed of two subsystems, each of which is subjected to an external force. This is achieved by using the H-theorem on the nonlinear Fokker–Planck equations (NFEs) characterizing the diffusing dynamics of each subsystem. In particular, we write a general NFE in terms of Hausdorff derivatives to t...
Article
Full-text available
The fractional reaction-diffusion equation has been used in many real-world applications in fields such as physics, biology, and chemistry. Motivated by the huge application of fractional reaction-diffusion, we propose a numerical scheme to solve the fractional reaction-diffusion equation under different kernels. Our method can be particularly empl...
Article
Full-text available
We investigate the dynamics of a system composed of two different subsystems when subjected to different nonlinear Fokker-Planck equations by considering the H-theorem. We use the H-theorem to obtain the conditions required to establish a suitable dependence for the system's interaction that agrees with the thermodynamics law when the nonlinearity...
Article
Full-text available
Obtaining thermal parameters based in the analysis only on the amplitude or phase of the photoacoustic (PA) signal from photothermal measurements is useful and valid once classical theoretical expectations are that the same parameters are contained in the photoacoustic signal. This work studies the issue of disagreement between experimentally measu...
Article
Full-text available
This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the m...
Article
Full-text available
We analyze the electrical impedance response established in terms of the time-fractional approach formulation of the Poisson-Nernst-Planck model by considering a general boundary condition. The total current across the sample is solenoidal, as the Maxwell equations require, and the boundary conditions can be related to different scenarios. We also...
Article
Full-text available
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid dif...
Article
Full-text available
In this work, we analyze the effects of fractional derivatives in the chaotic dynamics of a cancer model. We begin by studying the dynamics of a standard model, i.e., with integer derivatives. We study the dynamical behavior by means of the bifurca‑ tion diagram, Lyapunov exponents, and recurrence quantification analysis (RQA), such as the recurren...
Preprint
Full-text available
In this work, we analyze the effects of fractional derivatives in the chaotic dynamics of a cancer model. We begin by studying the dynamics of a standard model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by means of the bifurcation diagram, Lyapunov exponents, and recurrence quantification analysis (RQA), such as the recu...
Preprint
Full-text available
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid dif...
Article
Full-text available
We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of the main properties of these approaches and used the thermal Green fun...
Article
Full-text available
We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among th...
Preprint
Full-text available
We investigate the solutions for a time dependent potential by considering two scenarios for the fractional Schr\"odinger equation. The first scenario analyzes the influence of the time dependent potential in the absence of the kinetic term. We obtain analytical and numerical solutions for this case by considering the Caputo fractional time derivat...
Preprint
Full-text available
Recent advances in deep learning methods have enabled researchers to develop and apply algorithms for the analysis and modeling of complex networks. These advances have sparked a surge of interest at the interface between network science and machine learning. Despite this, the use of machine learning methods to investigate criminal networks remains...
Article
We present the temperature distribution predictions for photothermal systems by considering an extension of dual-phase lag. It is an extension of the GCE-II and GCE-III models with a fractional dual-phase lag from kinetic relaxation time. Solving the one-dimensional problem considering a planar and periodic excitation, we obtained the temperature d...
Article
Full-text available
We investigate the solutions for a time-dependent potential by considering two scenarios for the fractional Schrödinger equation. The first scenario analyzes the influence of the time-dependent potential in the absence of the kinetic term. We obtain analytical and numerical solutions for this case by considering the Caputo fractional time derivativ...
Article
Full-text available
We analyze an extension of the dual-phase lag model of thermal diffusion theory to accurately predict the contribution of thermoelastic bending (TE) to the Photoacoustic (PA) signal in a transmission configuration. To achieve this, we adopt the particular case of Jeffrey’s equation, an extension of the Generalized Cattaneo Equations (GCEs). Obtaini...
Article
Freeze- and spray-dried inclusion complexes (ICs) of chlorhexidine (CHX) in β-cyclodextrin were characterized by Fourier transform (FT)-Raman, 1H nuclear magnetic resonance (NMR), and photoacoustic spectroscopy. The active Raman modes of CHX were simulated using the density functional theory. By considering semiempirical calculations, it was observ...
Article
Full-text available
We investigate the solutions of a generalized diffusion-like equation by considering a spatial and time fractional derivative and the presence of non-local terms, which can be related to reaction or adsorption–desorption processes. We use the Green function approach to obtain solutions and evaluate the spreading of the system to show a rich class o...
Chapter
This chapter deals with illustrative problems involving anomalous diffusion behavior in connection with adsorption phenomena at the interface between a solid and a fluid phase. The kinetic balance equations at the interface are of Langmuir’s type and their generalizations, which are mostly developed using memory kernels and also considering reversi...
Chapter
In this chapter, we start by investigating the adsorption-desorption phenomenon followed by a reaction process that may occur on a surface in contact with a system composed of two different kinds of particles, 1 and 2. We consider that generalized diffusion equations govern the diffusion of particles of the system in the bulk. Depending on the cond...
Chapter
This chapter is devoted to introducing the elements of fractional calculus, Fractional calculusemphasizing some aspects of the historical development of the concepts of differentiation and integration of arbitrary order. A discussion about the significance and meaning of fractional calculus, Fractional calculusin general, is presented with didactic...
Chapter
This chapter provides the essential mathematical tools to be used in the subsequent chapters, and is intended to make the book as self-contained as possible. The first part of the chapter is dedicated to review some useful properties of the integral transformsIntegral transforms of Fourier and Laplace, illustrating their applicability with a few ex...
Chapter
This chapter deals with the description of constrained motion in connection with the Schrödinger equationSchrödinger equationusual with the help of the comb modelComb model. Exact solutions are obtained to investigate the time evolution of the initial conditions and the asymptotic behavior in two-, three-, and non-integer dimensions as a tool to ha...
Chapter
This chapter opens explaining the main concepts necessary to describe the diffusion phenomena. It contains a short account of the theories developed to build their mathematical description, emphasizing the approaches of EinsteinEinstein, Albert and LangevinLangevin, Paul. The treatment of EinsteinEinstein, Albert is extended and reformulated as a w...
Chapter
In this chapter, we discuss the general problem of fractional diffusion equationFractional diffusion equation in connection with the anomalous behaviorAnomalous behavior. We consider first the fundamental solution for the space-time fractional diffusion equationFractional diffusion equation involving the CaputoCaputo fractional derivative operator...
Chapter
This chapter deals with the random walkRandom walks problem and its connections with the diffusion processes. Its first part is dedicated to an elementary approach to the classical random walkRandom walkss or random flights problem. Then, a generalization of the random walkRandom walks, starting from a nonlinear diffusion equation (or nonlinear Fok...
Chapter
In this and the next chapter, we shall examine the relaxation behavior of classical and quantum systemQuantumsystemss under geometric constraints represented by structures known as comb modelsComb model. These models with fractional time derivatives are a reasonable abstraction for systems in which the interplay between temporal and spatial disorde...
Article
Full-text available
We apply an extension of dual-phase lag in thermal systems to predict the photoacoustic (PA) signal for transmission configuration and characteristics of the Open Photoacoustic Cell (OPC) technique. For this, we consider a particular case from Jeffrey?s equation as an extension of the generalized Cattaneo equations (GCEs). In this context, we obtai...
Article
Full-text available
In this work, we investigate the effect of the number of available adsorption sites for diffusing particles in a liquid confined between walls where the adsorption (desorption) phenomena occur. We formulate and numerically solve a model for particles governed by Fickian’s law of diffusion, where the dynamics at the surfaces obey the Langmuir kineti...
Article
Full-text available
The application of fractional calculus in the field of kinetic theory begins with questions raised by Bernoulli, Clausius, and Maxwell about the motion of molecules in gases and liquids. Causality, locality, and determinism underly the early work, which led to the development of statistical mechanics by Boltzmann, Gibbs, Enskog, and Chapman. Howeve...
Preprint
Full-text available
The photoacoustic (PA) signal is the pressure variation in the PA cell and by means of the open photoacoustic cell (OPC) technique, its amplitude and phase components are measured. In this work, the issue of disagreement between experimental measured amplitude and phase for AISI 316 samples with the expected theoretical result from the classical mo...
Article
The objective of this work was to investigate and model the viscoelastic creep behavior of two Brazilian crude oils: A (API 16.8) and B (API 24.6), with different contents of aromatics, resins and asphaltenes and their W/O emulsions with water contents between 0 to 55%. Stable emulsions were prepared using an Ultra-Turrax homogenizer and the viscoe...
Article
We investigate an extension of the Schrödinger equation by considering a fractional differential operator for the spatial variable, which simultaneously takes the heterogeneity of the media and Lévy like distributions into account. By using the Green’s function method, we obtain solutions to the equation in the case of the free particle and when it...
Article
Full-text available
Recent research has shown that criminal networks have complex organizational structures, but whether this can be used to predict static and dynamic properties of criminal networks remains little explored. Here, by combining graph representation learning and machine learning methods, we show that structural properties of political corruption, police...
Preprint
Full-text available
Recent research has shown that criminal networks have complex organizational structures, but whether this can be used to predict static and dynamic properties of criminal networks remains little explored. Here, by combining graph representation learning and machine learning methods, we show that structural properties of political corruption, police...
Article
We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equations. Only in this case the electric impedance of a cell can be determined as the ratio between the...
Article
The approaches developed for studying the polarization of molecules and the dynamics of ions in dielectric materials are usually considered separately. The two effects are often believed to take place in different frequency ranges. The low frequency response is usually dominated by ionic migration, whereas the high frequency response is played by m...
Article
Full-text available
We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which are given in terms of stretched exponential...
Article
Full-text available
We propose an anomalous diffusion approach to analyze the electrical impedance response of electrolytic cells using time-fractional derivatives. We establish, in general terms, the conservation laws connected to a modified displacement current entering the fractional approach formulation of the Poisson–Nernst–Planck (PNP) model. In this new formali...
Article
We analyze the influence of the generalizations of hyperbolic (Cattaneo) heat equations (GCE) on temperature profile and photoacoustic signal for the two-layer samples. The GCE extensions employ fractional-order derivatives related to the anomalous thermal diffusion in solid. We compare the superdiffusive (GCEII) and subdiffusive (GCEIII) generaliz...
Article
Full-text available
We investigate diffusion in three dimensions on a comb-like structure in which the particles move freely in a plane, but, out of this plane, are constrained to move only in the perpendicular direction. This model is an extension of the two-dimensional version of the comb model, which allows diffusion along the backbone when the particles are not in...
Preprint
Full-text available
We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a power-law dependence on particles' positions. We use the Green function approach to obtain exact solutions for the pro...
Preprint
Full-text available
We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equation. Only in this case the electric impedance of a cell can be determined as the ratio between the a...