arXiv subjects

Luiz Bevilacqua

Publications and source records attributed to Luiz Bevilacqua.

5 recordsLinked to original sources

arXiv2022

Numerical analysis of growth-mediated autochemotactic pattern formation in self-propelling bacteria

In this paper, a decoupled characteristic Galerkin finite element procedure is provided for simulating growth-mediated autochemotactic pattern formation in self-propelling bacteria. In this procedure, a modified characteristic Galerkin method is established to solve the bacterial density equation, while the classical finite element procedure is considered for the self-secreted chemical density and polarization dynamics equations system. The convergence of this proposed method is considered under some regularity assumptions and the corresponding error estimate is derived. Numerical experiments are carried out to support the theoretical analysis. Furthermore, several new wave type pattern formations are found.

math.NA↗

arXiv2022

The inverse problem for fractal curves solved with the dynamical approach method

The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal dimension. It is shown that the dynamical approach extends the characterization of a curve as a fractal object introducing the effects of mass density, elastic properties, and transverse geometry. The dynamical dimension characterizes material objects and suggests that biological characterization can be much more complete with the methodology presented here.

nlin.PS↗

arXiv2021

Energy exchange in a dual flow diffusion process that consists of particles of the same nature divided into two different microstates

This article presents a new approach to the dynamics of a particle system, divided into two distinct microstates spreading out in a homogeneous medium. The particles belonging to the main microstate spread according to classical Fick's law and the complementary set moves excitedly by a new potential. Each set is associated with a certain energy level. The particles can move between the two sets, introducing a third flow that is internal to the system. The governing equation is a fourth order PDE containing two new parameters, which can be time-dependent functions, in addition to the classical diffusion constant. It is shown that the solutions can avoid violations of the mass conservation requirements.

physics.flu-dyn↗

arXiv2014

Dynamical Characterization of Fractal Objects: Determination of the Fine Fractal Topology Using the Energy Cover

The foundation of the theory presented here has already been proved to be effective for the case of curves belonging to the Koch family. The present paper extends the investigation to more complex curves, namely randomly generated curves and the Weierstrass-Mandelbrot curve. The analysis is focused on numerical experiments. The results obtained with the numerical analysis allow advancing some interesting proposition concerning the fine fractal structure of plane curves. The method uses the dynamical response of appropriate harmonic oscillators built up according to the geometry of the fractal set. For the plane motion three fundamental periods are determined. Each period plotted against the characteristic length of the corresponding curve in a log-log scale estimates the fractal dimension. It is shown that each degree of freedom corresponds to a distinct energy covering associate to a certain topological property. Using this technique it is possible to distinguish the fine fractal structure of plane curves. The dynamic technique is proved to work also for the identification problem, that is, to determine the fractal characteristics embedded in some sample of a given fractal set. It is proposed the classification of fractal structures into at least two categories, perfectly fractal and partially fractal. The affine similarity can be precisely detected using this method.

math.MG↗

arXiv2008

A Mathematical Approach to the Plato's Problem

Maybe the first inverse problem presented in the history of the occidental thought is described in the book Republic, written by Plato. The problem is posed in the Book VII in a text known as the Allegory of the Cave. That text motivated us to formulate a simple mathematical model that simulates, in a sense, the situation of the persons described in that problem.

math.HO↗