Vol. 3 No. 3 (2025)

Open Access

Article

Article ID: 2741

Schwarzschild black hole spacetimes with viscous hot unmagnetized plasma Milky Way optically thin disc

by Orchidea Maria Lecian

Journal of AppliedMath, Vol.3, No.3, 2025;

The Schwarzschild spacetimes with hot viscous rarefied unmagnetized plasma are investigated under adiabatic perturbations of the 4-velocity of the plasma of the slim disc. The r-component of the 4-velocity and the ϕ-component of the 4-velocity are analytically written. The ϕ component of the 4-velocity is found not to depend on the 4-position. Indeed, the functional dependence of the canonical energy of the perturbation on the component uϕ of the 4-velocity is studied: it is defined to be unvaried for a vanishing value of uϕ and for a constant non-vanishing value of uϕ; differently, it varies with different characterizations of uϕ. The results are a comparison with the current understanding of the central region of the Milky Way and of the further regions. The position of the outer boundary conditions is newly discussed. The speed of sound in the disc is newly found to be dependent on the radial position, the accretion rate of the black hole object and the variation of the gravitational potential of the gravitating disc. The position of the outer boundary conditions is therefore newly discussed according to the transonic behavior of the disc and to the determination of the sonic points.

Open Access

Article

Article ID: 2386

A duality principle and an existence result for a non-linear model in elasticity and relaxation for related models in phase transition

by Fabio Silva Botelho

Journal of AppliedMath, Vol.3, No.3, 2025;

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual variational formulation for a non-linear model in elasticity. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. In a subsequent section, we present a global existence result for such a concerning model in elasticity. Finally, in the last sections, we develop duality principles and relaxation procedures for a related model in phase transition.

Open Access

Article

Article ID: 2311

Free surface flow over a trapezoidal cavity with surface tension effect

by Abdelkader Laiadi

Journal of AppliedMath, Vol.3, No.3, 2025;

This paper investigates two-dimensional free surface flows over a trapezoidal cavity in a fluid with finite depth. By assuming that the flow is steady, irrotational, and that the fluid is non-viscous and incompressible. We suppose that the surface tension is included in the nonlinear boundary condition derived from Bernoulli’s equation. A numerical approach using the series truncation method is employed to solve the problem. Solutions are computed for a symmetric trapezoidal obstacle for each value of the Weber number and the height of obstacle. The influence of the Weber number, the bottom height, and the angle of the obstacle are discussed.

Open Access

Article

Article ID: 2609

On galaxies of sequences of matrix Pythagorean triples and completely Pythagorean maps

by Joachim Moussounda Mouanda, Jean Raoul Tsiba, Kinvi Kangni

Journal of AppliedMath, Vol.3, No.3, 2025;

We develop an algorithm that allows us to construct the sequences of matrix Pythagorean triples of any size. We prove that there exists an infinite number of galaxies of sequences of matrix Pythagorean triples. We construct the semiring of sequences of matrix Pythagorean triples called the astral body of the set Mm(ℕ) associated to a galaxy. We show that every galaxy of sequences of matrix Pythagorean triples is associated with a semiring, and every semiring is associated with a homomorphism of semirings. We construct the astral body of the set of complex polynomials over the unit disk D. We construct the semiring of astral bodies of the set Mm(ℕ) associated with several galaxies. We also introduce the sequences of completely Pythagorean maps over N³.

Open Access

Article

Article ID: 2837

Mathematical modeling of the process of hydrotreating diesel fuel from organosulfur impurities

by Naum A. Samoilov

Journal of AppliedMath, Vol.3, No.3, 2025;

Hydrotreating of diesel fuel is a major catalytic process for motor fuel production. This process aims to reduce the organosulfur content in the fuel to 10 parts per million (ppm) in order to meet environmental standards. However, this deep purification of diesel fuel requires the use of an expensive catalyst at hydrotreating plants, which have giant reactors with a capacity of 200–600 cubic meters. Such a volume of reactors is associated with the use of methods of classical kinetics of chemical reactions, when all the raw materials of the process are in the reactor until the required conversion depth is reached, while hydrotreating has its own specific features. All known mathematical models for diesel fuel hydrotreating take into account different nuances of the process, but they all have one common disadvantage: they use approximate, often crude, ideas about the composition of multicomponent raw materials, such as diesel oil fractions, which contain several dozen different organosulfur compounds with varying activity in hydrogenation reactions. Most often, these raw materials are represented in a mathematical model as a combination of two to six pseudo-components, or lumps, that combine sulfo-organic impurities from one or more homologous groups. Such a theoretical framework allows us to model the current state of hydrotreating technology, but it does not advance it. We propose a new approach to mathematical modeling of diesel fuel hydrotreatment, which better takes into account the actual features of the process. The structure of the mathematical model considers the composition of the raw material as a set of 10–20 narrow fractions. In each fraction, the set of hydrogenated organosulfur impurities is treated as a single pseudo-component. Another feature of the model is the use of different rate constants for different organosulfur impurities in the raw material, represented as a continuous kinetic characteristic that changes over time. This allows us to integrate the system of differential equations in the model and adapt the rate constant to the concentration of the hydrogenated organosulfur impurity at any given time during the process. The developed model has also made it possible to propose a new technology, hydrotreatment: separating the feedstock into two or three wide fractions, combining the corresponding narrow fractions, and then subjecting them to separate hydrogenation processes. This differential hydrotreatment technique will allow for a reduction of the catalyst load in the hydrotreatment unit by almost 50% while maintaining its efficiency or for doubling the efficiency while maintaining the same catalyst load with traditional technology.

Open Access

Opinion

Article ID: 2984

A direct trial function approach for solving nonlinear evolution equations

by Yuanxi Xie

Journal of AppliedMath, Vol.3, No.3, 2025;

The Klein equation, Infeld equation, and Sivashinsky equation not only start from realistic physical phenomena but can also be widely used in many physically significant fields such as plasma physics, fluid dynamics, crystal lattice theory, nonlinear circuit theory, and astrophysics. As a consequence, it is a very significant and challenging topic to research the explicit and accurate travelling wave solutions to these three equations. In this paper, in order to solve these three nonlinear partial differential equations (NPDEs), we have made some modifications to the trial function technique proposed by Xie and Tang by bringing in an ansatz solution containing two E-exponential functions. On this basis, we have developed a direct trial function technique to seek the explicit and accurate travelling wave solutions of nonlinear evolution equations (NEEs). We have illustrated its feasibility by applying it to the Klein equation, Infeld equation, and Sivashinsky equation. As a result, a lot of more general explicit and accurate travelling wave solutions of these three equations, including the solitary wave solutions and the singular travelling wave solutions, are successfully constructed in a straightforward and simple manner. The obtained solutions are quite equivalent to those given in the existing references. In addition, compared with the proposed approaches in the existing references, the approach described herein appears to be less calculative. Our technique may provide a novel way of thinking for solving NEEs. It is our firm conviction that the procedure used herein may also be utilized to explore the explicit and accurate travelling wave solutions of other NEEs. We try to generalize this approach to search for the explicit and accurate traveling wave solutions of other NEEs.