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Axioms
Special Issues
Advancements in Applied Mathematics and Computational Physics
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Advancements in Applied Mathematics and Computational Physics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 28 January 2025 | Viewed by 5452

Special Issue Editors

Dr. Branislav Randjelovic

E-Mail Website
Guest Editor
Associate Professor, Department of Mathematics, Faculty of Electronic Engineering, University of Nis, Nis, Serbia
Interests: applied mathematics; graph theory; numerical mathematics; discrete mathematics; material science and nanoelectronics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Branislav Vlahovic

E-Mail Website
Guest Editor
Department of Mathematics and Physics, North Carolina Central University, Durham, NC, USA
Interests: genomics and mathematics; experimental and theoretical nuclear and hypernuclear physics; material science; nanotechnology; photonics and photovoltaics; chemistry; cosmology

Special Issue Information

Dear Colleagues,

Mathematics and physics, as basic natural sciences, are the root of almost all processes in nature and technology. There are a large number of situations where those two sciences can offer the best models and most appropriate explanations for natural processes or technological problems.

The aim of this Special Issue is to present various ways and new solutions to explain the nature of matter, biophysical systems and systems in technical sciences in the frame of overall reality, using the latest achievements in applied mathematics and computational physics.

The focus of this Special Issue is on new results and solutions in contemporary applied mathematics, algebra, mathematical logic, graph theory, fractals, chaos theory, numerical mathematics, mathematical physics and the latest results in experimental physics, computational physics and physical electronics for problems in nature, technology, technics and electronics.

This Special Issue will cover a broad range of topics to provide new insight into the exploration of the world of electronics, physical electronics, nuclear and hyper-nuclear physics, nanotechnology, material science, photonics and photovoltaics, cosmology, genomics and nature.

The content of this Special Issue will link to other existing literature and already published results as both applied mathematics and computational physics successfully integrate and open up new insights in natural phenomena, offering incredible tools to explain them.

Dr. Branislav Randjelovic
Prof. Dr. Branislav Vlahovic
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • applied mathematics
  • computational physics
  • experimental and theoretical physics
  • physical electronics
  • algebra

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Published Papers (7 papers)

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Research

37 pages, 424 KiB  
Article
The Robin Problems in the Coupled System of Wave Equations on a Half-Line
by Po-Chun Huang and Bo-Yu Pan
Axioms 2024, 13(10), 673; https://doi.org/10.3390/axioms13100673 - 29 Sep 2024
Viewed by 486
Abstract
This article investigates the local well-posedness of a coupled system of wave equations on a half-line, with a particular emphasis on Robin boundary conditions within Sobolev spaces. We provide estimates for the solutions to linear initial-boundary-value problems related to the coupled system of [...] Read more.
This article investigates the local well-posedness of a coupled system of wave equations on a half-line, with a particular emphasis on Robin boundary conditions within Sobolev spaces. We provide estimates for the solutions to linear initial-boundary-value problems related to the coupled system of wave equations, utilizing the Unified Transform Method in conjunction with the Hadamard norm while considering the influence of external forces. Furthermore, we demonstrate that replacing the external force with a nonlinear term alters the iteration map defined by the unified transform solutions, making it a contraction map in a suitable solution space. By employing the contraction mapping theorem, we establish the existence of a unique solution. Finally, we show that the data-to-solution map is locally Lipschitz continuous, thus confirming the local well-posedness of the coupled system of wave equations under consideration. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
24 pages, 6028 KiB  
Article
Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations
by Zhenyu Lang, Xiuling Yin, Yanqin Liu, Zhiguo Chen and Shuxia Kong
Axioms 2024, 13(9), 574; https://doi.org/10.3390/axioms13090574 - 23 Aug 2024
Viewed by 442
Abstract
Good Boussinesq equations are considered in this work. First, we apply three combined compact schemes to approximate spatial derivatives of good Boussinesq equations. Then, three fully discrete schemes are developed based on a symplectic scheme in the time direction, which preserves the symplectic [...] Read more.
Good Boussinesq equations are considered in this work. First, we apply three combined compact schemes to approximate spatial derivatives of good Boussinesq equations. Then, three fully discrete schemes are developed based on a symplectic scheme in the time direction, which preserves the symplectic structure. Meanwhile, the convergence and conservation of the fully discrete schemes are analyzed. Finally, we present numerical experiments to confirm our theoretical analysis. Both our analysis and numerical tests indicate that the fully discrete schemes are efficient in solving the spatial derivative mixed equation. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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39 pages, 514 KiB  
Article
Well-Posedness of the Schrödinger–Korteweg–de Vries System with Robin Boundary Conditions on the Half-Line
by Po-Chun Huang and Bo-Yu Pan
Axioms 2024, 13(8), 508; https://doi.org/10.3390/axioms13080508 - 28 Jul 2024
Cited by 1 | Viewed by 626
Abstract
The Schrödinger–Korteweg–de Vries (SKdV) system can describe the nonlinear dynamics of phenomena such as Langmuir and ion acoustic waves, which are highly valuable for studying wave behavior and interactions. The SKdV system has wide-ranging applications in physics and applied mathematics. In this article, [...] Read more.
The Schrödinger–Korteweg–de Vries (SKdV) system can describe the nonlinear dynamics of phenomena such as Langmuir and ion acoustic waves, which are highly valuable for studying wave behavior and interactions. The SKdV system has wide-ranging applications in physics and applied mathematics. In this article, we investigate the local well-posedness of the SKdV system with Robin boundary conditions and polynomial terms in the Sobolev space. We want to enhance the applicability of this type of SKdV system. Our verification process is as follows: We estimate Fokas solutions for the Robin problem with external forces. Next, we define an iteration map in suitable solution space and prove the iteration map is a contraction mapping and onto some closed ball B(0,r). Finally, by the contraction mapping theorem, we obtain the uniqueness solution. Moreover, we show that the data-to-solution map is locally Lipschitz continuous and conclude with the well-posedness of the SKdV system. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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12 pages, 275 KiB  
Article
Special Geometric Objects in Generalized Riemannian Spaces
by Marko Stefanović, Nenad Vesić, Dušan Simjanović and Branislav Randjelović
Axioms 2024, 13(7), 463; https://doi.org/10.3390/axioms13070463 - 9 Jul 2024
Viewed by 527
Abstract
In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications [...] Read more.
In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications in physics. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
22 pages, 693 KiB  
Article
Biequivalent Planar Graphs
by Bernard Piette
Axioms 2024, 13(7), 437; https://doi.org/10.3390/axioms13070437 - 28 Jun 2024
Viewed by 533
Abstract
We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an [...] Read more.
We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an algebraic method, which is followed by an algorithmic method, to determine all such graphs with up to 300 nodes each with valencies ranging between three and six. We also present a graphic representation of every graph found. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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14 pages, 1633 KiB  
Article
An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons
by Sakander Hayat, Azri Arfan, Asad Khan, Haziq Jamil and Mohammed J. F. Alenazi
Axioms 2024, 13(6), 342; https://doi.org/10.3390/axioms13060342 - 22 May 2024
Cited by 1 | Viewed by 687
Abstract
For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=∑xy∈EGϕ(dx,dy), [...] Read more.
For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=∑xy∈EGϕ(dx,dy), where ϕ is a symmetric map and di is the degree of i∈VG. For α∈R, if ϕ=(dxdy)α (resp. ϕ=(dx+dy)α), the index is called the general product-connectivity Rα (resp. general sum-connectivity SCIα) index. In this paper, by formulating an optimization problem, we determine the value(s) of α, for which the linear/multiple correlation coefficient of Rα and SCIα with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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24 pages, 20089 KiB  
Article
Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying)
by Adan Ramirez-Lopez
Axioms 2024, 13(5), 313; https://doi.org/10.3390/axioms13050313 - 10 May 2024
Cited by 1 | Viewed by 1324
Abstract
This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. [...] Read more.
This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. Here, the flight is divided into maneuvers and the aircraft conditions are defined as boundary conditions. Then the aircraft position is calculated using nested loops, which execute the calculation procedure at every step time (Δt). The calculation of the aircraft displacement is obtained as a function of the aircraft speed and heading angles. The simulator was created using the C++ programming language, and each part of the algorithm was compiled independently to reduce the source code, allow easy modification, and improve the programming efficiency. Aerial navigation involves very complex phenomena to be considered for an appropriate representation; moreover, in this manuscript, the influence of the mathematical approach to properly represent the aircraft flight is described in detail. The flight simulator was successfully tested by simulating some basic theoretical flights with different maneuvers, which include stationary position, running along the way, take off, and some movements in the airspace. The maximum aircraft speed tested was 120 km/h, the maximum maneuver time was 12 min, and the space for simulation was assumed to be without obstacles. Here, the geometrical description of path and speed is analyzed according to the symmetric and asymmetric results. Finally, an analysis was conducted to evaluate the approach of the numerical methods used; after that, it was possible to confirm that precision increased as the step time was reduced. According to this analysis, no more than 500 steps are required for a good approach in the calculation of the aircraft displacement. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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