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: 31 July 2025 | Viewed by 8572

Special Issue Editors


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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

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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

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Keywords

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

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Published Papers (12 papers)

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Research

19 pages, 560 KiB  
Article
Eigenvalue Spectra of Rabi Models with Infinite Matrix Representations
by Hongbin Liang, Shucan Xia, Yixiang Chen, Yuguo Su and Jie Chen
Axioms 2025, 14(4), 263; https://doi.org/10.3390/axioms14040263 - 30 Mar 2025
Viewed by 37
Abstract
We investigate the relationship between confluent Heun functions and the eigenvalue spectra of infinite matrices related to the semi-classical and quantum Rabi models, revealing distinct connections in each case. In the semi-classical model, the eigenvalues are explicitly expressed through confluent Heun functions, whereas [...] Read more.
We investigate the relationship between confluent Heun functions and the eigenvalue spectra of infinite matrices related to the semi-classical and quantum Rabi models, revealing distinct connections in each case. In the semi-classical model, the eigenvalues are explicitly expressed through confluent Heun functions, whereas in the quantum Rabi model, they are determined by zeros of a condition involving confluent Heun functions. Our findings establish a unified framework for solving the eigenvalue problem of infinite-dimensional unbounded matrices related to the Rabi models. We derive some new identities for confluent Heun functions, enabling simplifications and broader applications in mathematics and physics. The explicit eigenvalue expressions in the semi-classical case align with approximate results from earlier studies, while the derived conditions for the quantum model provide a concise and unified form, encompassing special cases that are typically treated as exceptions. We also discuss the energy spectrum of the quantum Rabi model, uncovering intriguing phenomena and patterns. Our results deepen the understanding of Rabi models and extend their potential applications in quantum optics and quantum information. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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11 pages, 501 KiB  
Article
Relativistic Scalar Particle Systems in a Spacetime with a Spiral-like Dislocation
by Ricardo L. L. Vitória
Axioms 2025, 14(3), 227; https://doi.org/10.3390/axioms14030227 - 19 Mar 2025
Viewed by 238
Abstract
We have analyzed solutions of bound states of a scalar particle in spacetime with torsion. In the first analysis, we investigate the confinement of a scalar particle in a cylindrical shell. In the second step, we investigate the Klein–Gordon oscillator. Then, we finish [...] Read more.
We have analyzed solutions of bound states of a scalar particle in spacetime with torsion. In the first analysis, we investigate the confinement of a scalar particle in a cylindrical shell. In the second step, we investigate the Klein–Gordon oscillator. Then, we finish our analysis by searching for solutions of bound states of the Klein–Gordon oscillator by interacting with a hard-wall potential. In all these systems, we determine the relativistic energy profile in the background characterized by the presence of torsion in spacetime represented by a spiral-like dislocation. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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13 pages, 3104 KiB  
Article
Interaction of a Four-Level Atom with a Deformed Quantum Field: Mathematical Model and Quantum Resources
by Mariam Algarni, Sayed Abdel-Khalek and Kamal Berrada
Axioms 2025, 14(3), 211; https://doi.org/10.3390/axioms14030211 - 13 Mar 2025
Viewed by 205
Abstract
We introduce a framework presenting the interaction between a four-level atom (F-LA) and a field mode that begins in a coherent state within the para-Bose field (P-BF). The F-LA is considered in a cascade configuration and initially prepared in the upper level. We [...] Read more.
We introduce a framework presenting the interaction between a four-level atom (F-LA) and a field mode that begins in a coherent state within the para-Bose field (P-BF). The F-LA is considered in a cascade configuration and initially prepared in the upper level. We display the system dynamics by solving the motion equation. We discuss various dynamical behaviors of fundamental quantum resources used in quantum optics and information tasks, including atomic population inversion, quantum entanglement (QE), and the statistical properties of the P-BF based on the parameters of the quantum model. In this context, we demonstrate the impact of various system parameters on these quantum resources. Finally, we illustrate the dynamic relationships among the quantum resources within the model. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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14 pages, 264 KiB  
Article
Strong Stability of the Thermoelastic Bresse System with Second Sound and Fractional Delay
by Khaled Zennir and Loay Alkhalifa
Axioms 2025, 14(3), 176; https://doi.org/10.3390/axioms14030176 - 27 Feb 2025
Viewed by 232
Abstract
The thermoelastic Bresse system is a mathematical model that describes the dynamic behavior of elastic beams accounting for both mechanical deformations and thermal effects. Incorporating concepts such as second sound and fractional delay into this system enhances its ability to model complex physical [...] Read more.
The thermoelastic Bresse system is a mathematical model that describes the dynamic behavior of elastic beams accounting for both mechanical deformations and thermal effects. Incorporating concepts such as second sound and fractional delay into this system enhances its ability to model complex physical phenomena. The paper studies a Bresse thermoelastic system with fractional delay and second sound. Firstly, we prove the existence and uniqueness of the solution for our system using semi-group theory. Additionally, we derive an exponential decay estimate for the associated semi-group utilizing suitable multiplier techniques. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
18 pages, 2240 KiB  
Article
The Characteristic Relation in Two-Dimensional Type I Intermittency
by Juan Colman and Sergio Elaskar
Axioms 2025, 14(1), 24; https://doi.org/10.3390/axioms14010024 - 31 Dec 2024
Viewed by 466
Abstract
To explore intermittency in discrete systems with two or more degrees of freedom, we analyze the general characteristics of type I intermittency within a two-dimensional map. This investigation is carried out numerically, concentrating on the system’s attractors, bifurcation diagrams, and the characteristic relation [...] Read more.
To explore intermittency in discrete systems with two or more degrees of freedom, we analyze the general characteristics of type I intermittency within a two-dimensional map. This investigation is carried out numerically, concentrating on the system’s attractors, bifurcation diagrams, and the characteristic relation associated with type I intermittency. We present two methods for determining the laminar interval and the channel structure. Our computations yield numerical results for the average laminar length as a function of the control parameter, which we then compare with findings from intermittency in one-dimensional maps. We observe a strong agreement between the numerical data and the theoretical predictions. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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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 734
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 623
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 790
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 673
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
Cited by 2 | Viewed by 727
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 827
Abstract
For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=xyEGϕ(dx,dy), [...] Read more.
For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=xyEGϕ(dx,dy), where ϕ is a symmetric map and di is the degree of iVG. For αR, 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 2 | Viewed by 1811
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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