Volume 80, Issue 10

Degree-based and neighbourhood degree-sum-based (or hybrid degree-based) topological indices (TIs) for some benzenoid hydrocarbons viz. linear polyacences, methylene substituated linear polyacences, cyclacenes, linear poly ( p -phenylenes), methylene substituated linear poly ( p -phenylenes), and cylindrical poly ( p -phenylenes) with r hexagonal rings are expressed as linear functions of r . For a given system the variation of degree-based Randić and harmonic indices or that of their hybrid indices with r is quite similar while that differs with their corresponding hybrid degree-based indices. The geometric-arithmetic index is the only one among the indices for a given system which is found to remain unaffected under consideration of neighbourhood effect. Total π -electron energies for such systems have also been derived as linear functions of r from their respective eigenspectra. Although all such TIs discussed here have good linear correlations with the total π -electron energies of the respective systems but among them the geometric-arithmetic degree-based and hybrid degree-based TIs are the best to correlate total π -electron energies for such systems. The inverses of the degree-based and hybrid degree-based TIs of cyclacenes and cylindrical poly ( p -phenylenes) are found to correlate excellently well with their strain energies. The good linear correlations are also found with the inverses of the TIs of linear poly ( p -phenylenes) with 2–6 hexagonal rings and their respective bulk modulus.

This study aims to investigate the structural, mechanical, and tribological properties of titanium carbide coatings, focusing on the influence of deposition techniques, including chemical vapor deposition and physical vapor deposition, on their phase composition, morphology, and adhesion. The research combines experimental characterization and numerical modeling to analyze grain structure, hardness, adhesion strength, and thermal stability. The findings reveal that coatings obtained through chemical vapor deposition exhibit superior crystallinity with a hardness of 2,500 Vickers hardness and a critical adhesion load exceeding 80 N, alongside a denser microstructure. In contrast, coatings produced by physical vapor deposition present finer grains and improved surface smoothness, making them particularly advantageous for tribological applications. Thermal expansion modeling has been performed to assess the role of deposition techniques in stress development, identifying potential failure points when exposed to high temperatures. Furthermore, the study explores titanium carbide–hydroxyapatite composites, demonstrating their enhanced wear resistance, bioactivity, and nontoxic characteristics, which make them promising candidates for biomedical applications. The results significantly contribute to the optimization of deposition strategies, improving the mechanical performance and extending the range of potential applications of titanium carbide coatings. These applications include cutting tools, aerospace components, high-temperature protective coatings, and medical implants. The insights gained from this research offer valuable guidance for advancing the development of titanium carbide-based materials and enhancing their practical utility in modern engineering and biomedical fields.

A new type of high-dimensional Lie superalgebras is constructed, including Lie superalgebras spo(4, 2) and osp(4, 2). Based on it, two different coupled nonisospectral super AKNS hierarchies and their bi-Hamiltonian structures are obtained. Then, the Lie superalgebras spo(4, 2) and osp(4, 2) are expanded to infinite-dimensional Lie superalgebras spo(2N, 2) and osp(2N, 2). It follows that we present the generation of multi-component super integrable hierarchy, and deduce two different multi-component super integrable AKNS hierarchies and their Hamiltonian structures.

This work advances our 2D scalar electrodynamics (SED) model, a relativistic analogue of type-II superconductivity, by implementing a cylindrical coordinate representation. This adaptation addresses the importance of cylindrical symmetry in describing 2D systems, especially those featuring Dirac fermion bound states in magnetic fields. Focusing on a specific example, we explore the relativistic limit, significant in astrophysical environments like neutron-star cores, where magnetic fields reach critical levels. Along the lines of the Ginzburg–Landau theory we postulate the structure the proton vortex-supercurrent, and connect it with the SED current. From this connection we analytically determine the squared modulus of the relativistic order parameter state which is to be proportional to the local density of Cooper pairs in the superconducting condensate. This study could contribute to the theoretical understanding of superconductivity in strong electromagnetic fields within the SED framework, with potential applications to neutron star physics.

This work examines the propagation of dissipative dust-ion-acoustic (DIA) waves in a plasma with non-thermal electrons, heated positive ions, and stationary negative dust particles. This discussion also includes dissipative rogue waves (DRWs) and breathers. The linear damped nonlinear Schrödinger equation (dNLSE) and its detailed derivation are described here. When it comes to differential equations, the dNLSE is believed to be one that cannot be integrated. As a result of this, even with the inclusion of the linear damping term, there is still no solution that is accurate. In light of this, we will proceed to meticulously derive and present the semi-analytical solution today. This method allows for the analytical solution of the fundamental nonlinear Schrödinger equation (NLSE), with the damping term being left out of the equation. Using this method as a starting point, one can begin the process of solving the linearly damped NLSE. In addition to this, we will evaluate the analytical solutions of the standard NLSE in comparison to the approximate analytical solutions of the dNLSE. The manner in which plasma properties influence the characteristics of dissipatively modulated DIA waves is the subject of extensive research. To be more specific, the nonthermal electron count, the kinematic viscosity of the ions, and the temperature ratio of the ions to electrons are all taken into consideration. There is a possibility that this work will shed light on the modulated DIA structures that are present in both laboratory plasmas and space plasmas, as well as make predictions regarding such structures.

The reaction 7 Be(p,γ) 8 B plays a significant role in the evaluation of solar neutrino fluxes. Therefore, this reaction has a significant place in the proton-proton chain. Particularly at low energies, the reaction cross-sections and astrophysical S-factor values play a crucial role to explain its effects in the proton-proton chain. TALYS 1.95 nuclear reaction code were used to calculate theoretical cross-sections which are used to obtain both theoretical astrophysical s-factors and semi-empirical formula. In this way, more suitable estimates are made for the low energy range. The obtained results were analyzed in comparison with experimental data extracted from the EXFOR nuclear database.

The thermal vibration behavior of a butterfly auxetic core sandwich nanoplate with Piezoelectric surface layers is the main subject of this study. Used model employs the Nonlocal Strain Gradient Theory (NSGT) and Higher-Order Shear Deformation Theory (HSDT). The research systematically examines the combined effects of thermal loading, auxetic core geometry, and piezoelectric properties on the dynamic response of the nanoplate. Through numerical analysis, the influence of key parameters, including auxetic core dimensions, temperature rise, electric field, and plate thickness on the non-dimensional frequency and buckling characteristics is evaluated. The results reveal that auxetic structures significantly modify vibrational behavior, with increased auxeticity (negative Poisson’s ratio) leading to reduced stiffness under thermal loading. Furthermore, the study highlights the critical role of boundary conditions, demonstrating that clamped edges exhibit greater rigidity compared to simply supported configurations. These findings provide information for the design and optimization of sandwich structures, particularly in applications where thermal and mechanical loads are prevalent, such as microelectromechanical systems, aerospace, and other advanced engineering systems.