Volume 80, Issue 3

In this study, we have managed to model the energy surface of the aminophenol derivative azomethine molecule mathematically depending on two torsion angles SC1(C9C10C12N14) and SC2(C2C1C6C11). For this purpose, firstly, discrete data obtained from Density Functional Theory calculations have been converted into continuous data with the help of the Fuzzy Inference System. Thus, it is possible to calculate energy values for untested data, which are very costly in terms of time to obtain with other methods/experiments. Then, the continuous and non-smooth surface obtained from the fuzzy inference system and representing the energy values of the molecule has been transformed into a differentiable surface with the help of Bezier surfaces. Thus, an objective function has been obtained in which global optimization methods based on the derivative (or gradient) operator could be used.

Coronene, a polycyclic aromatic hydrocarbon (PAH) consisting of six benzene rings fused in a hexagonal arrangement, exhibits a fractal structure that is significant in various fields such as condensed matter physics, materials science, surface science, and interdisciplinary areas like nanotechnology and astrochemistry. Topological descriptors, which characterize the geometric and connectivity properties of a structure independently of specific spatial coordinates, are crucial for understanding coronene’s complex geometry and connectivity. In this study, we compute the atom-bond sum (ABS)-connectivity index and four versions of the Sombor indices for three different configurations of the coronene fractal structure: Zig-zag Hexagonal Coronene Fractal (ZHCF), Armchair Hexagonal Coronene Fractal (AHCF), and Rectangular Coronene Fractal (RCF). To assess their chemical applicability, we develop linear regression models to estimate the physicochemical properties boiling point (BP) and molecular weight (MW) of benzene derivatives using these topological indices. The regression parameters for each case are provided, and the results show that the ABS index outperforms all other topological indices, making it the most effective predictor for these properties.

In this article, classical Cauchy reaction-diffusion equations are converted into the corresponding time-fractional Cauchy reaction-diffusion equations using Caputo–Fabrizio fractional order derivative. The obtained equations are then solved using a semi-analytical method, which is the combination of Laplace transform and Picard’s iterative scheme. The derived solutions are innovative, and such derivations are not found in the previous literature. In addition, the Banach fixed-point principle and G -stable mapping are used to analyze stability of the implemented semi-analytical method. Error estimation and comparison of derived results with exact solutions already available in the literature through graphical illustrations and tables reveal that the implemented semi-analytical method is more efficient and fruitful for solution of time-fractional Cauchy reaction-diffusion equations.

This study focuses on a (3 + 1)-dimensional nonlinear evolution model derived from the Jaulent–Miodek hierarchy. Our research employed analytical tools to scrutinize the invariance characteristics of this model. However, our primary emphasis is on utilizing the potent Lie group method, which effectively reveals the inherent symmetries within the model and explores solutions that remain invariant under group transformations using symmetry algebra. Furthermore, we investigated the application of Ibragimov’s approach to examine the conservation laws relevant to the model under consideration. This theorem is employed to identify and analyze the conservation laws associated with the (3 + 1)-dimensional nonlinear evolution model, which is essential for understanding the behavior of the system. Our research is significant as it contributes to exploring this particular model and addresses a specific gap in the group theoretic approach within this context.

This study investigates the temperature-dependent elastic, mechanical, thermal, and acoustic features of alkaline earth semiconductors calcium monochalcogenides CaX (X = S, Se, Te). First of all, the second- and third-order elastic constants have been calculated in the temperature range 0–500 K using the Born-potential model. The evaluated SOECs values were utilized to compute the mechanical constants at 0 K and 300 K. Selected materials in the present investigation have been found mechanically stable and brittle, in nature. The elastic anisotropy of the mechanical moduli has been presented using the 3D surface. SOECs have also been employed to perceive the acoustical wave velocities for longitudinal and shear modes of propagation and Debye mean velocities along <100>, <110>, and <111> directions. SOECs and TOECs were used to calculate the acoustic Grüneisen parameters. Further, the Debye characteristic temperature, thermal conductivity, specific heat, and energy density were computed for CaX. Finally, the direction-dependent ultrasonic attenuation due to phonon–phonon interaction and thermelastic relaxation process has been computed for CaX at room temperature. The results obtained have been validated with existing results that are accessible for the chosen materials.

Titanium aluminum nitride and aluminum silicon alloys (TiAlN/AlSi) or for simplicity (TAN/AS) bilayer system were deposited on glass and piston aluminum substrates by following three steps. First, AlSi films realized by thermal evaporation with different Si content (7, 10, 13, 22) %. Then, TiAl films were deposited on AlSi layers using a reactive DC magnetron sputtering system, and finally the realization of TAN/AS multilayers were done by nitriding via Direct Current Plasma Nitriding (DCPN) in a custom setup, with pure nitrogen gas. For each sample, the structural properties like phase’s formation and vibration modes were investigated by X-ray diffraction and Raman spectroscopy, while AFM microscopy investigated surface topography. The mechanical and tribological properties in terms of hardness and friction coefficient were determined using the nanoindentation technique and tribometer. It has been found that all the coatings TAN/AS have crystalline structures with the presence of TiAlN, TiN, AlN, TiAl, and α-Al phases. Raman spectroscopy reveals the appearance of TO/LO, 2O, and 2TO/LO modes for all layers. AFM images show that the coatings have low roughness, Ra values decrease from 17.3 nm for 7 % Si to 5.5 nm for 13 % Si and increases to 9.9 nm at 22 % Si. The grain size exhibits a reversed behavior compared to that of roughness. The hardness and Young modulus reach their optimum values at 13 % Si with no respect to Hall–Petch law. The friction coefficient of TAN/AS coatings decreases with Si content and reaches its lowest value (<0.1) at 22 % Si as a potential protective layer.

DNA denaturation, the process of separating double-stranded DNA into single strands, plays a critical role in fundamental biological processes such as transcription, replication, and repair. Despite extensive studies on its thermodynamic properties, the effects of thermal fluctuations on DNA denaturation have not yet been explored. This paper addresses this gap by developing a statistical mechanical model to analyze homogeneous DNA denaturation thermodynamics with thermal fluctuations. Using the partition function framework, this study introduces two major corrections to the entropy of the system induced by thermal fluctuations: (1) a logarithmic correction of the leading order and (2) a higher-order correction term proportional to the inverse of the entropy. Analytical calculations and numerical analysis reveal that these corrections significantly influence the thermodynamic properties, including specific heat and free energy, leading to a more nuanced understanding of the DNA melting process. The corrected entropy modifies the specific heat profile, resulting in a sharp peak that reflects a first-order phase transition during DNA denaturation. The inclusion of higher-order corrections introduces asymmetry in the specific heat curve, highlighting the cooperative behavior of DNA melting. Furthermore, the free-energy analysis suggests the presence of intermediate states during strand separation, which are critical for understanding the initiation and propagation of the denaturation process. The results align well with experimental DNA melting profiles, particularly in the transition region, and provide insights into the microscopic mechanisms underlying DNA melting. This study not only advances the theoretical framework for DNA denaturation by explicitly incorporating thermal fluctuations but also offers a platform for future experimental validation and applications in biological systems. These findings have broader implications for understanding DNA stability under physiological conditions, cellular processes such as transcription initiation, and the role of ionic environments in modulating DNA thermodynamics.