Volume 80, Issue 12

Topological indices are numerical descriptors that capture key structural information of molecular graphs, enabling the quantitative prediction of chemical properties. This study employs five degree-based topological indices to develop quantitative structure property relationship (QSPR) models for twenty fundamental building blocks of organic semiconductors. Strong correlations are established between these indices and critical physicochemical properties including melting point, boiling point, and molecular mass using linear, quadratic, and logarithmic regression approaches. Molecular mass and boiling point are found to be particularly well predicted, with correlation coefficients exceeding 0.99 in multiple models. The results are validated against experimental data, confirming the practical utility of the proposed models. These findings underscore the value of topological indices as efficient computational tools for the high-throughput screening and rational design of organic semiconductor materials.

This study bridges graph-theoretical methods and computational physics by evaluating degree-based topological indices for sixteen indole derivatives-indole, 2-Formylformanilide, indoxyl, isatin, anthranilic acid, isatoic anhydride, indigo dye, indirubin, tryptanthrin, indoxyl red, 1H-indole-4-amine, 2-methyl-1H-Indole, 2-phynel-1H-indole, 1H-indole-6-carbaldehydel, 1h-indole-3-carbaldehyde, and 5-chloro-1h-indole to predict their physicochemical properties. By interpreting molecular structures as quantum-mechanical graphs, we compute topological indices as descriptors of electronic and structural connectivity, which are then employed in linear, quadratic, and logarithmic regression models to estimate density, boiling point, melting point, water solubility, molecular weight, and vapor pressure. These properties are critical for understanding molecular interactions, phase transitions, and material behavior in condensed matter systems. Statistical evaluation ( r , r 2 , F-statistic, p -value) reveals robust predictive accuracy for boiling point ( r > 0.824) and molecular weight ( r > 0.99), aligning with their direct dependence on molecular topology and quantum mechanical parameters. The models for vapor pressure and solubility also demonstrate moderate success, reflecting their sensitivity to intermolecular forces and entropy-driven processes. By linking graph invariants to measurable physical properties, this work advances computational strategies for rapid material characterization, offering a scalable alternative to resource-intensive quantum simulations. The results highlight the potential of topological indices as low-cost, high-efficiency tools for designing organic semiconductors, photonic materials, and molecular sensors, with implications for condensed matter physics and nanotechnology. This approach underscores the synergy between discrete mathematics and physical chemistry, enabling predictive modeling of complex systems through a unified theoretical framework.

Four binary mixtures are isolated from two hydrogen bond mesogenic complexes that are formed between p-n alkyloxy benzoic acids and 4-Nitrobenzaldehyde. The carbon chain length chosen for the formation of binary mixtures are heptyloxy and octyloxy benzoic acids. 4-Nitrobenzaldehyde (NBA) and heptyloxy benzoic acid mesogenic complex is treated as X component while 4-Nitrobenzaldehyde (NBA) and octyloxy benzoic acid mesogenic complex is treated as Y component. Binary mixtures are obtained by varying the molar ratio of the two mesogenic complexes ( X and Y ) in even steps viz., from 0.2 to 0.8. Hydrogen bond existence between the binary mixtures is confirmed through Fourier Transform Infrared Spectroscopy. Mesogenic phase variance is investigated through polarizing optical microscope study. The phase transition temperature and their corresponding enthalpy values are analyzed via differential scanning calorimetry. Thermal equilibrium, thermal stability, order of phase transition and specific heat capacity of the binary mixtures are also elucidated from the thermograms of the mesogenic mixtures. The results obtained make these binary mixtures a potential candidate for opto-electronic and thermal energy based applications.

Fractional partial differential equations are essential for a more accurate description of complex physical phenomena than their integer-order versions. The equations offer better insight into different dynamic processes in physics and engineering with the inclusion of the memory effects and non-local interactions associated with fractional derivatives. In the present research, we are interested in the soliton dynamics of two important fractional partial differential equations: the Landau–Ginzburg–Higgs equation and the generalized Kadomtsev–Petviashvili modified equal width Burgers equation for the truncated M-fractional derivative. The Landau–Ginzburg–Higgs equation is central to field theory and condensed matter physics, used to model phase transitions, super-conductivity, and other critical phenomena. The generalized Kadomtsev–Petviashvili modified equal width Burgers equation is an important model for the generation and analysis of long-wave structures in nonlinear dispersive and dissipative media. We use the extended hyperbolic function method, a robust analytical method for finding exact solutions to nonlinear fractional differential equations, to study these equations. In the present analysis, we build a range of solution types such as bright solitons, dark solitons, kink-type waves, dark-singular solitons and periodic solutions, which reveal the qualitative richness of the models under the effect of the truncated M-fractional derivative. The investigation also examines how various fractional-order parameters influence the derived solutions and how the soliton structures change as the fractional order changes from non-integer to integer. To enable a thorough comprehension of these effects, we depict two-dimensional and three-dimensional graphical plots of solutions for different fractional orders. These plots emphasize the progressive evolution of soliton profiles and the effects of fractional differentiation on wave propagation.

In this paper, we investigate the nonlinear Schrödinger equation with a linear external potential, which describes the propagation of quasi-monochromatic waves in weakly nonlinear media. By leveraging the periodicity of two Jacobian elliptic functions, namely the dn- and cn-functions, we construct explicit rogue wave solutions within a periodic background. For perturbations in the form of solitary waves, we demonstrate that the resulting rogue wave solutions associated with the dn- and cn-functions exhibit modulational instability. Using the Darboux transformation and the Lax spectral problem of the equation, we derive the analytical expressions for these rogue wave solutions, which can also be reduced to the Peregrine breather wave solutions. Our findings contribute to a deeper understanding of rogue wave dynamics in the context of the nonlinear Schrödinger equation.

This article presents the precise approximations for modified Bessel functions of the second kind. Building on a well-established method for function approximation, the enhanced approach, incorporating machine learning techniques, is used to approximate Bessel functions such as K 0 , K 1 , K 1/4 , I 0 , I 1 , and I 1/3 . These approximations are demonstrated to be highly effective in various applications, such as thermal average and partition function, providing a robust alternative to repeated numerical integration.

We report a systematic investigation of neutron capture reactions on 79,81 Br and 85,87 Rb under conditions characteristic of the weak s -process in massive stars. Employing the Hauser–Feshbach frameworks in TALYS v1.97 and YAHFC v3.66, we explore a broad suite of nuclear level density and γ strength models, both phenomenological and microscopic, to assess their influence on Maxwellian-averaged cross sections. By benchmarking our predictions against available experimental data, we identify model combinations that consistently reproduce observed trends, thereby greatly reducing uncertainties in the cross sections. The results provide experimentally validated reaction rates that can strengthen the reliability of s -process nucleosynthesis simulations.

Although the solidification behavior of eutectic alloys has been widely studied, the growth rate of solid fraction as a function of local temperature remains less explored. A theoretical model of the three-region solidification process is proposed that includes the linear relationship between the solid fraction and the temperature of the mushy zone. A physically realistic, time-dependent heat transfer is considered a driving function of the solidification process. The analytical solution of the proposed model is determined by converting the given partial differential equations into ordinary differential equations by using the similarity transformation. The detailed discussion of the model is presented by taking the thermal–physical properties of Al–Cu composition with 5 % Cu. The validity of the current model is shown with the previous model and found that the current model offers a faster solidification rate with the least energy consumption and thus minimizes the operating time. It is found that material solidifies slower after formation of the mush form due to thermal resistance. Due to the greater value of heat transfer constant Ω, greater heat is removed from the surface of the liquid alloy and material gets solidified faster. The observations found in this study may be relevant for solid solutions and eutectic alloys.