Journal of Mathematical Chemistry最新文献

The time-fractional fourth-order reaction-diffusion problem, which contains more than one time-fractional derivative of orders lying between 0 and 1, is considered. This problem is the generalized version of the problem discussed by Nikan et al. Appl. Math. Model. 89 (2021), 819–836 that has only one time-fractional derivative. It is widely used in the study of chemical waves and patterns in reaction-diffusion systems. The analysis of non-smooth solutions to this problem is discussed broadly using the Caputo-time fractional derivative. The non-smooth solutions to the problem have a weak singularity close to zero that can be efficiently handled by considering the non-uniform mesh. The method based on the non-uniform time stepping is an efficacious way to regain accuracy. The current study presents the trigonometric quintic B-spline approach to solve this multi-term time-fractional fourth-order problem using graded mesh and effective grading parameters. The stability and convergence results are proved through rigorous analysis, which helps choose the optimal grading parameter. The accuracy and effectiveness of our technique are observed in our numerical experiments that manifest the comparison of uniform and non-uniform meshes.

The diatomic molecules have gained increased interest over the past several years in both experiment and theoretical studies because of their importance in astrophysical processes and many chemical reactions. Thermodynamical quantities such as enthalpy, entropy, heat capacity and free energy have their potential applications in various fields of science. Investigations in high temperature chemistry, astrophysics, and other disciplines require the knowledge of the thermodynamic properties of diatomic molecules. The plausibility of predictive models obtained in such investigations relies on the accuracy of these data. The scrutiny of the literature reveals that thermodynamic data are often absent or have scattered values in different research articles and handbooks. The main requirements to thermodynamic values are their reliability, mutual consistency, and so forth. In the present theoretical study, thermodynamic values are estimated by using spectroscopic data which are microscopic in nature, whereas thermodynamical quantities are macroscopic in nature. Attempts have been made to calculate the thermodynamical quantities of silver monohalides (AgF, AgCl, AgBr and AgI) from spectroscopic data with the help of partition function theory. The results have been calculated in the temperature range 100–3000 °C. In order to increase accuracy of the calculated quantities, we have incorporated non-rigidity, anharmonocity, and stretching effects of molecules. The variation of these quantities with temperature have been studied and explained in terms of various modes of molecular motions.

One of the most often used methods of summing divergent series in physics is the Borel-type summation with control parameters improving convergence, which are defined by some optimization conditions. The well known annoying problem in this procedure is the occurrence of multiple solutions for control parameters. We suggest a method for resolving this problem, based on the minimization of cost functional. Control parameters can be introduced by employing the Borel–Leroy or Mittag–Leffler transforms. Also, two novel transformations are proposed using fractional integrals and fractional derivatives. New cost functionals are advanced, based on lasso and ridge selection criteria, and their performance is studied for a number of models. The developed method is shown to provide good accuracy for the calculated quantities.

This paper considers a distillation column used in heavy crude oil separation where pairings exhibit negative Niederlinski Index values, potentially leading to system instability. In this study, we address this issue by constructing a Relative Gain Array matrix from a transfer matrix of order 3. We employ mathematical techniques to steer the system towards stability. Through subtle modifications to matrix entries, we achieve stable configurations.

In this paper, we develop a stochastic multi-molecule chemical reaction model with reaction rate perturbed by log-normal (Ornstein-Uhlenbeck) process in order to consider the effects of random factors on chemical reaction dynamics. Firstly, we prove the existence and uniqueness of the global positive solution for the stochastic model. In addition, we obtain the conditions under which the corresponding stochastic system exist a stationary distribution. Then, we derive a sufficient condition to end the reaction. Furthermore, the stochastic system has been transformed into a linearized system, by solving (Fokker-Planck) equation, we obtain the exact expression of the density function around the quasi-equilibrium of this system. Finally, we draw a conclusion that the dynamical behaviors of the stochastic system will be affected by random factor, (Ornstein-Uhlenbeck) process respectively

Molecular interactions aid in our understanding of how proteins function and behave. As they can help us predict the biological functions of unknown proteins in living organisms in this work, DNA nucleobases are studied, which can assist us in characterizing protein complexes, cellular pathways, and functional modules. Density functional theory examines how different gold nanoparticles interact with DNA nucleobase monomers (DFT). At B3LYP, the 6-311-G basis set was used to optimize the molecular geometries of various nucleobases. At LANL2DZ as the basis set, molecular geometries of diverse gold nanoparticles are optimized. At standard pressure and temperature, binding energy, interaction energy, and Bandgap were estimated along with its IR and UV spectrum were studied. Our simulation results clearly show that the hydrogen bondings are intensified and more likely to occur as the size of the nucleobases and gold nanoparticles increases. Hydrogen bonding is also essential for the delivery of medications and the sequencing of genes in molecules. In our computational investigations, the interaction between different DNA nucleobases and gold nanoparticles is examined to find out how other nucleobases are affected by gold nanoparticles. The interaction between gold nanoparticles and diverse nucleobases is investigated to understand the behavior of nanoparticles with different nucleobases. The molecule composed of six gold atoms was discovered to be the most stable of all the optimized gold compounds. Our computational results can be explained by the polarization of gold molecules and their electronic energy.

An oxide of the perovskite type, barium zirconate (BaZrO3), has attracted a lot of interest for use as a potential candidate for electrolyte of solid oxide fuel cells (SOFCs) that conduct protons. The perovskite crystal structure of BaZrO3 is well-known for its adaptability in accepting various dopants and preserving stability in a range of circumstances. BaZrO3 is appropriate for the severe operating conditions of SOFCs because it is chemically stable in both reducing and oxidizing environments. When doped, BaZrO3 acts as an electrolyte that conducts protons. Protons (H+), which travel through the crystal structure to complete the fuel cell circuit, are the main charge carriers in these materials. BaZrO3 can function at lower temperatures, which lessens thermal stress and lengthens the life of fuel cells. Additionally, a greater variety of fuels, including ones with higher hydrogen contents, are permitted. The examination of the mechanism underlying the enhanced performance requires the atomic knowledge. We have used the ab-initio DFT computation for that. Band-gap and electrochemical stability assessments have been made more accurate by using Grimme d3 dispersion correction and PBE. A distinct metric, the global instability index (GII), was employed to evaluate the thermodynamic stability of BaZrO3 and the doped structures. It bases its calculation on the bond valence sum technique utilized in SoftBV. All DFT calculations were carried out using Quantum ESPRESSO pwscf codes. XCrySDen and VESTA, two open-source programs, were used to create all of the visuals.

This paper investigates the temporally loaded time-fractional diffusion equation with initial and Dirichlet-type boundary conditions. To begin with, a solution form is established using the method of eigenfunction expansions, and its existence and uniqueness are examined along with some apriori estimates. Thereafter, a finite difference approximation is performed using the so-called L1 method for the Caputo fractional derivative, resulting in a loaded difference scheme. The superposition property of systems of linear algebraic equations is applied to solve the loaded difference scheme by appointing an appropriate solution representation. The unique solvability of the proposed scheme is set up. The stability and convergence of the proposed difference scheme are analysed by the discrete energy method with an order of accuracy (mathcal {O}(tau ^{2-alpha }+h^2)). Numerical results via two test problems are presented to validate the theoretical findings of the proposed scheme by observing the errors.

The first inverse Nirmala index is a novel degree-based topological descriptor that was introduced in 2021. Preliminary QSPR investigations suggest that this index deserves further consideration because of its unusually good predictive potential. This paper investigates the relations between this index with some elementary graph quantities and some related degree-based topological index. Further, the computational analysis will reveal extremal graphs among trees, molecular trees, all connected graphs, and their molecular counterparts.