Journal of Mathematical Chemistry最新文献

This article describes the production of biogas in a cellulose-based substrate using a multifractional dynamic model. The objective is to give more precise depiction of the nonlinear characteristics of the chemical reactions involved in anaerobic digestion. In addition well-posedness and consistency, we present the sensitivity analysis used to determine which system equations follow non-integer order dynamics. We illustrate the efficacy of the model with numerical simulations that compare experimental data with the conventional model. The multifractional model’s outputs are in good agreement with the biogas production process’s overall response, which may lead to more effective control strategies.

Turing’s model to explains the formation of patterns in morphogenesis considered a system of chemicals, termed morphogens, that react and diffuse through tissues. These reaction–diffusion systems can start homogeneously but later develop patterns due to instabilities triggered by random disturbances. Building on this foundation, Kepper realized the Chlorite-Iodide Malonic-Acid reaction, an example of an oscillatory reaction in a homogeneous solution that forms spatial patterns in a non-homogeneous environment. This work led to further studies, such as the Lengyel-Epstein reaction–diffusion model, which describes the dynamics of chemical concentrations of activator and inhibitor species. This paper extends these classical models by investigating a general reaction–diffusion system through the lens of Lie symmetries. We analyze the system using Lie point symmetry generators and Lie symmetry groups, enabling us to reduce the equations via these symmetries. Furthermore, we compute the conservation laws for the general reaction–diffusion model using the multipliers approach, involving dependent variables, independent variables, and their derivatives up to a certain order. By applying various symmetry groups, we derive new solutions from known ones, offering deeper insights into the dynamics of pattern formation in biological systems.

In this paper, we examine the Gutman–Milovanović index and establish new upper and lower bounds for it. These bounds include terms related to the general sum connectivity index, the general second Zagreb index, and the hyperbolicity constant of the underlying graph. Also, we model physicochemical properties of polyaromatic hydrocarbons using the Gutman–Milovanović index.

In this work, we employed the techniques of complex dynamics to perform stability analysis of an optimal mean-based family of iterative methods of order four. Taking into consideration the stability aspect of the specified method, one can describe the method’s sensitivity to the initial guesses. A rational function corresponding to the iterative family is developed. The convergence and stability of a certain method can be analyzed upon finding the fixed points, critical points, periodic points, etc. of the rational function. Furthermore, the dynamical and parametric planes are drawn which help us to detect the stable as well as non-stable regions. It has been observed that stable iterative methods generally yield better performance on complex problems compared to unstable methods. This observation has been supported by numerical experiments that compare our proposed family with some existing methods for representing some chemistry problems, like conversion in a chemical reactor, equations of state, and continuous stirred tank reactor problem.

In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential (V(x) = frac{1}{2} omega ^2 x^2 + g x^4) is presented. Using a path integral formalism, the exact partition function is approximated by the partition function of a harmonic oscillator with an effective frequency depending both on the temperature and coupling constant g. By invoking a Principle of Minimal Sensitivity (PMS) of the path integral to the effective frequency, we derive a mathematically well-defined analytic formula for the partition function. Quite remarkably, the formula reproduces qualitatively and quantitatively the key features of the exact partition function. The free energy is accurate to a few percent over the entire range of temperatures and coupling strengths g. Both the harmonic ((grightarrow 0)) and classical (high-temperature) limits are exactly recovered. The divergence of the power series of the ground-state energy at weak coupling, characterized by a factorial growth of the perturbational energies, is reproduced as well as the functional form of the strong-coupling expansion along with accurate coefficients. Explicit accurate expressions for the ground- and first-excited state energies, (E_0(g)) and (E_1(g)) are also presented.

Using a technique that accounts for disappearing phase-lag might lead to the elimination of phase-lag and all of its derivatives up to order four. The new technique known as the cost-efficient approach aims to improve algebraic order (AOR) and decrease function evaluations (FEvs). The one-of-a-kind approach is shown by Equation PF4DPHFITN142SPS. This method is endlessly periodic since it is P-Stable. The proposed method may be used to solve many different types of periodic and/or oscillatory problems. This innovative method was used to address the difficult issue of Schrödinger-type coupled differential equations in quantum chemistry. The new technique might be seen as a cost-efficient solution since it only requires 5FEvs to execute each step. We are able to greatly ameliorate our current situation with an AOR of 14.

This paper discusses mathematical model of hydrogen evolution via ({H}^{+}) and ({H}_{2}O) reduction at a rotating disc electrode. Rotating disc electrodes are the preferred technology for analysing electrochemical processes in electrically powered cells and another rotating machinery, such as combustion engines, air compressors, gearboxes, and generators. The theory of nonlinear convection–diffusion equations provides the foundation for the model. In the present study, the Akbari-Ganji approach is utilised to solve, concurrently, the mass transport equations of ({H}^{+}) and ({OH}^{-})  in the electrolyte and on the electrode surface under steady-state circumstances. A general and simple analytical expression is obtained for the reactants' hydrogen and hydroxide ion concentrations. Additionally, numerical solutions using non-standard finite difference methods are presented, and compared with the analytical solution. The exact solution for the limiting case results is presented and examined with the general results. Furthermore, the graphs and tables that compare the theoretical and numerical solutions demonstrated the accuracy and dependability of our paradigm.

Lorentz, Gauss, Voigt and pseudo-Voigt functions play an important role in hard modeling of NMR spectra. This paper shows the uniqueness of continuous NMR hard models in terms of these functions by proving their linear independence. For the case of discrete hard models, where the spectra are represented by finite-dimensional vectors, criteria are given under which the models are also unique.

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.