Journal of Mathematical Chemistry最新文献

Kinetic chemical reactions find applications across various fields. In industrial processes, they drive the production of essential materials like fertilizers and pharmaceuticals. In environmental science, they are crucial to understanding pollution dynamics. Additionally, in biochemistry, they underpin vital cellular processes, offering insights into disease mechanisms and drug development. In this work, we present a new advancement of a dynamical system for kinetically controlled chemical reactions and the dependency of its solution on the initial conditions using mathematical techniques for fractional orders. By utilizing this fixed-point approach, we can derive the existence and uniqueness theorem of the proposed model. We further show that the chemical kinetics of the fractional model are stable through the Hyers-Ulam stability condition. We finally run a numerical simulation to verify our conclusions. The manuscript concludes with demonstrative examples.

This work is based on the productive idea of Mulliken about the alignment of electronegativities of atoms in the process of bond formation to their geometric mean value. The paper considers in detail the case of a binary molecule and obtains formulas for the dependence of the current values of the electronegativities of the two atoms forming the molecule on time, and finds a mathematical connection between the current and initial values of electronegativities. Also, in the work the theorem on the relation between the rates of alignment of electronegativities of atoms entering into chemical bonding is formulated and proved, and a special case of this theorem is considered.

In response to the challenges posed by complex boundary conditions and singularities in molecular systems and quantum chemistry, accurately determining energy levels (eigenvalues) and corresponding wavefunctions (eigenfunctions) is crucial for understanding molecular behavior and interactions. Mathematically, eigenvalues and normalized eigenfunctions play crucial role in proving the existence and uniqueness of solutions for nonlinear boundary value problems (BVPs). In this paper, we present an iterative procedure for computing the eigenvalues ((mu )) and normalized eigenfunctions of novel fractional singular eigenvalue problems,

with boundary condition,

where (D^alpha , D^{2alpha }) represents the Caputo fractional derivative, (k ge 1). We propose a novel method for computing Lagrange multipliers, which enhances the variational iteration method to yield convergent solutions. Numerical findings suggest that this strategy is simple yet powerful and effective.

The phenomenon of isothermal supersaturation of solutions in a porous medium at ion exchange is studied on the basis of mathematical modeling. The phenomenon consists in the fact that the solution with concentration significantly higher than the maximal solubility of the substance is formed in the pores of sorbent and no precipitation occurs. The question of why sediment does not appear in the pores between the grains is investigated in the article. It is shown that the phenomenon under consideration can be explained by the effect of dynamic equilibrium between the association of condensed phase particles in the inner part of the pores, their diffusion, and decomposition near the surface of the sorbent grains caused by a change in potential. The degree of possible supersaturation of the solution is estimated depending on the process parameters. The proposed hypothesis is confirmed by quantitative studies using the available experimental data.

A fullerene graph is a 3-connected plane cubic graph in which every face is pentagonal or hexagonal. A set of hexagons (mathcal {H}) of G is called a resonant pattern if there exists a perfect matching M of G such that exactly three edges of H is contained in M for each member H of (mathcal {H}). In this paper we prove for any natural number k that almost all of the family of k disjoint hexagons are resonant patterns in sufficiently large fullerene graphs.

Throughout this research paper, we represent a highly effective Haar wavelet technique to determine the solution of the complex nonlinear dynamical system with three variables chemical reaction model. The foremost objective of this study is to represent the dynamical behavior of chemical reaction model in the sense of Caputo derivative. The convergent analysis and stability analysis of the three variable chemical reaction model are discussed. The existence and uniqueness of the given model is also verified. Furthermore, the residual error analysis for this model is also presented. In addition, graphically the numerical solutions in a 2-dimensional and 3-dimensional manner are obtained by using MATLAB (2023a).

The Gruneisen parameter offers crucial insights into the frequency distribution of the phonon spectrum in solids. In present study, we focus on the theoretical prediction of Gruneisen parameter for magnesium chalcopyrites MgSiP₂, MgSiAs₂, and MgSiSb₂ by using three different logarithmic equation of state (EOS) viz. Poirier Tarantola EOS, Third-Order EOS, and Bardeen EOS at varying compression values (V/V₀). These EOSs are subjected to rigorous testing against the fundamental thermodynamic requirements, especially at extreme compression limits. It is observed that at low compressions, all three EOSs—Poirier Tarantola, Third-Order EOS and Bardeen EOS yield identical results. However, when estimating the Gruneisen parameter at high compression, we found that after compression range V/V₀ = 0.98 for MgSiAs₂ the Poirier Tarantola EOS gets deviated with other two EOSs and also after compression range V/V₀ = 0.99 for MgSiP₂ the Poirier Tarantola EOS gets deviated with other two EOSs and after compression range V/V₀ = 0.99 for MgSiSb₂ the third order EOS get deviated with other two EOS.

The study utilized the theory of interionic potentials and included analytical functions to account for the volume-dependent short-range force constant. Specifically, a modified version of the Shanker equation of state was used, and expressions were established for isothermal bulk modulus and its pressure derivatives. The researcher extensively analyzed the bismuth ferrite (BiFeO₃) material at pressures up to 10 GPa. The result obtained by the newly derived equation of state is compared against previously obtained equations of state, including the Shanker and Vinet equation of state and experimental data. Graphical representations demonstrate the changes in pressure, bulk modulus, and pressure derivative of bulk modulus with compression. The result shows that the newly developed equation of state provides superior outcomes compared to the Shanker and Vinet equations, particularly at high compression levels, due to the inclusion of higher-order compression terms.

In this paper, two novel classes of implicit exponential Runge–Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, symplectic conditions for two kinds of exponential integrators are derived, and we present a first-order symplectic method. High accurate implicit ERK methods (up to order four) are formulated by comparing the Taylor expansion of the exact solution, it is shown that the order conditions of two new kinds of exponential methods are identical to the order conditions of classical Runge–Kutta (RK) methods. Moreover, we investigate the linear stability properties of these exponential methods. Numerical examples not only present the long time energy preservation of the first-order symplectic method, but also illustrate the accuracy and efficiency of these formulated methods in comparison with standard ERK methods.

Enzyme catalysis in reactors for industrial applications usually require an external intervention of the species involved in the chemical reactions. We analyze the most elementary open enzyme catalysis with competitive inhibition where a time-dependent inflow of substrate and inhibitor supplies is modeled by almost periodic functions. We prove global stability of an almost periodic solution for the non-autonomous dynamical system arising from the mass-law action. This predicts a well behaved situation in which the reactor oscillates with global stability. This is a first case study in the path toward broader global stability results regarding intraspecific and monotone open reaction networks.