Journal of Mathematical Chemistry最新文献

This study investigates a sequential first-order chemical reaction modeled via the Gerasimov-Caputo fractional derivative framework. We derive an exact analytical solution employing Mittag–Leffler and Prabhakar functions, and develop a robust numerical algorithm for its implementation. Our computational experiments demonstrate that fractional-order operators effectively capture slow reaction kinetics, particularly in systems with memory effects. The proposed approach bridges the gap between stoichiometric and kinetic descriptions while offering new tools for modeling inhibited reactions and corrosion processes.

We consider a one-dimensional cubic autocatalytic reaction–diffusion–advection system based on the scheme (A+2Brightarrow 3B), (Brightarrow C). Focusing on perturbations of a travelling reaction front, we study the regime of weak nonlinearity and long wavelengths in which a controlled asymptotic reduction is possible. Using a multiple-scale expansion near a marginally stable front, we obtain an effective Korteweg–de Vries (KdV)-type amplitude equation governing small, localized modulations of the autocatalyst concentration. Within this asymptotic framework, classical KdV soliton solutions provide a coarse-grained description of localized chemical pulses. Standard soliton invariants and phase shifts are interpreted in chemically meaningful terms, including excess autocatalyst content, effective pulse energy, and front displacement during pairwise interactions. Numerical simulations of the full reaction–diffusion system show quantitative agreement with the KdV approximation within its range of validity, confirming that the reduced description accurately captures the shape, propagation, and elastic interaction of localized pulses in the weakly nonlinear regime.

This contribution reports the study of a set of molecular electronic-structure reorganization representations related to light-induced electronic transitions, modeled in the framework of time-dependent density-functional response theory. More precisely, the work related in this paper deals with the consequences, for the electronic transitions natural-orbital characterization, that are inherent to the use of auxiliary many-body wavefunctions constructed a posteriori and assigned to excited states—since time-dependent density-functional response theory does not provide excited state ansatze in its native formulation. Three types of such auxiliary many-body wavefunctions are studied, and the structure and spectral properties of the relevant matrices (the one-electron reduced difference and transition density matrices) is discussed and compared with the native equation-of-motion time-dependent density functional response theory picture of an electronic transition—we see for instance that within this framework the detachment and attachment density matrices can be derived without diagonalizing the one-body reduced difference density matrix. The common “departure/arrival” wavefunction-based representations of electronic transitions are also extensively discussed.

The non-parametric and parametric derivative fast Padé transform (dFPT) were applied to time signals encoded by in vitro magnetic resonance spectroscopy (MRS) from benign and malignant ovarian cyst fluid. Several chemical shift regions in which diagnostically-important metabolites resonate were scrutinized. Consecutive derivative orders were inspected until convergence was attained, with concordance between the two versions of the dFPT. In most of the examined chemical shift regions, this occurred with the third derivative order, which was sufficient for the resonances to appear as tall, thin peaks, emerging from an entirely flat baseline with clearly identifiable integration limits. Thereby, the prominent lactate doublet resonating at (sim )1.41 parts per million (ppm), as well as many other, much less abundant, surrounding metabolites could be unambiguously identified and quantified. This was likewise the case for numerous other recognized and potential cancer biomarkers in the other examined aliphatic chemical shift regions. In the extremely dense spectral region below (sim)1.0 ppm, heretofore presenting major assessment difficulties in reported in vitro MRS studies, convergence was attained at ((m=4)). Besides the demonstrated concordance of the two completely different computational algorithms, the present results are fully amenable to clinical interpretation. This is an essential precondition to justify further application of the dFPT to urgent clinical problems such as timely and accurate ovarian cancer detection via MRS.

Carbon nanotubes (CNTs) exhibit tunable electronic and structural properties based on their chiral indices, making them versatile for nanoscale applications. The electronic behavior at CNT junctions is particularly significant, prompting a theoretical exploration of their geometric foundations. The Contub algorithm, designed to connect CNTs with arbitrary chiral vectors, identifies the positioning of pentagon and heptagon defects. Despite its theoretical efficiency, the geometrical interpretation of how chiral vectors relate to defect positions remain unclear. In this study, we introduce a unified geometric framework based on carbon nanocones (CNCs). This approach maps all possible chiral indices onto a CNC, providing a direct visual guide to defect positions. We show that all junctions can be systematically classified into two fundamental types: Type I (cone-mediated) and Type II (mitered pipe), with the former recovering the known conical junctions and the latter addressing the limiting cases where cone-based constructions fail. A phase diagram based on the relative diameter difference ((eta)) and the angle between chiral vectors ((phi)) not only classifies all possible connections but, crucially, provides an analytical boundary that separates the regime of each junction type.

In this paper, we first introduce a Fourier–Legendre spectral collocation method to solve the two-dimensional static Cauchy–Navier equations with variable coefficients in irregular annular domains. We then present a space-time Fourier–Legendre spectral collocation method for time-dependent Cauchy–Navier equations in such domains. The process begins by applying a polar coordinate transformation to map the irregular annular domain onto a regular one, followed by a linear transformation to map this domain onto the reference element. Classical spectral collocation methods are then employed for numerical simulation on the reference element. The numerical results demonstrate that the proposed method achieves high accuracy.

In this work, we develop multi-step vectorial iterative schemes for solving nonlinear systems, achieving fourth and sixth-order convergence. The proposed methods are designed to minimize computational costs by employing a single inverse operator and reducing the number of functional evaluations per iteration. Furthermore, we generalize the sixth-order three-step scheme into a ((q+1))-step family, increasing the convergence order to (2q+2). While standard local convergence analysis based on Taylor series expansion is common, it limits applicability as it requires the use of higher-order derivatives. To overcome this limitation, our theoretical analysis is conducted in a Banach space setting and relies solely on first-order derivatives. The existence of a unique solution is guaranteed within a specific domain, whose radius of convergence is formally obtained using Lipschitz constants. A detailed computational complexity analysis confirms the superior efficiency of our methods compared to existing approaches. Numerical experiments on different problems demonstrate significantly improved performance, while stability is validated through basins of attraction in the complex plane.

The definition of the recently introduced hitting time index suggests its close relation with the Kirchhoff index. Here, this relation is computationally investigated for trees and molecular trees. Additionally, the usability of these molecular descriptors as tools for modeling physicochemical properties of alkanes is compared. The second part of the paper is reserved for closed formulas of the hitting time index for bi-stars and the broom graphs. Finally, the upper and lower bounds, in terms of the maximum degree, the hyper-Wiener index, the Wiener index, and the Harary index for the hitting time index of trees are derived.

Using the transfer matrix method, we obtain the calculation method for the numbers of perfect matchings of m-layer hexagonal chains. Especially, we give out the linear recurrences, generating functions and general terms for the numbers of the perfect matchings in two types of special m-layer hexagonal chains–alternating and parallelogram hexagonal chains.

This work presents a numerical method for solving a three-dimensional time-fractional reaction-diffusion equation (TFRDE). The solution to this problem has a weak singularity near the initial time. The fractional time derivative is discretized using the L1 method on a nonuniform time grid, while the spatial derivatives are approximated by a fourth-order compact finite difference (CFD) scheme. The resulting fully discrete formulation is computationally expensive, therefore, an alternating direction implicit (ADI) technique is introduced to improve efficiency. The stability and convergence of the proposed scheme are rigorously analyzed. Two numerical experiments are conducted to verify the accuracy and computational efficiency of the proposed method. Theoretical analysis demonstrates that the proposed scheme attains a temporal convergence rate of (min { 2 - gamma ,, rgamma ,, 1 + gamma }) and fourth-order spatial accuracy. Numerical findings validate the theoretical convergence rates. To demonstrate the advantage of the proposed method, the numerical results obtained by the proposed method are compared with the result reported in Xiao et al., (Commun. Anal. Mech. 16(1):53–70, 2024).