Journal of Mathematical Chemistry最新文献

Boundary values for the charge transferred during an electronic transition: insights from matrix analysis 在电子跃迁期间转移的电荷的边界值：来自矩阵分析的见解

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-05-08 DOI: 10.1007/s10910-026-01793-6

Enzo Monino, Jérémy Morere, Thibaud Etienne

引用次数: 0

The extremal molecular trees with respect to the first inverse Nirmala index 关于第一逆Nirmala指数的极值分子树

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-05-07 DOI: 10.1007/s10910-026-01794-5

Wei Gao

{"title":"The extremal molecular trees with respect to the first inverse Nirmala index","authors":"Wei Gao","doi":"10.1007/s10910-026-01794-5","DOIUrl":"10.1007/s10910-026-01794-5","url":null,"abstract":"<div><p>Let <i>G</i> be a simple connected graph with vertex set <i>V</i>(<i>G</i>) and edge set <i>E</i>(<i>G</i>). The first inverse Nirmala index of <i>G</i> is defined as </p><div><div><span>$$IN_1(G)=sum _{uvin E(G)}sqrt{frac{1}{d_G(u)}+frac{1}{d_G(v)}},$$</span></div></div><p>where <span>(d_G(u))</span> and <span>(d_G(v))</span> are the degrees of the vertices <i>u</i> and <i>v</i> in <i>G</i>, respectively. The first inverse Nirmala index is a novel degree-based topological descriptor introduced in 2021. It has been noted that this index merits further investigation due to its remarkably strong predictive potential in chemical studies. In Furtula and Oz (J Math Chem 63, 96–104, 2025) demonstrated that among molecular trees, the path attains the maximum value of the first inverse Nirmala index. This result was obtained through a powerful computer search, but rigorous mathematical proofs were not provided. For the minimum values of the index, the authors identified the extremal molecular trees only for orders ranging from 10 to 20 vertices. The contributions of this paper are as follows: (1) We provide a mathematical proof that any molecular tree of order <i>n</i> achieving the maximum value of the first inverse Nirmala index must be a path of order <i>n</i>. (2) For molecular trees attaining the minimum value of the first inverse Nirmala index, we establish a complete characterization for all orders <span>(nge 10)</span>. (3) We present explicit formulas for computing the minimum value referred to in (2).</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Crowding-modified Schnakenberg reaction–diffusion dynamics: exact equilibrium feasibility, Hopf/Turing bifurcations, Turing–Hopf interaction, and spatio-temporal complexity 群体修正Schnakenberg反应扩散动力学：精确平衡可行性、Hopf/Turing分岔、图灵- Hopf相互作用和时空复杂性

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-05-05 DOI: 10.1007/s10910-026-01791-8

Qamar Din

{"title":"Crowding-modified Schnakenberg reaction–diffusion dynamics: exact equilibrium feasibility, Hopf/Turing bifurcations, Turing–Hopf interaction, and spatio-temporal complexity","authors":"Qamar Din","doi":"10.1007/s10910-026-01791-8","DOIUrl":"10.1007/s10910-026-01791-8","url":null,"abstract":"<div><p>We study a crowding-modified Schnakenberg activator–inhibitor model in which the autocatalytic flux is saturated by a free-volume (volume-exclusion) factor, preserving the classical Schnakenberg mass-balance identity while preventing unrealistically large reaction rates at high concentrations. For the well-mixed kinetics we prove forward invariance of the nonnegative quadrant and global existence, derive the unique equilibrium in closed form together with a sharp feasibility condition, and give a complete linear stability classification. Treating the crowding parameter as a bifurcation parameter, we obtain an explicit Hopf threshold and verify transversality in closed form; moreover, using normal-form multilinear forms we provide an explicit evaluation-ready formula for the first Lyapunov coefficient and show that the Hopf bifurcation (when it occurs) is supercritical. Embedding the kinetics into a two-species reaction–diffusion system with Neumann boundary conditions, we derive the dispersion relation and sharp necessary and sufficient conditions for diffusion-driven (Turing) instability, including the unstable waveband and critical wavenumber. We further develop a weakly nonlinear steady Turing reduction in a tuned threshold setting, present modal Hopf thresholds for the PDE, and characterize codimension-two Turing–Hopf interaction points. Finally, numerical experiments illustrate the theoretical predictions and reveal parameter regimes with mixed-mode dynamics and spatio-temporal irregularity, quantified via spectral and Lyapunov-type diagnostics.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Regulation of spatiotemporal patterns in a discrete Lengyel–Epstein system using PD control 利用PD控制对离散lengyell - epstein系统的时空模式进行调节

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-30 DOI: 10.1007/s10910-026-01789-2

Xiangyi Ma, Yanhua Zhu, Jinliang Wang

引用次数: 0

Fourth-order RBF-CFD scheme for solving the one-dimensional time-fractional convection–diffusion equation with initial weak singularity 求解具有初始弱奇点的一维时间分数对流扩散方程的四阶RBF-CFD格式

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-28 DOI: 10.1007/s10910-026-01790-9

Ziyu Guo, Kaysar Rahman, Junping Guan

{"title":"Fourth-order RBF-CFD scheme for solving the one-dimensional time-fractional convection–diffusion equation with initial weak singularity","authors":"Ziyu Guo, Kaysar Rahman, Junping Guan","doi":"10.1007/s10910-026-01790-9","DOIUrl":"10.1007/s10910-026-01790-9","url":null,"abstract":"<div>\u0000 \u0000 <p>The time-fractional convection–diffusion equation (TFCDE) arises in various fields of science and engineering. However, its numerical solution presents challenges stemming from the weak singularity at the initial time. To efficiently address this singularity, temporal discretization is performed via the <i>L</i>2-<span>(1_{sigma })</span> scheme on a non-uniform graded mesh, and spatial derivatives are approximated by a fourth-order radial basis function compact finite difference (RBF-CFD) method. The linear system from the scheme, a typical tridiagonal system, allows fast solution with the Thomas algorithm, enhancing computational efficiency. The proposed scheme achieves a temporal convergence rate of <span>({min {rgamma , 2}})</span> and fourth-order spatial convergence, where <span>(r)</span> is the mesh grading parameter and <span>(gamma )</span> denotes the order of the Caputo fractional derivative. Rigorous theoretical analyses, including proofs of stability and convergence, are presented. The proposed method is applied to several numerical examples, and the results are compared with those from existing methods in the literature. The results confirm that the method demonstrates good stability and consistently attains the theoretically predicted convergence order.</p>\u0000 </div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An adaptive weak galerkin method for multi-scale reaction–convection–diffusion systems in chemical applications 化学应用中多尺度反应-对流-扩散系统的自适应弱伽辽金方法

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-27 DOI: 10.1007/s10910-026-01781-w

Ujwal Warbhe

{"title":"An adaptive weak galerkin method for multi-scale reaction–convection–diffusion systems in chemical applications","authors":"Ujwal Warbhe","doi":"10.1007/s10910-026-01781-w","DOIUrl":"10.1007/s10910-026-01781-w","url":null,"abstract":"<div><p>This paper presents a novel computational framework for the numerical solution of multi-parameter singularly perturbed reaction–convection–diffusion problems that arise frequently in chemical modeling applications. We develop an <i>hp</i>-adaptive Weak Galerkin finite element method that operates on anisotropic meshes, specifically designed to handle the intricate boundary layers, interior layers, and evolving patterns that characterize chemical systems such as electrochemical cells and excitable media. The method incorporates three key innovations: a stable weak formulation tailored for multi-parameter problems, a robust a posteriori error estimator in a chemically-informed balanced norm that properly weights errors in critical regions, and an adaptive algorithm that simultaneously performs anisotropic <i>h</i>-refinement and <i>p</i>-enrichment based on local solution properties. Numerical experiments demonstrate the method’s effectiveness in resolving electrochemical boundary layers without non-physical oscillations, tracking rotating chemical waves in excitable media, and outperforming state-of-the-art approaches in both accuracy and computational efficiency. The proposed method achieves exponential convergence rates for problems with complex layer structures while maintaining robust performance across a wide range of parameter values. This work provides chemists and computational researchers with a powerful tool for simulating multi-scale phenomena in electrochemical systems, pattern formation, and reaction–diffusion processes that were previously computationally prohibitive.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Improving operator splitting and effective reaction probability for a reactive-step based molecular dynamics workflow 改进了基于反应步骤的分子动力学工作流的算子分裂和有效反应概率

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-21 DOI: 10.1007/s10910-026-01780-x

Souvik Mitra, Diddo Diddens, Andreas Heuer

{"title":"Improving operator splitting and effective reaction probability for a reactive-step based molecular dynamics workflow","authors":"Souvik Mitra, Diddo Diddens, Andreas Heuer","doi":"10.1007/s10910-026-01780-x","DOIUrl":"10.1007/s10910-026-01780-x","url":null,"abstract":"<div><p>Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods. However, due to fixed force-field parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a simple approach that incorporates quantum reactions by periodically halting the MD simulation and allowing the possibility for reactions at each halt, based on a Poisson-type reaction probability. But, this simple approach cannot capture the simultaneous involvement of diffusion and reaction processes, and because the reaction probability does not include the influence of the diffusion step, errors can be introduced, especially when the diffusion process is not significantly slower than the reaction process. In this work, the efficiency of the RSMD model is increased by reducing these errors and by addressing the influence of the diffusion process on the reaction probability. To reduce these errors, we modify the RSMD mathematical framework by replacing the Trotter splitting employed in previous works with the Strang splitting scheme. To implement these Strang schemes in MD simulations and to scrutinize their validity, we introduce mathematical models involving three and four states, which correspond to two common reaction scenarios: association-dissociation reactions and homogeneous charge transfer reactions, respectively in the presence of diffusion processes. Using these mathematical models, effective reaction probability functions are derived for various diffusion limits, for example, when diffusion processes are extremely fast or extremely slow compared to the reaction processes. All the derived reaction probability functions, in combination with appropriate Strang schemes, are validated for various diffusion regimes with respect to the reaction time scale.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-026-01780-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniformly convergent NIPG methods for solving singularly perturbed convection-diffusion equations with a discontinuous source term 具有不连续源项的奇摄动对流扩散方程的一致收敛NIPG方法

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-20 DOI: 10.1007/s10910-026-01786-5

Ke Liu, Li-Bin Liu

引用次数: 0

Structural characteristics of sustained scientific co-authorship networks on molecular chirality 分子手性持续科学合作网络的结构特征

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-17 DOI: 10.1007/s10910-026-01784-7

Béla Barabás, Ottilia Fülöp, Róbert Kurdi

引用次数: 0

Numerical analysis of non-linear complex biochemical reaction model using HPM and HAM 非线性复杂生化反应模型的HPM和HAM数值分析

IF 2 3区化学

Journal of Mathematical Chemistry Pub Date : 2026-04-17 DOI: 10.1007/s10910-026-01783-8

L. Dhanuja, C. Monica

{"title":"Numerical analysis of non-linear complex biochemical reaction model using HPM and HAM","authors":"L. Dhanuja, C. Monica","doi":"10.1007/s10910-026-01783-8","DOIUrl":"10.1007/s10910-026-01783-8","url":null,"abstract":"<div><p>The dynamics of a non-linear fractional-order chemical reaction model that describes the interactions between an enzyme, substrate, inhibitor and the related intermediate complexes are examined in this paper. Iterative numerical simulations are used to derive analytical approximations using the Homotopy Analysis Method (HAM) and the Homotopy Perturbation Method (HPM). The fractional-order model indicates that the concentrations of free enzyme and inhibitor decrease gradually and the concentration of substrate remains relatively constant over the time period. The enzyme-substrate conversion is represented by the monotonic growth of product concentration. Among the intermediates, <span>(C_1(t))</span> varies slightly, <span>(C_2(t))</span> reaches relatively higher values and <span>(C_3(t))</span> is relatively small, as expected from the reaction schemes described by the model. Both HAM and HPM are successful in describing the overall kinetic behaviour of the system. Error analysis reveals that both approaches are better for different components of the system, with improved agreement of HPM for some components and better convergence properties of HAM. The findings demonstrate that both semi-analytical approaches are reliable and efficient tools for solving nonlinear fractional-order chemical kinetic systems and the numerical approximation provides a trustworthy benchmark.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"64 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0