Journal of Mathematical Chemistry最新文献_第6页

Analysis of a general reaction–diffusion model using Lie symmetries and conservation laws 用李氏对称和守恒定律分析一般反应-扩散模型

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-10-01 DOI: 10.1007/s10910-024-01679-5

Sol Sáez-Martínez

{"title":"Analysis of a general reaction–diffusion model using Lie symmetries and conservation laws","authors":"Sol Sáez-Martínez","doi":"10.1007/s10910-024-01679-5","DOIUrl":"10.1007/s10910-024-01679-5","url":null,"abstract":"<div><p>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.\u0000</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 2","pages":"419 - 434"},"PeriodicalIF":1.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373175","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

Bounds for the Gutman–Milovanović index and some applications gutman - milovanovivic指数的界及一些应用

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-30 DOI: 10.1007/s10910-024-01677-7

Ana Granados, Ana Portilla, Yamilet Quintana, Eva Tourís

引用次数: 0

Stability analysis and dynamical behavior of optimal mean-based iterative methods 最优均值迭代法的稳定性分析及动力学行为

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-25 DOI: 10.1007/s10910-024-01674-w

Himani Sharma, Munish Kansal

引用次数: 0

Path integral for the quartic oscillator: an accurate analytic formula for the partition function 四次振子的路径积分：配分函数的精确解析公式

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-20 DOI: 10.1007/s10910-024-01671-z

Michel Caffarel

{"title":"Path integral for the quartic oscillator: an accurate analytic formula for the partition function","authors":"Michel Caffarel","doi":"10.1007/s10910-024-01671-z","DOIUrl":"10.1007/s10910-024-01671-z","url":null,"abstract":"<div><p>In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential <span>(V(x) = frac{1}{2} omega ^2 x^2 + g x^4)</span> 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 <i>g</i>. 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 <i>g</i>. Both the harmonic (<span>(grightarrow 0)</span>) 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, <span>(E_0(g))</span> and <span>(E_1(g))</span> are also presented.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 2","pages":"353 - 382"},"PeriodicalIF":1.7,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-024-01671-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373319","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

A first-rate fourteenth-order phase-fitting approach to solving chemical problems 解决化学问题的一流十四阶相位拟合方法

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-17 DOI: 10.1007/s10910-024-01668-8

Mei Hong, Chia-Liang Lin, T. E. Simos

引用次数: 0

Mathematical modeling of hydrogen evolution by ({{{H}}}^{+}) and ({{{H}}}_{2}{{O}}) reduction at a rotating disk electrode: theoretical and numerical aspects 通过旋转盘电极上的 $${{{H}}^{+}$ 和 $${{{{H}}}_{2}{{O}}$ 还原进行氢演化的数学建模：理论和数值方面的问题

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-17 DOI: 10.1007/s10910-024-01675-9

K. V. Tamil Selvi, Navnit Jha, A. Eswari, L. Rajendran

{"title":"Mathematical modeling of hydrogen evolution by ({{{H}}}^{+}) and ({{{H}}}_{2}{{O}}) reduction at a rotating disk electrode: theoretical and numerical aspects","authors":"K. V. Tamil Selvi, Navnit Jha, A. Eswari, L. Rajendran","doi":"10.1007/s10910-024-01675-9","DOIUrl":"10.1007/s10910-024-01675-9","url":null,"abstract":"<div><p>This paper discusses mathematical model of hydrogen evolution via <span>({H}^{+})</span> and <span>({H}_{2}O)</span> 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 <span>({H}^{+})</span> and <span>({OH}^{-})</span> 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.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 2","pages":"333 - 352"},"PeriodicalIF":1.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262387","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

On the uniqueness of continuous and discrete hard models of NMR-spectra 论 NMR 光谱连续和离散硬模型的唯一性

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-16 DOI: 10.1007/s10910-024-01673-x

Jan Hellwig, Klaus Neymeyr

引用次数: 0

Numerical analysis of fourth-order multi-term fractional reaction-diffusion equation arises in chemical reactions 化学反应中出现的四阶多期分数反应-扩散方程的数值分析

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-09-06 DOI: 10.1007/s10910-024-01670-0

Reetika Chawla, Devendra Kumar, J. Vigo-Aguiar

{"title":"Numerical analysis of fourth-order multi-term fractional reaction-diffusion equation arises in chemical reactions","authors":"Reetika Chawla, Devendra Kumar, J. Vigo-Aguiar","doi":"10.1007/s10910-024-01670-0","DOIUrl":"10.1007/s10910-024-01670-0","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 1","pages":"237 - 266"},"PeriodicalIF":1.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179938","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

Thermodynamical quantities of silver mono halides from spectroscopic data 从光谱数据得出卤化银的热力学量

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-08-27 DOI: 10.1007/s10910-024-01664-y

Shipra Tripathi, Abhi Sarika Bharti, Kailash Narayan Uttam, C. K. Dixit, Anjani K. Pandey

{"title":"Thermodynamical quantities of silver mono halides from spectroscopic data","authors":"Shipra Tripathi, Abhi Sarika Bharti, Kailash Narayan Uttam, C. K. Dixit, Anjani K. Pandey","doi":"10.1007/s10910-024-01664-y","DOIUrl":"10.1007/s10910-024-01664-y","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 1","pages":"222 - 236"},"PeriodicalIF":1.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179939","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

Resolving the problem of multiple control parameters in optimized Borel-type summation 解决优化伯尔式求和中的多控制参数问题

IF 1.7 3区化学

Journal of Mathematical Chemistry Pub Date : 2024-08-26 DOI: 10.1007/s10910-024-01669-7

V. I. Yukalov, S. Gluzman

引用次数: 0