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Optimizing Arrhenius parameters for multi-step reactions via metaheuristic algorithms 通过元启发式算法优化多步反应的阿伦尼乌斯参数
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-02-06 DOI: 10.1007/s10910-025-01710-3
AliReza Eshaghi, Zeinab Pouransari
{"title":"Optimizing Arrhenius parameters for multi-step reactions via metaheuristic algorithms","authors":"AliReza Eshaghi,&nbsp;Zeinab Pouransari","doi":"10.1007/s10910-025-01710-3","DOIUrl":"10.1007/s10910-025-01710-3","url":null,"abstract":"<div><p>In combustion simulation, the Arrhenius equation is a key tool for modeling multi-step reactions such as propane and methane reactions. It describes a relationship between the reaction rate, temperature, the pre-exponential factor, and activation energy. Applying these parameters outside their validated temperature and pressure ranges, or for unverified reactions, can result in important errors. The present study optimizes the coefficients of the Arrhenius model for multi-step combustion reactions, by utilizing experimental data and advanced optimization techniques. Our methodology incorporates metaheuristics techniques such as least squares minimization, particle swarm optimization, ant colony optimization, the slime mold algorithm, and the whale optimization algorithm. The results indicate that the optimized coefficients significantly improve the predictions while reducing computational time and associated costs. Furthermore, this paper presents a comprehensive comparative analysis of the various optimization techniques utilized and clarifies the advantages and limitations of each technique in the context of Arrhenius equation optimization.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 4","pages":"1065 - 1092"},"PeriodicalIF":1.7,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612055","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
Numerical treatment of singularly perturbed turning point problems with delay in time 具有时间延迟的奇异扰动转折点问题的数值处理
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-02-04 DOI: 10.1007/s10910-025-01707-y
Satpal Singh, Devendra Kumar, J. Vigo-Aguiar
{"title":"Numerical treatment of singularly perturbed turning point problems with delay in time","authors":"Satpal Singh,&nbsp;Devendra Kumar,&nbsp;J. Vigo-Aguiar","doi":"10.1007/s10910-025-01707-y","DOIUrl":"10.1007/s10910-025-01707-y","url":null,"abstract":"<div><p>This paper proposes a uniformly convergent numerical method for a class of singularly perturbed turning point problems with a time-lag defined on a rectangular domain. We consider an interior repulsive turning point with odd multiplicity <span>(geqslant 1)</span>. Twin boundary layers arise in the proximity of endpoints of the spatial domain due to the presence of the perturbation parameter. Preliminary results such as minimum principle, stability estimate, and solution derivative bounds for the continuous problem applicable in the convergence analysis are presented. First, we employ the Crank–Nicolson scheme to semi-discretize the continuous problem in the time direction, and then the cubic <span>(mathscr {B})</span>-spline functions on an appropriate Shishkin mesh are used to get a full discretization. The convergence analysis uses the maximum norm to obtain parameter-uniform error estimates. Three test problems are solved numerically to validate the theoretical results and confirm the scheme’s effectiveness.\u0000</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 4","pages":"1035 - 1064"},"PeriodicalIF":1.7,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612061","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
Vertex and face colorings of dodecahedron and its distortions for all irreducible representations: insights into dynamic chirality, pentagonal, Jahn–Teller and elongated distortions 十二面体的顶点和面着色及其所有不可约表示的畸变：对动态手性、五边形、扬-泰勒和拉长畸变的见解
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-02-03 DOI: 10.1007/s10910-025-01704-1
Krishnan Balasubramanian
{"title":"Vertex and face colorings of dodecahedron and its distortions for all irreducible representations: insights into dynamic chirality, pentagonal, Jahn–Teller and elongated distortions","authors":"Krishnan Balasubramanian","doi":"10.1007/s10910-025-01704-1","DOIUrl":"10.1007/s10910-025-01704-1","url":null,"abstract":"<div><p>We present combinatorial cum group theoretical generating function methods for vertex and face colorings of a dodecahedron for all irreducible representations of the icosahedral group. We demonstrate the usefulness of the Mȍbius inversion method. We consider several types of distortions arising from the highly symmetric dodecahedron, in particular, to an elongated dodecahedron and a pyrithohedron (T<sub>h</sub>). Elaborate combinatorial enumerations and tables of combinatorial numbers are explicitly constructed for all irreducible representations of both the distorted and the parent undistorted structures. It is shown that the combinatorial cum computational techniques provide new insights into the dynamic chirality arising from such distortions which include the pentagonal distortions, elongated distortions and so forth. We point out applications to the dynamic NMR and ESR spectroscopies as well to the dynamic stereochemistry of topological metamorphosis through a combination of combinatorics and group theory.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 4","pages":"982 - 1034"},"PeriodicalIF":1.7,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612029","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
The application of a fourteenth-order phase-fitting approach to enhance chemical problem-solving 十四阶相拟合方法的应用，以提高化学问题的解决
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-01-31 DOI: 10.1007/s10910-024-01701-w
Chia-Liang Lin, T. E. Simos
{"title":"The application of a fourteenth-order phase-fitting approach to enhance chemical problem-solving","authors":"Chia-Liang Lin,&nbsp;T. E. Simos","doi":"10.1007/s10910-024-01701-w","DOIUrl":"10.1007/s10910-024-01701-w","url":null,"abstract":"<div><p>By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The <b>cost-efficient approach</b> is a new strategy whose aims are to boost algebraic order (<i>AOR</i>) and reduce function evaluations (<i>FEVs</i>). The symbolic representation of the one-of-a-kind approach is <i>PF</i>6<i>DPHFITN</i>142<i>SPS</i>. This method is infinitely periodic since it is <b>P-Stable</b>. The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires <span>(5 , FEVs)</span>, the new method could be seen as a cost-effective strategy. With a <i>AOR</i> of 14, we can greatly enhance our current situation.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 4","pages":"919 - 961"},"PeriodicalIF":1.7,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612152","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
Investigation of real-world second-order singular differential equations by optimal homotopy analysis technique 用最优同伦分析技术研究现实世界二阶奇异微分方程
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-01-31 DOI: 10.1007/s10910-025-01703-2
Randhir Singh, Prabal Datta, Vandana Guleria, Nirupam Sahoo
{"title":"Investigation of real-world second-order singular differential equations by optimal homotopy analysis technique","authors":"Randhir Singh,&nbsp;Prabal Datta,&nbsp;Vandana Guleria,&nbsp;Nirupam Sahoo","doi":"10.1007/s10910-025-01703-2","DOIUrl":"10.1007/s10910-025-01703-2","url":null,"abstract":"<div><p>Extensive studies have investigated second-order singular differential equations to model various phenomena in astrophysics, reaction-diffusion processes, and electrohydrodynamics. However, finding numerical and analytical solutions for these problems with appropriate boundary conditions is challenging due to their inherent nonlinearity. Our current study explores singular second-order differential equations (SSODEs) with boundary conditions, specifically those modelling the distribution of heat sources in the human head and the steady-state temperature distribution in a vessel before a thermal explosion. The fundamental idea behind our approach is initially transforming the differential equation into an equivalent integral form, thereby circumventing the singular behaviour. Subsequently, the optimal homotopy analysis method is employed to scrutinize two distinct models, i.e., the heat conduction model, the thermal explosion model and the spherical catalyst equation. Further, a detailed convergence analysis is conducted in a Banach space framework to ensure the method’s reliability. The accuracy of the new approach is checked by considering various numerical examples with different values of thermogenesis heat production, the Biot number, and metabolic thermogenesis slope. It has been shown that the proposed approach qualitatively and quantitatively approximates the solutions with higher precision than the existing Adomian decomposition method.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 4","pages":"962 - 981"},"PeriodicalIF":1.7,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612153","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 Rayleigh-Ritz method 关于瑞利-里兹方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-01-29 DOI: 10.1007/s10910-025-01706-z
Francisco M. Fernández
{"title":"On the Rayleigh-Ritz method","authors":"Francisco M. Fernández","doi":"10.1007/s10910-025-01706-z","DOIUrl":"10.1007/s10910-025-01706-z","url":null,"abstract":"<div><p>We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz method are increasingly accurate upper bounds to the exact ones. To this end, we resort to the variational principle and to a set of suitable projection operators.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 3","pages":"911 - 918"},"PeriodicalIF":1.7,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529961","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
Pattern formation for a reversible biochemical reaction model with cross-diffusion and Michalis saturation 具有交叉扩散和米凯利斯饱和的可逆生化反应模型的模式形成
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-01-28 DOI: 10.1007/s10910-025-01705-0
Jing You, Gaihui Guo
{"title":"Pattern formation for a reversible biochemical reaction model with cross-diffusion and Michalis saturation","authors":"Jing You,&nbsp;Gaihui Guo","doi":"10.1007/s10910-025-01705-0","DOIUrl":"10.1007/s10910-025-01705-0","url":null,"abstract":"<div><p>This paper presents a qualitative study of a reversible biochemical reaction model with cross-diffusion and Michalis saturation. For the system without diffusion, the existence, stability and Hopf bifurcation of the positive equilibrium have been clearly determined. For the cross-diffusive system, the stability and Turing instability driven by cross-diffusion are studied according to the relationship between the self-diffusion and the cross-diffusion coefficients. Stability and cross-diffusion instability regions are theoretically determined in the plane of the cross-diffusion coefficients. The amplitude equation is derived by using the technique of multiple time scale. With the help of numerical simulation, we verify the analysis results.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 3","pages":"888 - 910"},"PeriodicalIF":1.7,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529960","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 chemical problem-solving through the use of a fourteenth-order phase-fitting method 通过使用十四阶相拟合方法改进化学问题的解决
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-12-23 DOI: 10.1007/s10910-024-01694-6
Dan Tan, Haiming Liu, Chia-Liang Lin, T. E. Simos
{"title":"Improving chemical problem-solving through the use of a fourteenth-order phase-fitting method","authors":"Dan Tan,&nbsp;Haiming Liu,&nbsp;Chia-Liang Lin,&nbsp;T. E. Simos","doi":"10.1007/s10910-024-01694-6","DOIUrl":"10.1007/s10910-024-01694-6","url":null,"abstract":"<div><p>It is possible to eliminate phase-lag and all of its derivatives up to order five by employing a method that takes fading phase-lag into consideration. Improving algebraic order (<i>AOR</i>) and decreasing function evaluations (<i>FEvs</i>) are the goals of the new method called the <b>cost-efficient approach</b>. The unique method is illustrated by the symbol <i>PF</i>5<i>DPHFITN</i>142<i>SPS</i>. This approach is <b>P-Stable</b>, which means it is infinitely periodic. A wide variety of periodic and oscillatory issues can be solved using the suggested approach. The challenging problem of Schrödinger-type coupled differential equations in quantum chemistry was tackled using this novel approach. With only <span>(5,FEvs)</span> needed to complete each step, the new method could be considered as a cost-effective approach. An <i>AOR</i> of 14 allows us to significantly improve our present condition.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 3","pages":"852 - 887"},"PeriodicalIF":1.7,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529959","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
Regions of existence and uniqueness for singular nonlinear diffusion problems 奇异非线性扩散问题的存在唯一性区域
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-12-14 DOI: 10.1007/s10910-024-01700-x
Shih-Hsiang Chang
{"title":"Regions of existence and uniqueness for singular nonlinear diffusion problems","authors":"Shih-Hsiang Chang","doi":"10.1007/s10910-024-01700-x","DOIUrl":"10.1007/s10910-024-01700-x","url":null,"abstract":"<div><p>This paper presents a novel approach for constructing the lower and upper boundaries of closed regions where solutions to the singular nonlinear diffusion problems </p><div><div><span>$$begin{aligned} begin{aligned} y''(x)+ frac{m}{x}y'(x)= f(x,y(x)), quad x in (0,1], quad m ge 0 , y'(0) = 0, quad Ay(1)+By'(1) = C, quad A&gt;0, B ge 0, C ge 0 , end{aligned} end{aligned}$$</span></div></div><p>exist. This existence result is proved using the method of lower and upper solutions with monotone iterative technique under the restriction that <i>f</i>(<i>x</i>, <i>y</i>) is continuous in <span>(x in [0,1])</span> and non-increasing in <i>y</i> in such regions. Additional uniqueness criteria is also established. The approach is illustrated on four singular nonlinear diffusion problems including some real life applications.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 3","pages":"816 - 828"},"PeriodicalIF":1.7,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529955","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
Molecular dynamics simulation of the mechanical properties of multi-walled nanotube comprising X-graphene and Y-graphene with different stacking orders 不同堆叠顺序的x -石墨烯和y -石墨烯多壁纳米管力学性能的分子动力学模拟
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-12-14 DOI: 10.1007/s10910-024-01698-2
Haichao Zhao, Haoran Wang
{"title":"Molecular dynamics simulation of the mechanical properties of multi-walled nanotube comprising X-graphene and Y-graphene with different stacking orders","authors":"Haichao Zhao,&nbsp;Haoran Wang","doi":"10.1007/s10910-024-01698-2","DOIUrl":"10.1007/s10910-024-01698-2","url":null,"abstract":"<div><p>This study employs Molecular Dynamics (MD) simulations to investigate the mechanical properties of single-layer X-graphene and Y-graphene in both armchair and zigzag configurations, as well as multi-walled nanotubes with varying stacking orders. The nanotubes are constructed using various combinations of armchair and zigzag configurations for the X-graphene and Y-graphene layers, arranged in distinct stacking patterns. Analysis of fracture and stress distribution in the X-graphene and Y-graphene nanotubes indicates a soft mechanical behavior. Additionally, stress–strain curve analysis shows that, within the initial elastic range, the curves coincide, suggesting that nanotube length does not significantly affect behavior in this region. The ultimate stress and strain of the X-graphene and Y-graphene nanotubes decrease with increasing length, while the toughness also diminishes as the length of the nanotubes increases. Notably, for double-walled nanotubes with both layers oriented in the zigzag configuration, the stress–strain response is slightly higher compared to other configurations.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 3","pages":"829 - 851"},"PeriodicalIF":1.7,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529954","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
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