arXiv - MATH - Dynamical Systems最新文献_第10页

Mathematical modelling of the vitamin C clock reaction: a study of two kinetic regimes 维生素 C 时钟反应的数学建模：两种动力学机制的研究

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.04108

Aliya Alsaleh, David J. Smith, Sara Jabbari

{"title":"Mathematical modelling of the vitamin C clock reaction: a study of two kinetic regimes","authors":"Aliya Alsaleh, David J. Smith, Sara Jabbari","doi":"arxiv-2408.04108","DOIUrl":"https://doi.org/arxiv-2408.04108","url":null,"abstract":"Chemically reacting systems exhibiting a repeatable delay period before a\u0000visible and sudden change are referred to as clock reactions; they have a long\u0000history in education and provide an idealisation of various biochemical and\u0000industrial processes. We focus on a purely substrate-depletive clock reaction\u0000utilising vitamin C, hydrogen peroxide, iodine and starch. Building on a recent\u0000study of a simplified two-reaction model under high hydrogen peroxide\u0000concentrations, we develop a more detailed model which breaks the slow reaction\u0000into two steps, one of which is rate-limiting unless hydrogen peroxide levels\u0000are very high. Through asymptotic analysis, this model enables the effect of\u0000hydrogen peroxide concentration to be elucidated in a principled way, resolving\u0000an apparent discrepancy with earlier literature regarding the order of the slow\u0000reaction kinetics. The model is analysed in moderate- and high-hydrogen\u0000peroxide regimes, providing approximate solutions and expressions for the\u0000switchover time which take into account hydrogen peroxide concentration. The\u0000solutions are validated through simultaneously fitting the same set of\u0000parameters to several experimental series, then testing on independent\u0000experiments across widely varying hydrogen peroxide concentration. The study\u0000thereby presents and further develops a validated mechanistic understanding of\u0000a paradigm chemical kinetics system.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Permutations of periodic points of Weierstrass Prym eigenforms 魏尔斯特拉斯-普赖姆特征形式周期点的排列

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.03832

Rodolfo Gutiérrez-Romo, Angel Pardo

{"title":"Permutations of periodic points of Weierstrass Prym eigenforms","authors":"Rodolfo Gutiérrez-Romo, Angel Pardo","doi":"arxiv-2408.03832","DOIUrl":"https://doi.org/arxiv-2408.03832","url":null,"abstract":"A Weierstrass Prym eigenform is an Abelian differential with a single zero on\u0000a Riemann surface possessing some special kinds of symmetries. Such surfaces\u0000come equipped with an involution, known as a Prym involution. They were\u0000originally discovered by McMullen and only arise in genus 2, 3 and 4. Moreover,\u0000they are classified by two invariants: discriminant and spin. We study how the fixed points for the Prym involution of Weierstrass Prym\u0000eigenforms are permuted. In previous work, the authors computed the permutation\u0000group induced by affine transformations in the case of genus 2, showing that\u0000they are dihedral groups depending only on the residue class modulo 8 of the\u0000discriminant $D$. In this work, we complete this classification by settling the\u0000case of genus 3, showing that the permutation group induced by the affine group\u0000on the set of its three (regular) fixed points is isomorphic to\u0000$mathrm{Sym}_2$ when $D$ is even and a quadratic residue modulo 16, and to\u0000$mathrm{Sym}_3$ otherwise. The case of genus 4 is trivial as the Pyrm\u0000involution fixes a single (regular) point. In both cases, these same groups\u0000arise when considering only parabolic elements of the affine group. By recent work of Freedman, when the Teichm\"uller curve induced by\u0000Weierstrass Prym eigenform is not arithmetic, the fixed points of the Prym\u0000involution coincide with the periodic points of the surface. Hence, in this\u0000case, our result also classifies how periodic points are permuted.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Monochromatic nonuniform hyperbolicity 单色非均匀双曲性

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.03878

Jairo Bochi

引用次数: 0

Force-Motion Control For A Six Degree-Of-Freedom Robotic Manipulator 六自由度机器人机械手的力-运动控制

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.04106

Sagar Ojha, Karl Leodler, Lou Barbieri, TseHuai Wu

引用次数: 0

Tangent Space of the Stable And Unstable Manifold of Anosov Diffeomorphism on 2-Torus 2-Torus 上阿诺索夫衍射的稳定与不稳定漫域的切线空间

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.03607

Federico Bonneto, Jack Wang, Vishal Kumar

引用次数: 0

On orbit complexity of dynamical systems: intermediate value property and level set related to a Furstenberg problem 论动力系统的轨道复杂性：与弗斯滕伯格问题有关的中间值特性和水平集

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.04010

Yuanyang Chang, Bing Li, Meng Wu

引用次数: 0

Holomorphic foliations tangent to Rolle-pfaffian hypersurfaces 与罗尔-普法非超曲面相切的全形叶面

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.03914

Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas

引用次数: 0

Contraction and Synchronization in Reservoir Systems 储层系统的收缩与同步

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI: arxiv-2408.04058

Adrian S. Wong, Robert S. Martin, Daniel Q. Eckhardt

引用次数: 0

Slow-fast systems in infinite measure, with or without averaging 有或没有平均值的无限慢-快系统

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-06 DOI: arxiv-2408.03009

Maxence Phalempin

引用次数: 0

Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator 通过条件扩散模型和神经运算器建立数据驱动的随机闭合模型

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-06 DOI: arxiv-2408.02965

Xinghao Dong, Chuanqi Chen, Jin-Long Wu

{"title":"Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator","authors":"Xinghao Dong, Chuanqi Chen, Jin-Long Wu","doi":"arxiv-2408.02965","DOIUrl":"https://doi.org/arxiv-2408.02965","url":null,"abstract":"Closure models are widely used in simulating complex multiscale dynamical\u0000systems such as turbulence and the earth system, for which direct numerical\u0000simulation that resolves all scales is often too expensive. For those systems\u0000without a clear scale separation, deterministic and local closure models often\u0000lack enough generalization capability, which limits their performance in many\u0000real-world applications. In this work, we propose a data-driven modeling\u0000framework for constructing stochastic and non-local closure models via\u0000conditional diffusion model and neural operator. Specifically, the Fourier\u0000neural operator is incorporated into a score-based diffusion model, which\u0000serves as a data-driven stochastic closure model for complex dynamical systems\u0000governed by partial differential equations (PDEs). We also demonstrate how\u0000accelerated sampling methods can improve the efficiency of the data-driven\u0000stochastic closure model. The results show that the proposed methodology\u0000provides a systematic approach via generative machine learning techniques to\u0000construct data-driven stochastic closure models for multiscale dynamical\u0000systems with continuous spatiotemporal fields.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0