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Generalized kinetic theory of coarse-grained systems. II. Comparison of various approximations and coarse-grainings
IF 5.3 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-03-02 DOI: 10.1016/j.chaos.2025.116093
Bernard Gaveau, Michel Moreau
{"title":"Generalized kinetic theory of coarse-grained systems. II. Comparison of various approximations and coarse-grainings","authors":"Bernard Gaveau,&nbsp;Michel Moreau","doi":"10.1016/j.chaos.2025.116093","DOIUrl":"10.1016/j.chaos.2025.116093","url":null,"abstract":"<div><div>In the first part of this article, recently published, the general kinetic theory of coarse-grained systems has been presented in the abstract formalism of communication theory developed by Shannon, Khinchin, Kolmogorov and other authors. In the second part of the article, presented below, we compare various approximations of this theory, and several kinds of coarse-grainings, focusing on their asymptotics. In particular, we introduce extensions of classical ergodic theorems and derive some rigorous results which allow for such comparison, although explicit calculations may be problematic.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116093"},"PeriodicalIF":5.3,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability, convergence, and energy preservation robust methods for fully implicit and fully explicit coupling schemes
IF 5.3 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-03-01 DOI: 10.1016/j.chaos.2025.116131
Taj Munir , Can Kang , Hongchu Chen , Hussan Zeb , Muhammad Naveed Khan , Muhammad Usman Farid
{"title":"Stability, convergence, and energy preservation robust methods for fully implicit and fully explicit coupling schemes","authors":"Taj Munir ,&nbsp;Can Kang ,&nbsp;Hongchu Chen ,&nbsp;Hussan Zeb ,&nbsp;Muhammad Naveed Khan ,&nbsp;Muhammad Usman Farid","doi":"10.1016/j.chaos.2025.116131","DOIUrl":"10.1016/j.chaos.2025.116131","url":null,"abstract":"<div><div>This paper presents an analysis of the Godunov–Ryabenkii stability, Generalized Mini-mal Residual(GMRES) convergence, and energy-preserving properties of partitioned and monolithic approaches (fully implicit and fully explicit schemes) for solving coupled parabolic problems. Specifically, we consider a bi-domain parabolic diffusion problem with two types of coupling conditions at the interface: Dirichlet–Neumann and heat-flux coupling. Our findings shows that the Dirichlet–Neumann coupling is unconditionally stable for both approaches. In contrast, the heat-flux coupling requires additional conditions to ensure the stability of the coupled problem. For numerical approximations, finite volume and finite difference schemes are used. The results show that energy preservation is achieved with one-sided differences in the finite volume method, while the finite difference method achieves conservation when central difference approximations are used for both the coupling and boundary conditions in the heat-flux coupling case. Additionally, Dirichlet–Neumann coupling maintains stability and energy preservation in both methods using the one-sided approach without requiring extra conditions. However, for heat-flux coupling, an additional restriction is necessary to ensure stability. The challenge for the convergence of coupled interface problems arise due to strong domain interactions and sensitive interface conditions, like Dirichlet–Neumann or heat-flux coupling. The poor system conditioning and discretization choices can slow the rate of convergence. For this purpose we used the GMRES method. This work provides a comprehensive framework for addressing coupled parabolic diffusion problems using robust, stable, and energy-preserving numerical methods.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116131"},"PeriodicalIF":5.3,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit solutions and finite-time stability for fractional delay systems
IF 3.5 2区 数学
Applied Mathematics and Computation Pub Date : 2025-03-01 DOI: 10.1016/j.amc.2025.129388
Ahmed M. Elshenhab , Xing Tao Wang , Mohamed Hosny
{"title":"Explicit solutions and finite-time stability for fractional delay systems","authors":"Ahmed M. Elshenhab ,&nbsp;Xing Tao Wang ,&nbsp;Mohamed Hosny","doi":"10.1016/j.amc.2025.129388","DOIUrl":"10.1016/j.amc.2025.129388","url":null,"abstract":"<div><div>Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve, extend, and complement the previous works. Finally, an example is provided to illustrate the importance of the results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129388"},"PeriodicalIF":3.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some rigidity results for charged initial data sets 带电初始数据集的一些刚度结果
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-03-01 DOI: 10.1016/j.na.2025.113780
Gregory J. Galloway , Abraão Mendes
{"title":"Some rigidity results for charged initial data sets","authors":"Gregory J. Galloway ,&nbsp;Abraão Mendes","doi":"10.1016/j.na.2025.113780","DOIUrl":"10.1016/j.na.2025.113780","url":null,"abstract":"<div><div>In this note, we consider some initial data rigidity results concerning marginally outer trapped surfaces (MOTS). As is well known, MOTS play an important role in the theory of black holes and, at the same time, are interesting spacetime analogues of minimal surfaces in Riemannian geometry. The main results presented here expand upon earlier works by the authors, specifically addressing initial data sets incorporating charge.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"256 ","pages":"Article 113780"},"PeriodicalIF":1.3,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symplectic resolutions of the quotient of ( {{mathbb {R}}}^2 ) by an infinite symplectic discrete group
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-03-01 DOI: 10.1007/s10455-024-09971-y
Hichem Lassoued, Camille Laurent-Gengoux
{"title":"Symplectic resolutions of the quotient of ( {{mathbb {R}}}^2 ) by an infinite symplectic discrete group","authors":"Hichem Lassoued,&nbsp;Camille Laurent-Gengoux","doi":"10.1007/s10455-024-09971-y","DOIUrl":"10.1007/s10455-024-09971-y","url":null,"abstract":"<div><p>We construct smooth symplectic resolutions of the quotient of <span>({mathbb {R}}^2 )</span> under some <i>infinite</i> discrete sub-group of <span>({textrm{ GL}}_2({mathbb {R}}) )</span> preserving a log-symplectic structure. This extends from algebraic geometry to smooth real differential geometry the Du Val symplectic resolution of <span>({mathbb {C}}^2 hspace{-1.5pt} / hspace{-1.5pt}G)</span>, with <span>(G subset {textrm{ SL}}_2({mathbb {C}}) )</span> a finite group. The first of these <i>infinite</i> groups is <span>(G={mathbb {Z}})</span>, identified to triangular matrices with spectrum <span>({1} )</span>. Smooth functions on the quotient <span>(mathbb {R}^2 hspace{-1.5pt} / hspace{-1.5pt} G )</span> come with a natural Poisson bracket, and <span>(mathbb {R}^2hspace{-1.5pt} / hspace{-1.5pt}G)</span> is for an arbitrary <span>(k ge 1)</span> set-isomorphic to the real Du Val singular variety <span>(A_{2k} = {(x,y,z) in {mathbb {R}}^3, x^2 +y^2= z^{2k}})</span>. We show that each one of the usual minimal resolutions of these Du Val varieties are symplectic resolutions of <span>(mathbb {R}^2hspace{-1.5pt} / hspace{-1.5pt}G)</span>. The same holds for <span>(G'={mathbb {Z}} rtimes {mathbb {Z}}hspace{-1.5pt} / hspace{-1.5pt}2mathbb {Z})</span> (identified to triangular matrices with spectrum <span>({pm 1} )</span>), with the upper half of the Du Val singularity <span>(D_{2k+1} )</span> playing the role of <span>(A_{2k})</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09971-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimizing Variational Physics-Informed Neural Networks Using Least Squares
IF 2.9 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-03-01 DOI: 10.1016/j.camwa.2025.02.022
Carlos Uriarte , Manuela Bastidas , David Pardo , Jamie M. Taylor , Sergio Rojas
{"title":"Optimizing Variational Physics-Informed Neural Networks Using Least Squares","authors":"Carlos Uriarte ,&nbsp;Manuela Bastidas ,&nbsp;David Pardo ,&nbsp;Jamie M. Taylor ,&nbsp;Sergio Rojas","doi":"10.1016/j.camwa.2025.02.022","DOIUrl":"10.1016/j.camwa.2025.02.022","url":null,"abstract":"<div><div>Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a least squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid least-squares/gradient-descent optimizer and explains how to implement it efficiently. In particular, we show that a traditional implementation based on backward-mode automatic differentiation leads to a prohibitively expensive algorithm. To remedy this, we propose using either forward-mode automatic differentiation or an ultraweak-type scheme that avoids the differentiation of trial functions in the discrete weak formulation. The proposed alternatives are up to one hundred times faster than the traditional one, recovering a computational cost-per-iteration similar to that of a conventional gradient-descent-based optimizer alone. To support our analysis, we derive computational estimates and conduct numerical experiments in one- and two-dimensional problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"185 ","pages":"Pages 76-93"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trimming of finite subsets of the Manhattan plane
IF 0.9 4区 数学
Discrete Optimization Pub Date : 2025-03-01 DOI: 10.1016/j.disopt.2025.100880
Gökçe Çakmak , Ali Deniz , Şahin Koçak
{"title":"Trimming of finite subsets of the Manhattan plane","authors":"Gökçe Çakmak ,&nbsp;Ali Deniz ,&nbsp;Şahin Koçak","doi":"10.1016/j.disopt.2025.100880","DOIUrl":"10.1016/j.disopt.2025.100880","url":null,"abstract":"<div><div>V. Turaev defined recently an operation of “Trimming” for pseudo-metric spaces and analyzed the tight span of (pseudo-)metric spaces via this process. In this work we investigate the trimming of finite subspaces of the Manhattan plane. We show that this operation amounts for them to taking the metric center set and we give an algorithm to construct the tight spans via trimming.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"56 ","pages":"Article 100880"},"PeriodicalIF":0.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic analysis for an age-structured predator–prey model with Beddington–Deangelis functional response
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-01 DOI: 10.1016/j.nonrwa.2025.104345
Yuan Yuan , Xianlong Fu
{"title":"Asymptotic analysis for an age-structured predator–prey model with Beddington–Deangelis functional response","authors":"Yuan Yuan ,&nbsp;Xianlong Fu","doi":"10.1016/j.nonrwa.2025.104345","DOIUrl":"10.1016/j.nonrwa.2025.104345","url":null,"abstract":"<div><div>This paper focuses on the asymptotic behavior of an age-structured predator–prey model with Beddington–Deangelis functional response and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Then, the global asymptotic stability of the boundary equilibrium is successfully established by determining the distribution of eigenvalues. Hopf bifurcation results with two parameters are also well described under some conditions by the method of stability switching curves. Finally, some numerical examples are presented to further deepen the understanding of the obtained results.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104345"},"PeriodicalIF":1.8,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hurwitz numbers for reflection groups III: Uniform formulae
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-01 DOI: 10.1112/jlms.70102
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales
{"title":"Hurwitz numbers for reflection groups III: Uniform formulae","authors":"Theo Douvropoulos,&nbsp;Joel Brewster Lewis,&nbsp;Alejandro H. Morales","doi":"10.1112/jlms.70102","DOIUrl":"https://doi.org/10.1112/jlms.70102","url":null,"abstract":"<p>We give uniform formulae for the number of full reflection factorizations of a parabolic quasi-Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus-0 Hurwitz numbers. This paper is the culmination of a series of three.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reservoir computing system using discrete memristor for chaotic temporal signal processing
IF 5.3 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-03-01 DOI: 10.1016/j.chaos.2025.116230
Yue Deng , Shuting Zhang , Fang Yuan , Yuxia Li , Guangyi Wang
{"title":"Reservoir computing system using discrete memristor for chaotic temporal signal processing","authors":"Yue Deng ,&nbsp;Shuting Zhang ,&nbsp;Fang Yuan ,&nbsp;Yuxia Li ,&nbsp;Guangyi Wang","doi":"10.1016/j.chaos.2025.116230","DOIUrl":"10.1016/j.chaos.2025.116230","url":null,"abstract":"<div><div>Reservoir computing (RC) is a highly efficient neural network for processing temporal signals, primarily due to its significantly lower training cost compared to standard recurrent neural networks. In this work, a novel discrete memristor (DM) model is investigated and a simple two-dimensional chaotic map based on the DM model is presented, in which complex dynamics are simulated. By utilizing this DM-based map as a reservoir, a dynamic DM-based RC system is constructed, and the performance is verified through nonlinear regression and time-series prediction tasks. Our system achieves a high accuracy rate of 99.99 % in the nonlinear recognitions, as well as a low root mean square error of 0.0974 in the time-series prediction of the Logistic map. This work may pave the way for the future development of high-efficiency memristor-based RC systems to handle more complex temporal tasks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116230"},"PeriodicalIF":5.3,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","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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