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Memory Based Approaches to One-Dimensional Nonlinear Models 基于记忆的一维非线性模型方法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-12-16 DOI: 10.1007/s10440-024-00703-9
Amir Naseem, Ioannis K. Argyros, Sania Qureshi, Muhammad Aziz ur Rehman, Amanullah Soomro, Krzysztof Gdawiec, Ridwanulahi Iyanda Abdulganiy
{"title":"Memory Based Approaches to One-Dimensional Nonlinear Models","authors":"Amir Naseem,&nbsp;Ioannis K. Argyros,&nbsp;Sania Qureshi,&nbsp;Muhammad Aziz ur Rehman,&nbsp;Amanullah Soomro,&nbsp;Krzysztof Gdawiec,&nbsp;Ridwanulahi Iyanda Abdulganiy","doi":"10.1007/s10440-024-00703-9","DOIUrl":"10.1007/s10440-024-00703-9","url":null,"abstract":"<div><p>Algorithms that locate roots are used to analyze nonlinear equations in computer science, mathematics, and physical sciences. In order to speed up convergence and increase computational efficiency, memory-based root-seeking algorithms may look for the previous iterations. Three memory-based methods with a convergence order of about 2.4142 and one method without memory with third-order convergence are devised using both Taylor’s expansion and the backward difference operator. We provide an extensive analysis of local and semilocal convergence. We also use polynomiography to analyze the methods visually. Finally, the proposed iterative approaches outperform a number of existing memory-based methods when applied to one-dimensional nonlinear models taken from different fields of science and engineering.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826093","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
Preservation of Relative Hazard Rate and Relative Reversed Hazard Rate Orders by Distorted Distributions 通过扭曲分布保留相对危险率和相对反向危险率阶次
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-12-13 DOI: 10.1007/s10440-024-00704-8
Mohamed Kayid, Raghad A. Almohsen
{"title":"Preservation of Relative Hazard Rate and Relative Reversed Hazard Rate Orders by Distorted Distributions","authors":"Mohamed Kayid,&nbsp;Raghad A. Almohsen","doi":"10.1007/s10440-024-00704-8","DOIUrl":"10.1007/s10440-024-00704-8","url":null,"abstract":"<div><p>In this paper, we establish preservation properties of relative aging orders under distorted distributions. The relative hazard rate order and the relative reversed hazard rate order are considered. Using the derived results, a preservation property of the relative hazard rate order and a preservation property of the relative reversed hazard rate order derived perviously by Misra and Francis (Stat. Probab. Lett. 106:272–280, 2015) for, respectively, parallel and series systems are strengthened. Examples are also presented to illustrate the applicability of the obtained results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821483","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
Influence of Gauges in the Numerical Simulation of the Time-Dependent Ginzburg-Landau Model 量规在时变金兹堡-朗道模型数值模拟中的影响
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-15 DOI: 10.1007/s10440-024-00701-x
Cyril Tain, Jean-Guy Caputo, Ionut Danaila
{"title":"Influence of Gauges in the Numerical Simulation of the Time-Dependent Ginzburg-Landau Model","authors":"Cyril Tain,&nbsp;Jean-Guy Caputo,&nbsp;Ionut Danaila","doi":"10.1007/s10440-024-00701-x","DOIUrl":"10.1007/s10440-024-00701-x","url":null,"abstract":"<div><p>The time-dependent Ginzburg-Landau (TDGL) model requires the choice of a gauge for the problem to be mathematically well-posed. In the literature, three gauges are commonly used: the Coulomb gauge, the Lorenz gauge and the temporal gauge. It has been noticed (J. Fleckinger-Pellé et al. in Dynamics of the Ginzburg-Landau equations of superconductivity, Technical report, Argonne National Lab. (ANL), Argonne, IL, United States, 1997) that these gauges can be continuously related by a single parameter considering the more general <span>(omega )</span>-gauge, where <span>(omega )</span> is a non-negative real parameter. In this article, we study the influence of the gauge parameter <span>(omega )</span> on the convergence of numerical simulations of the TDGL model using finite element schemes. A classical benchmark is first analysed for different values of <span>(omega )</span> and artefacts are observed for lower values of <span>(omega )</span>. Then, we relate these observations with a systematic study of convergence orders in the unified <span>(omega )</span>-gauge framework. In particular, we show the existence of a tipping point value for <span>(omega )</span>, separating optimal convergence behaviour and a degenerate one. We find that numerical artefacts are correlated to the degeneracy of the convergence order of the method and we suggest strategies to avoid such undesirable effects. New 3D configurations are also investigated (the sphere with or without geometrical defect).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645417","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
Some Properties on the Reversibility and the Linear Response Theory of Langevin Dynamics 朗文动力学的可逆性和线性响应理论的一些特性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-14 DOI: 10.1007/s10440-024-00702-w
Yuan Gao, Jian-Guo Liu, Zibu Liu
{"title":"Some Properties on the Reversibility and the Linear Response Theory of Langevin Dynamics","authors":"Yuan Gao,&nbsp;Jian-Guo Liu,&nbsp;Zibu Liu","doi":"10.1007/s10440-024-00702-w","DOIUrl":"10.1007/s10440-024-00702-w","url":null,"abstract":"<div><p>Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin dynamics. We give some equivalent characterizations for reversible overdamped/underdamped Langevin dynamics, which is the unperturbed reference system. Then we clarify sufficient conditions for the smoothness and exponential convergence to the invariant measure for the overdamped case. We also clarify those sufficient conditions for the underdamped case, which corresponds to hypoellipticity and hypocoercivity. Based on these, the asymptotic dependence of the response function on the small perturbation is proved in both finite and infinite time horizons. As applications, Green-Kubo relations and linear response theory for a generalized Langevin dynamics are also proved in a rigorous fashion.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636905","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
Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation 基于减阶模型的一维赫尔姆霍兹方程非线性波形反演
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-13 DOI: 10.1007/s10440-024-00700-y
Andreas Tataris, Tristan van Leeuwen
{"title":"Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation","authors":"Andreas Tataris,&nbsp;Tristan van Leeuwen","doi":"10.1007/s10440-024-00700-y","DOIUrl":"10.1007/s10440-024-00700-y","url":null,"abstract":"<div><p>We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636919","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
Qualitative Behavior of Solutions of a Chemotaxis System with Flux Limitation and Nonlinear Signal Production 具有通量限制和非线性信号产生的趋化系统溶液的定性行为
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-11 DOI: 10.1007/s10440-024-00699-2
M. Marras, Y. Chiyo
{"title":"Qualitative Behavior of Solutions of a Chemotaxis System with Flux Limitation and Nonlinear Signal Production","authors":"M. Marras,&nbsp;Y. Chiyo","doi":"10.1007/s10440-024-00699-2","DOIUrl":"10.1007/s10440-024-00699-2","url":null,"abstract":"<div><p>In this paper we consider radially symmetric solutions of the following parabolic-elliptic cross-diffusion system </p><div><div><span>$$ left { textstylebegin{array}{l} begin{aligned} &amp;u_{t} = Delta u - nabla (u f(|nabla v|^{2} )nabla v), &amp;0= Delta v -mu (t)+ g(u), quad mu (t)= frac{1}{|Omega |} int _{Omega } g(u(cdot , t))dx &amp;u(x,0)= u_{0}(x), end{aligned} end{array}displaystyle right . $$</span></div></div><p> in <span>(Omega times (0,infty ))</span>, with <span>(Omega )</span> a ball in <span>(mathbb{R}^{N})</span>, <span>(Ngeq 1)</span> under homogeneous Neumann boundary conditions, <span>(g(u))</span> a regular function with the prototype <span>(g(u)= u^{k})</span>, <span>(ugeq 0)</span>, <span>(k&gt;0)</span>. The function <span>(f(xi ) = k_{f} (1+ xi )^{-alpha })</span>, <span>(k_{f} &gt;0)</span>, describes gradient-dependent limitation of cross diffusion fluxes. Under suitable conditions on the data, we prove that the solution is global in time. If <span>(Ngeq 3)</span>, under conditions on <span>(f)</span>, <span>(g)</span> and initial data, we prove that if the solution <span>(u(x,t))</span> blows up in <span>(L^{infty })</span>-norm at finite time <span>(T_{max})</span> then for some <span>(p&gt;1)</span> it blows up also in <span>(L^{p})</span>-norm. Moreover a lower bound of blow-up time is derived.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598816","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
Harris’s Method for Non-conservative Periodic Semiflows and Application to Some Non-local PDEs 非保守周期半流的哈里斯方法及其在一些非局部 PDE 中的应用
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-04 DOI: 10.1007/s10440-024-00698-3
Adil El Abdouni
{"title":"Harris’s Method for Non-conservative Periodic Semiflows and Application to Some Non-local PDEs","authors":"Adil El Abdouni","doi":"10.1007/s10440-024-00698-3","DOIUrl":"10.1007/s10440-024-00698-3","url":null,"abstract":"<div><p>In this paper we propose some Harris-like criteria in order to study the long time behavior of general positive and periodic semiflows. These criteria allow us to obtain new existence results of principal eigenelements, and their exponential attractiveness. We present applications to two biological models in a space-time varying environment: a non local selection-mutation equation and a growth-fragmentation equation. The particularity of this article is to study some inhomogeneous problems that are periodic in time, as it appears for instance when the environment changes, due for instance to the seasonal cycle or circadian rhythms.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579441","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
Global Well-Posedness for the 2D Keller-Segel-Navier-Stokes System with Fractional Diffusion 具有分数扩散的二维凯勒-西格尔-纳维尔-斯托克斯系统的全局良好假设性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-21 DOI: 10.1007/s10440-024-00696-5
Chaoyong Wang, Qi Jia, Qian Zhang
{"title":"Global Well-Posedness for the 2D Keller-Segel-Navier-Stokes System with Fractional Diffusion","authors":"Chaoyong Wang,&nbsp;Qi Jia,&nbsp;Qian Zhang","doi":"10.1007/s10440-024-00696-5","DOIUrl":"10.1007/s10440-024-00696-5","url":null,"abstract":"<div><p>In this paper, we consider Cauchy problem for the 2D incompressible Keller-Segel-Navier-Stokes equations with the fractional diffusion </p><div><div><span> $$begin{aligned} left { begin{aligned} &amp;partial _{t}n+ucdot nabla n-Delta n=-nabla cdot (nnabla c)- n^{3}, &amp;partial _{t}c+ucdot nabla c-Delta c=-c+n, &amp;partial _{t}u+ucdot nabla u+wedge ^{2alpha }u+nabla P=-nnabla phi , end{aligned} right . end{aligned}$$ </span></div></div><p> where <span>(wedge :=(-Delta )^{frac{1}{2}})</span> and <span>(alpha in [frac{1}{2},1])</span>. We get the global well-posedness for the above system with the rough initial data by a new priori estimate of the solutions.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453085","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
Regular Polygonal Vortex Filament Evolution and Exponential Sums 正多边形涡旋纤丝演化与指数和
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-21 DOI: 10.1007/s10440-024-00697-4
Fernando Chamizo, Francisco de la Hoz
{"title":"Regular Polygonal Vortex Filament Evolution and Exponential Sums","authors":"Fernando Chamizo,&nbsp;Francisco de la Hoz","doi":"10.1007/s10440-024-00697-4","DOIUrl":"10.1007/s10440-024-00697-4","url":null,"abstract":"<div><p>When taking a regular planar polygon of <span>(M)</span> sides and length <span>(2pi )</span> as the initial datum of the vortex filament equation, <span>(mathbf{X}_{t}= mathbf{X}_{s}wedge mathbf{X}_{ss})</span>, the solution becomes polygonal at times of the form <span>(t_{pq} = (p/q)(2pi /M^{2}))</span>, with <span>(gcd (p,q)=1)</span>, and the corresponding polygon has <span>(Mq)</span> sides, if <span>(q)</span> is odd, and <span>(Mq/2)</span> sides, if <span>(q)</span> is even. Moreover, that polygon is skew (except when <span>(q = 1)</span> or <span>(q = 2)</span>, where the initial shape is recovered), and the angle <span>(rho )</span> between two adjacent sides is a constant. In this paper, we give a rigorous proof of the conjecture that states that, at a time <span>(t_{pq})</span>, <span>(cos ^{q}(rho /2) = cos (pi /M))</span>, if <span>(q)</span> is odd, and <span>(cos ^{q}(rho /2) = cos ^{2}(pi /M))</span>, if <span>(q)</span> is even. Since the transition of one side of the polygon to the next one is given by a rotation in <span>(mathbb{R}^{3})</span> determined by a generalized Gauss sum, the idea of the proof consists in showing that a certain product of those rotations is a rotation of angle <span>(2pi /M)</span>, which is equivalent to proving that some exponential sums with arithmetic content are purely imaginary.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00697-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Total Absolute Curvature Estimation 总绝对曲率估算
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-21 DOI: 10.1007/s10440-024-00694-7
Loïc Mazo
{"title":"Total Absolute Curvature Estimation","authors":"Loïc Mazo","doi":"10.1007/s10440-024-00694-7","DOIUrl":"10.1007/s10440-024-00694-7","url":null,"abstract":"<div><p>Total (absolute) curvature is defined for any curve in a metric space. Its properties, finiteness, local boundedness, Lipschitz continuity, depending whether there are satisfied or not, permit a classification of curves alternative to the classical regularity classes. In this paper, we are mainly interested in the total curvature estimation. Under the sole assumption of curve simpleness, we prove the convergence, as <span>(epsilon to 0)</span>, of the <i>naive turn estimators</i> which are families of polygonal lines whose vertices are at distance at most <span>(epsilon )</span> from the curve and whose edges are in <span>(Omega (epsilon ^{alpha })cap text{O}(epsilon ^{beta }))</span> with <span>(0&lt;beta le alpha &lt;frac{1}{2})</span>. Besides, we give lower bounds of the speed of convergence under an additional assumption that can be summarized as being “convex-or-Lipschitz”.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00694-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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