Acta Applicandae Mathematicae最新文献

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, 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":null,"pages":null},"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

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

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

引用次数: 0

A Particle Method for the Multispecies Landau Equation 多物种朗道方程的粒子法

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-21 DOI: 10.1007/s10440-024-00692-9

José A. Carrillo, Jingwei Hu, Samuel Q. Van Fleet

{"title":"A Particle Method for the Multispecies Landau Equation","authors":"José A. Carrillo, Jingwei Hu, Samuel Q. Van Fleet","doi":"10.1007/s10440-024-00692-9","DOIUrl":"10.1007/s10440-024-00692-9","url":null,"abstract":"<div><p>The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00692-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453086","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

Compressed Sensing with Frames and Sparsity in Levels Class 用帧和稀疏度对等级进行压缩传感

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-17 DOI: 10.1007/s10440-024-00684-9

Chol-Guk Choe, Chol-Song Rim

引用次数: 0

Remarks on the Anisotropic Liouville Theorem for the Stationary Tropical Climate Model 关于固定热带气候模式的各向异性柳维尔定理的评论

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-17 DOI: 10.1007/s10440-024-00691-w

Huiting Ding, Fan Wu

引用次数: 0

Asymptotic Study of a Singular Time-Dependent Brinkman Flow with Application 奇异时变布林克曼流的渐近研究及应用

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-17 DOI: 10.1007/s10440-024-00689-4

Fatma Boumiza, Jamel Ferchichi, Houcine Meftahi

{"title":"Asymptotic Study of a Singular Time-Dependent Brinkman Flow with Application","authors":"Fatma Boumiza, Jamel Ferchichi, Houcine Meftahi","doi":"10.1007/s10440-024-00689-4","DOIUrl":"10.1007/s10440-024-00689-4","url":null,"abstract":"<div><p>In this article we address the problem of locating point forces within a time-dependent singular Brinkman flow. The context of the study is framed as an approximation of cerebrospinal fluid (CSF) around the central nervous system, with the point forces representing a model for the blood-brain barrier. We approach the problem by reformulating the identification task as an optimization problem, employing a tracking shape functional. A notable challenge in this study arises from the irregularity in the solution of the partial differential equation (PDE), which complicates the exploration of sensitivity analysis. To overcome this issue, we employ a relaxation method and compute the topological derivative of the cost function. The topological derivative, commonly used in shape optimization problems, offers insights into how the cost function responds to small perturbations in the domain. To determine the optimal position of the point forces, we employ a one-shot algorithm based on the derived topological gradient. Finally, we present numerical results that showcase the efficiency of our method in addressing the identified problem.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142443355","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

Characterization of Initial Layer for Fast Chemical Diffusion Limit in Keller-Segel System 凯勒-西格尔系统中快速化学扩散极限的初始层特征

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-16 DOI: 10.1007/s10440-024-00695-6

Min Li, Zhaoyin Xiang

引用次数: 0

Asymptotically Linear Euclidean Bosonic Equations 近似线性欧几里得玻色方程

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-15 DOI: 10.1007/s10440-024-00693-8

Cuicui Long, Jinggang Tan, Aliang Xia

{"title":"Asymptotically Linear Euclidean Bosonic Equations","authors":"Cuicui Long, Jinggang Tan, Aliang Xia","doi":"10.1007/s10440-024-00693-8","DOIUrl":"10.1007/s10440-024-00693-8","url":null,"abstract":"<div><p>We investigate the following nonlinear bosonic equation on Euclidean space arising in string theory and cosmology: </p><div><div><span>$$ -Delta e^{-cDelta }u+mu=f(x,u),quad xin {mathbb{R}}^{n}, $$</span></div><div>\u0000 (P)\u0000 </div></div><p> where <span>(nge 3)</span>, <span>(m>0)</span>, <span>(c>0)</span> and <span>(frac{f(x,u)}{u})</span> tends to a positive function <span>(h(x))</span> independent of <span>(u)</span> as <span>(urightarrow +infty )</span>, <span>(e^{-cDelta })</span> is given by a power series with <span>(Delta )</span> is the Euclidean Laplace operator. Here, the nonlinear term <span>(f(x,u))</span> does not satisfy the usual condition: </p><div><div><span>$$ 0le F(x,u):=int _{0}^{u}f(x,t),dtle frac{1}{2+theta }f(x,u)u, $$</span></div><div>\u0000 (AR)\u0000 </div></div><p> for <span>(theta >0)</span> and <span>(|u|)</span> is large, which is important in using the mountain pass theorem, see Alves et al. (J. Differ. Equ. 323:229-252, 2022) and Corrêa et al. (J. Differ. Equ. 363:491-517, 2023). This paper is devoted to discuss how to use the mountain pass theorem to obtain the existence of nontrivial solution to problem (P) without the (AR) condition.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438848","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

Unveiling the Interplay Between Degree-Based Graph Invariants of a Graph and Its Random Subgraphs 揭示基于度的图不变式与随机子图之间的相互作用

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-10-14 DOI: 10.1007/s10440-024-00688-5

Mohammad Ali Hosseinzadeh

{"title":"Unveiling the Interplay Between Degree-Based Graph Invariants of a Graph and Its Random Subgraphs","authors":"Mohammad Ali Hosseinzadeh","doi":"10.1007/s10440-024-00688-5","DOIUrl":"10.1007/s10440-024-00688-5","url":null,"abstract":"<div><p>This paper investigates the significance of employing random subgraphs and analyzing the expected values of Zagreb ndices within chemical graphs. By examining smaller, representative subsets, we uncover valuable insights into the properties and characteristics of complex networks. The expected values of Zagreb indices serve as critical mathematical measures for quantifying the structural complexity of chemical graphs, providing essential information about connectivity and branching patterns within molecules. Our primary contribution includes deriving theoretical expressions for these indices and validating them through extensive computational experiments on fullerene graphs <span>(C_{20})</span> and <span>(C_{60})</span>. The results demonstrate that our theoretical predictions closely align with experimental findings, affirming the robustness of Zagreb indices in characterizing molecular structures. Additionally, our analysis of specific cases, such as complete graphs and complete bipartite graphs, is consistent with previous studies, further reinforcing our methodology. This research emphasizes the relevance of random subgraphs and expected values of Zagreb indices in advancing our understanding of molecular behavior and stability, with important implications for materials science and drug design.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434802","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