Acta Applicandae Mathematicae最新文献

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, Jean-Guy Caputo, Ionut Danaila","doi":"10.1007/s10440-024-00701-x","DOIUrl":"10.1007/s10440-024-00701-x","url":null,"abstract":"<div>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 (omega )-gauge, where (omega ) is a non-negative real parameter. In this article, we study the influence of the gauge parameter (omega ) on the convergence of numerical simulations of the TDGL model using finite element schemes. A classical benchmark is first analysed for different values of (omega ) and artefacts are observed for lower values of (omega ). Then, we relate these observations with a systematic study of convergence orders in the unified (omega )-gauge framework. In particular, we show the existence of a tipping point value for (omega ), 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).</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

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

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, Y. Chiyo","doi":"10.1007/s10440-024-00699-2","DOIUrl":"10.1007/s10440-024-00699-2","url":null,"abstract":"<div>In this paper we consider radially symmetric solutions of the following parabolic-elliptic cross-diffusion system <div><div>$$ left { textstylebegin{array}{l} begin{aligned} &u_{t} = Delta u - nabla (u f(|nabla v|^{2} )nabla v), &0= Delta v -mu (t)+ g(u), quad mu (t)= frac{1}{|Omega |} int _{Omega } g(u(cdot , t))dx &u(x,0)= u_{0}(x), end{aligned} end{array}displaystyle right . $$</div></div> in (Omega times (0,infty )), with (Omega ) a ball in (mathbb{R}^{N}), (Ngeq 1) under homogeneous Neumann boundary conditions, (g(u)) a regular function with the prototype (g(u)= u^{k}), (ugeq 0), (k>0). The function (f(xi ) = k_{f} (1+ xi )^{-alpha }), (k_{f} >0), describes gradient-dependent limitation of cross diffusion fluxes. Under suitable conditions on the data, we prove that the solution is global in time. If (Ngeq 3), under conditions on (f), (g) and initial data, we prove that if the solution (u(x,t)) blows up in (L^{infty })-norm at finite time (T_{max}) then for some (p>1) it blows up also in (L^{p})-norm. Moreover a lower bound of blow-up time is derived.</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

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, Francisco de la Hoz","doi":"10.1007/s10440-024-00697-4","DOIUrl":"10.1007/s10440-024-00697-4","url":null,"abstract":"<div>When taking a regular planar polygon of (M) sides and length (2pi ) as the initial datum of the vortex filament equation, (mathbf{X}_{t}= mathbf{X}_{s}wedge mathbf{X}_{ss}), the solution becomes polygonal at times of the form (t_{pq} = (p/q)(2pi /M^{2})), with (gcd (p,q)=1), and the corresponding polygon has (Mq) sides, if (q) is odd, and (Mq/2) sides, if (q) is even. Moreover, that polygon is skew (except when (q = 1) or (q = 2), where the initial shape is recovered), and the angle (rho ) between two adjacent sides is a constant. In this paper, we give a rigorous proof of the conjecture that states that, at a time (t_{pq}), (cos ^{q}(rho /2) = cos (pi /M)), if (q) is odd, and (cos ^{q}(rho /2) = cos ^{2}(pi /M)), if (q) is even. Since the transition of one side of the polygon to the next one is given by a rotation in (mathbb{R}^{3}) 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 (2pi /M), which is equivalent to proving that some exponential sums with arithmetic content are purely imaginary.</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

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>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.</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/s10440-024-00692-9.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