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Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach 多孔板中的热粘性流体在两块不透水的平行板之间的相对运动中流动：四阶段算法方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-09-03 DOI: 10.21136/am.2024.0144-23
Nalimela Pothanna, Podila Aparna, M. Pavankumar Reddy, R. Archana Reddy, M. Clement Joe Anand
{"title":"Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach","authors":"Nalimela Pothanna, Podila Aparna, M. Pavankumar Reddy, R. Archana Reddy, M. Clement Joe Anand","doi":"10.21136/am.2024.0144-23","DOIUrl":"https://doi.org/10.21136/am.2024.0144-23","url":null,"abstract":"<p>The problem of an approximate solution of thermo-viscous fluid flow in a porous slab bounded between two impermeable parallel plates in relative motion is examined in this paper. The two plates are kept at two different temperatures and the flow is generated by a constant pressure gradient together with the motion of one of the plates relative to the other. The velocity and temperature distributions have been obtained by a four-stage algorithm approach. It is worth mentioning that reverse effects are noticed on velocity and temperature distributions. These effects can be attributed to Darcy’s friction offered by the medium. The approximation results obtained in the present paper are in good agreement with the earlier numerical results of thermo-viscous fluid flows in plane geometry.</p>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176627","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
Exponential expressivity of ReLUk neural networks on Gevrey classes with point singularities 具有点奇异性的 Gevrey 类上 ReLUk 神经网络的指数表达能力
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-08-27 DOI: 10.21136/am.2024.0052-24
Joost A. A. Opschoor, Christoph Schwab
{"title":"Exponential expressivity of ReLUk neural networks on Gevrey classes with point singularities","authors":"Joost A. A. Opschoor, Christoph Schwab","doi":"10.21136/am.2024.0052-24","DOIUrl":"https://doi.org/10.21136/am.2024.0052-24","url":null,"abstract":"<p>We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains D ⊂ ℝ<sup>d</sup>, <i>d</i> = 2, 3. We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in D, comprising the countably-normed spaces of I. M. Babuska and B. Q. Guo.</p><p>As intermediate result, we prove that continuous, piecewise polynomial high order (“<i>p</i>-version”) finite elements with elementwise polynomial degree <i>p</i> ∈ ℕ on arbitrary, regular, simplicial partitions of polyhedral domains D ⊂ ℝ<sup><i>d</i></sup>, <i>d</i> ⩾ 2, can be <i>exactly emulated</i> by neural networks combining ReLU and ReLU<sup>2</sup> activations.</p><p>On shape-regular, simplicial partitions of polytopal domains D, both the number of neurons and the number of nonzero parameters are proportional to the number of degrees of freedom of the <i>hp</i> finite element space of I. M. Babuška and B. Q. Guo.</p>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176629","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
Geodesic metrics for RBF approximation of some physical quantities measured on sphere 对球面上测量的某些物理量进行 RBF 近似的测地度量
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-08-08 DOI: 10.21136/am.2024.0051-24
Karel Segeth
{"title":"Geodesic metrics for RBF approximation of some physical quantities measured on sphere","authors":"Karel Segeth","doi":"10.21136/am.2024.0051-24","DOIUrl":"https://doi.org/10.21136/am.2024.0051-24","url":null,"abstract":"<p>The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula.</p><p>We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general.</p>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176630","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
Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems 一类时间分数半变量不等式的弱可解性和数值分析，应用于摩擦接触问题
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-07-20 DOI: 10.21136/AM.2024.0190-23
Mustapha Bouallala
{"title":"Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems","authors":"Mustapha Bouallala","doi":"10.21136/AM.2024.0190-23","DOIUrl":"10.21136/AM.2024.0190-23","url":null,"abstract":"<div><p>We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional derivative. All these results are applied to the analysis and numerical approximations of a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The constitutive relation is modeled using the fractional Kelvin-Voigt law. The contact and friction are described by the subdifferential boundary conditions. The variational formulation of this problem leads to a fractional hemivariational inequality. The error estimates for this problem are derived. Finally, here’s a second concrete example to illustrate the application. We propose a frictional contact model that incorporates normal compliance and Coulomb friction to describe the quasi-static contact between a viscoelastic body and a solid foundation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141769364","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
A new diagonal quasi-Newton algorithm for unconstrained optimization problems 针对无约束优化问题的新对角准牛顿算法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-07-15 DOI: 10.21136/AM.2024.0045-24
Mahsa Nosrati, Keyvan Amini
{"title":"A new diagonal quasi-Newton algorithm for unconstrained optimization problems","authors":"Mahsa Nosrati,&nbsp;Keyvan Amini","doi":"10.21136/AM.2024.0045-24","DOIUrl":"10.21136/AM.2024.0045-24","url":null,"abstract":"<div><p>We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141648673","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
Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors 双极半导体简化量子能量传输模型的半经典极限
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-07-15 DOI: 10.21136/AM.2024.0016-24
Sungjin Ra, Choljin Jang, Jinmyong Hong
{"title":"Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors","authors":"Sungjin Ra,&nbsp;Choljin Jang,&nbsp;Jinmyong Hong","doi":"10.21136/AM.2024.0016-24","DOIUrl":"10.21136/AM.2024.0016-24","url":null,"abstract":"<div><p>We are concerned with a simplified quantum energy-transport model for bipolar semiconductors, which consists of nonlinear parabolic fourth-order equations for the electron and hole density; degenerate elliptic heat equations for the electron and hole temperature; and Poisson equation for the electric potential. For the periodic boundary value problem in the torus <span>(mathbb{T}^{d})</span>, the global existence of weak solutions is proved, based on a time-discretization, an entropy-type estimate, and a fixed-point argument. Furthermore, the semiclassical limit is obtained by using a priori estimates independent of the scaled Planck constant.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141646715","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
Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations 一维扩散方程和三阶波方程的谱体积法超收敛性分析
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-06-27 DOI: 10.21136/am.2024.0235-23
Xu Yin, Waixiang Cao, Zhimin Zhang
{"title":"Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations","authors":"Xu Yin, Waixiang Cao, Zhimin Zhang","doi":"10.21136/am.2024.0235-23","DOIUrl":"https://doi.org/10.21136/am.2024.0235-23","url":null,"abstract":"<p>We present a unified approach to studying the superconvergence property of the spectral volume (SV) method for high-order time-dependent partial differential equations using the local discontinuous Galerkin formulation. We choose the diffusion and third-order wave equations as our models to illustrate approach and the main idea. The SV scheme is designed with control volumes constructed using the Gauss points or Radau points in subintervals of the underlying meshes, which leads to two SV schemes referred to as GSV and RSV schemes, respectively. With a careful choice of numerical fluxes, we demonstrate that the schemes are stable and exhibit optimal error estimates. Furthermore, we establish superconvergence of the GSV and RSV for the solution itself and the auxiliary variables. To be more precise, we prove that the errors of numerical fluxes at nodes and for the cell averages are superconvergent with orders of <span>(cal{O}(h^{2k+1}))</span> and <span>(cal{O}(h^{2k}))</span> for RSV and GSV, respectively. Superconvergence for the function value and derivative value approximations is also studied and the superconvergence points are identified at Gauss points and Radau points. Numerical experiments are presented to illustrate theoretical findings.</p>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141769365","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
A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration 用于无约束优化的修正弗莱彻-里维斯共轭梯度法在图像复原中的应用
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-06-07 DOI: 10.21136/AM.2024.0009-24
Zainab Hassan Ahmed, Mohamed Hbaib, Khalil K. Abbo
{"title":"A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration","authors":"Zainab Hassan Ahmed,&nbsp;Mohamed Hbaib,&nbsp;Khalil K. Abbo","doi":"10.21136/AM.2024.0009-24","DOIUrl":"10.21136/AM.2024.0009-24","url":null,"abstract":"<div><p>The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named “HZF” and “THZF”, preserve the descent property of the FR method while mitigating the drawbacks. The algorithms incorporate strong Wolfe line search conditions to ensure effective convergence. Through numerical comparisons with other conjugate gradient algorithms, our modified approach demonstrates superior performance. The results highlight the improved efficacy of the HZF algorithm compared to the FR and three-term FR conjugate gradient methods. The new algorithm was applied to the problem of image restoration and proved to be highly effective in image restoration compared to other algorithms.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141374192","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
Maxwell-Schrödinger equations in singular electromagnetic field 奇异电磁场中的麦克斯韦-薛定谔方程
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-05-31 DOI: 10.21136/AM.2024.0180-23
Qihong Shi, Yaqian Jia, Jianwei Yang
{"title":"Maxwell-Schrödinger equations in singular electromagnetic field","authors":"Qihong Shi,&nbsp;Yaqian Jia,&nbsp;Jianwei Yang","doi":"10.21136/AM.2024.0180-23","DOIUrl":"10.21136/AM.2024.0180-23","url":null,"abstract":"<div><p>We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness of the weak solutions to this system.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509880","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
Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media 导电介质中稳定麦克斯韦方程的能量规范误差估计和收敛分析
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-05-27 DOI: 10.21136/AM.2024.0248-23
Eric Lindström, Larisa Beilina
{"title":"Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media","authors":"Eric Lindström,&nbsp;Larisa Beilina","doi":"10.21136/AM.2024.0248-23","DOIUrl":"10.21136/AM.2024.0248-23","url":null,"abstract":"<div><p>The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0248-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509879","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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