IMA Journal of Applied Mathematics最新文献

The impact of confinement on the deformation of an elastic particle under axisymmetric tube flow 封闭对轴对称管流条件下弹性粒子变形的影响

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-09-18 DOI: 10.1093/imamat/hxae022

Simon M Finney, Matthew G Hennessy, Andreas Münch, Sarah L Waters

{"title":"The impact of confinement on the deformation of an elastic particle under axisymmetric tube flow","authors":"Simon M Finney, Matthew G Hennessy, Andreas Münch, Sarah L Waters","doi":"10.1093/imamat/hxae022","DOIUrl":"https://doi.org/10.1093/imamat/hxae022","url":null,"abstract":"We study an elastic particle translating axially along the centre-line of a rigid cylindrical tube filled with a Newtonian viscous fluid. The flow is pressure-driven and an axial body force is applied to the particle. We consider the regime in which the ratio of typical viscous fluid stress to elastic stiffness is small, leading to small elastic strains in the particle. In this case, there is a one-way decoupling of the fluid-structure interaction problem. The leading-order fluid problem is shown to be pressure-driven Stokes flow past a rigid sphere, and is solved using the semi-analytical method of reflections. The traction exerted by the fluid on the particle can be computed and used to formulate a pure solid-mechanics problem for the deformation of the particle, which can be solved analytically. This framework is used to investigate the role of the background flow, an axial body force, and the tube wall on the particle’s leading-order translational velocity, resulting deformation, and induced solid stress. By considering the first-order fluid problem the next-order correction to the translational velocity of the particle is shown to be zero. Depending on the magnitude of the ratio of applied body force to viscous forces, the particle can either have a bullet-like shape, an anti-bullet shape, or retain its original spherical shape. A non-linear arbitrary Lagrangian-Eulerian finite element implementation is used, in conjunction with various existing results from the literature, to validate the method of reflections solutions and interrogate their range of validity.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251247","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

On the P-Irreducibility of Quintic Positive Polynomials 论五次正多项式的 P-Irreducibility

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-08-18 DOI: 10.1093/imamat/hxae021

Takeo Kamizawa, Andrzej Jamiołkowski, Takashi Matsuoka, Noboru Watanabe

引用次数: 0

An explicit Maclaurin series solution to non-autonomous and non-homogeneous evolution equation, Omega Calculus, and associated applications 非自治和非均质演化方程的显式麦克劳林级数解、欧米茄微积分及相关应用

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-07-11 DOI: 10.1093/imamat/hxae020

Antônio Francisco Neto

{"title":"An explicit Maclaurin series solution to non-autonomous and non-homogeneous evolution equation, Omega Calculus, and associated applications","authors":"Antônio Francisco Neto","doi":"10.1093/imamat/hxae020","DOIUrl":"https://doi.org/10.1093/imamat/hxae020","url":null,"abstract":"We give a new Omega Calculus (a.k.a MacMahon’s Partition Analysis) based integral-free representation for the solution of a non-autonomous and non-homogeneous evolution equation. Our new representation generalizes some of the main results of the recent work of Francisco Neto (2024, A basis- and integral-free representation of time-dependent perturbation theory via the Omega matrix calculus. Ann. Inst. Henri Poincaré D, 11, 383) and Bassom et al. (2023, An explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation. Appl. Math. Lett., 139, 108537) and show that we can indeed compute the coefficients of the Maclaurin series solution associated with the evolution equation starting with the Peano-Baker series. Furthermore, we discuss in the context of our framework the inverse problem for homogeneous evolution equations in a Hilbert space answering a question left open by Bassom et al. in this case; that is, assuming the solution of the homogeneous evolution equation is a known analytic function the problem concerns the determination of the associated generator of the dynamics. Finally, in order to illustrate the versatility of our approach we explicitly determine the Maclaurin series solution related to the power series method in the context of the vibration problems for the non-uniform (tapered) Euler-Bernoulli beam and thus we explicitly solve the recursion relations considered by Adair and Jaeger (2018, A power series solution for rotating nonuniform Euler–Bernoulli cantilever beams. J. Vib. Control, 24, 3855-3864).","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614614","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

Can physics-informed neural networks beat the finite element method? 物理信息神经网络能否战胜有限元法？

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-05-23 DOI: 10.1093/imamat/hxae011

Tamara G Grossmann, Urszula Julia Komorowska, Jonas Latz, Carola-Bibane Schönlieb

{"title":"Can physics-informed neural networks beat the finite element method?","authors":"Tamara G Grossmann, Urszula Julia Komorowska, Jonas Latz, Carola-Bibane Schönlieb","doi":"10.1093/imamat/hxae011","DOIUrl":"https://doi.org/10.1093/imamat/hxae011","url":null,"abstract":"Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for instance, is a usual standard methodology to do so. The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of partial differential equations. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other. In this work, we compare the methodologies in a systematic computational study. Indeed, we employ both methods to numerically solve various linear and nonlinear partial differential equations: Poisson in 1D, 2D, and 3D, Allen–Cahn in 1D, semilinear Schrödinger in 1D and 2D. We then compare computational costs and approximation accuracies. In terms of solution time and accuracy, physics-informed neural networks have not been able to outperform the finite element method in our study. In some experiments, they were faster at evaluating the solved PDE.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141145861","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

Trust your source: quantifying source condition elements for variational regularisation methods 相信你的来源：量化变分正则化方法的来源条件要素

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-03-11 DOI: 10.1093/imamat/hxae008

Martin Benning, Tatiana A Bubba, Luca Ratti, Danilo Riccio

引用次数: 0

Global existence and boundedness in a two-species chemotaxis-fluid system with indirect pursuit-evasion interaction 具有间接追逐-逃避相互作用的双物种趋化-流体系统的全局存在性和有界性

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-03-03 DOI: 10.1093/imamat/hxae009

Chao Liu, Bin Liu

引用次数: 0

The comparison between effects of heterogeneous and homogeneous half-spaces underlying homogeneous layer on solitary Love waves 同质层下的异质半空间和同质半空间对孤爱波影响的比较

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-02-21 DOI: 10.1093/imamat/hxae007

Ekin Deliktas-Ozdemir

引用次数: 0

Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L2-Gradient Flows 可变形曲面上的切向张量场--如何推导一致的 L2 梯度流

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-02-19 DOI: 10.1093/imamat/hxae006

Ingo Nitschke, Souhayl Sadik, Axel Voigt

引用次数: 0

Learning a microlocal prior for limited-angle tomography 学习有限角度断层扫描的微局部先验

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-02-07 DOI: 10.1093/imamat/hxae005

Siiri Rautio, Rashmi Murthy, Tatiana A Bubba, Matti Lassas, Samuli Siltanen

引用次数: 0

The slow viscous flow around a general rectangular doubly-periodic arrays of infinite slender cylinders 无限细长圆柱体一般矩形双周期阵列周围的粘性慢流

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-02-01 DOI: 10.1093/imamat/hxae003

Lyndon Koens, Rohan Vernekar, Timm Krüger, Maciej Lisicki, David W Inglis

{"title":"The slow viscous flow around a general rectangular doubly-periodic arrays of infinite slender cylinders","authors":"Lyndon Koens, Rohan Vernekar, Timm Krüger, Maciej Lisicki, David W Inglis","doi":"10.1093/imamat/hxae003","DOIUrl":"https://doi.org/10.1093/imamat/hxae003","url":null,"abstract":"The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media and microfluidic arrays, this solution is important for many real-world systems. We asymptotically determine the flow around a general rectangular doubly-periodic array of infinite slender cylinders, extending the existing asymptotic solution for square arrays. The flow in the cell is represented by a collection of doubly-periodic, rapidly-convergent two-dimensional singularity solutions, and the boundary condition on the surface of the cylinder is solved asymptotically in powers of the cylinder radius. The asymptotic solution provides an easily computed closed-form estimate for the flow and forces as a function of the radius and the dimensions of the cell. The force is compared to results from lattice-Boltzmann simulations of low-Reynolds-number flows in the same geometry, and the accuracy of the no-slip condition on the surface of the cylinder, predicted by the asymptotic theory, is assessed. Finally, the behaviour of the flow, flux, force and effective permeability of the cell is investigated as a function of the geometric parameters. The structure of the asymptotic permeability is consistent with previous single-geometry predictions but provides a closed-form estimate for how the aspect ratio of the cell changes the leading-order behaviour. These models could be used to help understand the flows within porous systems composed of fibres and systems involving periodic arrays such as systems based on deterministic lateral displacement.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"29 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139661342","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