发布求助
文献互助 智能选刊 最新文献

European Journal of Applied Mathematics最新文献

筛选
英文 中文
Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions 小参数非线性偏微分方程的两个近似对称框架:比较，关系，近似解
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-12-16 DOI: 10.1017/S0956792522000407
Mahmood R. Tarayrah, Brian Pitzel, A. Cheviakov
{"title":"Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions","authors":"Mahmood R. Tarayrah, Brian Pitzel, A. Cheviakov","doi":"10.1017/S0956792522000407","DOIUrl":"https://doi.org/10.1017/S0956792522000407","url":null,"abstract":"Abstract The frameworks of Baikov–Gazizov–Ibragimov (BGI) and Fushchich–Shtelen (FS) approximate symmetries are used to study symmetry properties of partial differential equations with a small parameter. In general, it is shown that unlike the case of ordinary differential equations (ODEs), unstable BGI point symmetries of unperturbed partial differential equations (PDEs) do not necessarily yield local approximate symmetries for the perturbed model. While some relations between the BGI and FS approaches can be established, the two methods yield different approximate symmetry classifications. Detailed classifications are presented for two nonlinear PDE families. The second family includes a one-dimensional wave equation describing the wave motion in a hyperelastic material with a single family of fibers. For this model, approximate symmetries can be used to compute approximate closed-form solutions. Wave breaking times are found numerically and using the approximate solutions, which yield comparable results.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"1017 - 1045"},"PeriodicalIF":1.9,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42174109","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: 1
Constant rank factorisations of smooth maps, with applications to sonar 光滑地图的常秩因子分解及其在声纳中的应用
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-12-01 DOI: 10.1017/s0956792522000365
Michael Robinson
{"title":"Constant rank factorisations of smooth maps, with applications to sonar","authors":"Michael Robinson","doi":"10.1017/s0956792522000365","DOIUrl":"https://doi.org/10.1017/s0956792522000365","url":null,"abstract":"\u0000 Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object’s shape and composition. Traditional synthetic aperture processing is highly effective in solving classification problems when the conditions are favourable but relies on accurate knowledge of the sensor’s trajectory relative to the object being measured. This article provides several new theoretical tools that decouple object classification performance from trajectory estimation in synthetic aperture sonar processing. The key insight is that decoupling the trajectory from classification-relevant information involves factoring a function into the composition of two functions. The article presents several new general topological invariants for smooth functions based on their factorisations over function composition. These invariants specialise to the case when a sonar platform trajectory is deformed by a non-small perturbation. The mathematical results exhibited in this article apply well beyond sonar classification problems. This article is written in a way that supports full mathematical generality.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43371338","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 modelling framework for efficient reduced order simulations of parametrised lithium-ion battery cells 参数化锂离子电池单元高效降阶模拟的建模框架
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-11-29 DOI: 10.1017/S0956792522000353
M. Landstorfer, Mario Ohlberger, S. Rave, M. Tacke
{"title":"A modelling framework for efficient reduced order simulations of parametrised lithium-ion battery cells","authors":"M. Landstorfer, Mario Ohlberger, S. Rave, M. Tacke","doi":"10.1017/S0956792522000353","DOIUrl":"https://doi.org/10.1017/S0956792522000353","url":null,"abstract":"Abstract In this contribution, we present a modelling and simulation framework for parametrised lithium-ion battery cells. We first derive a continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterised non-linear system of partial differential equations, the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modelling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modelling framework.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"554 - 591"},"PeriodicalIF":1.9,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49274262","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: 1
Exact nonclassical symmetry solutions of Lotka–Volterra-type population systems lotka - volterra型种群系统的精确非经典对称解
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-11-25 DOI: 10.1017/S095679252200033X
P. Broadbridge, R. Cherniha, J. Goard
{"title":"Exact nonclassical symmetry solutions of Lotka–Volterra-type population systems","authors":"P. Broadbridge, R. Cherniha, J. Goard","doi":"10.1017/S095679252200033X","DOIUrl":"https://doi.org/10.1017/S095679252200033X","url":null,"abstract":"Abstract New classes of conditionally integrable systems of nonlinear reaction–diffusion equations are introduced. They are obtained by extending a well-known nonclassical symmetry of a scalar partial differential equation to a vector equation. New exact solutions of nonlinear predator–prey systems with cross-diffusion are constructed. Infinite dimensional classes of exact solutions are made available for such nonlinear systems. Some of these solutions decay towards extinction and some oscillate or spiral around an interior fixed point. It is shown that the conditionally integrable systems are closely related to the standard diffusive Lotka–Volterra system, but they have additional features.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"998 - 1016"},"PeriodicalIF":1.9,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42441098","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: 2
Existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field 具有平均场的分数阶Ginzburg-Landau方程奇异模式的存在性和稳定性
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-11-11 DOI: 10.1017/s0956792522000286
Mingchen Gao, M. Winter, Wen Yang
{"title":"Existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field","authors":"Mingchen Gao, M. Winter, Wen Yang","doi":"10.1017/s0956792522000286","DOIUrl":"https://doi.org/10.1017/s0956792522000286","url":null,"abstract":"\u0000 In this paper, we consider the existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field. We prove the existence of three types of singular steady-state patterns (double fronts, single spikes, and double spikes) by solving their respective consistency conditions. In the case of single spikes, we prove the stability of single small spike solution for sufficiently large spatial period by studying an explicit non-local eigenvalue problem which is equivalent to the original eigenvalue problem. For the other solutions, we prove the instability by using the variational characterisation of eigenvalues. Finally, we present the results of some numerical computations of spike solutions based on the finite difference methods of Crank–Nicolson and Adams–Bashforth.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45218613","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 deterministic gradient-based approach to avoid saddle points 基于确定性梯度的避鞍点方法
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-11-09 DOI: 10.1017/s0956792522000316
L. M. Kreusser, S. J. Osher, B. Wang
{"title":"A deterministic gradient-based approach to avoid saddle points","authors":"L. M. Kreusser, S. J. Osher, B. Wang","doi":"10.1017/s0956792522000316","DOIUrl":"https://doi.org/10.1017/s0956792522000316","url":null,"abstract":"<p>Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230705121909977-0335:S0956792522000316:S0956792522000316_inline1.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$lfloor (n-1)/2rfloor$\u0000</span></span>\u0000</span>\u0000</span>, and hence it is significantly smaller than that of GD whose dimension is <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230705121909977-0335:S0956792522000316:S0956792522000316_inline2.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$n-1$\u0000</span></span>\u0000</span>\u0000</span>.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"22 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539587","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 deterministic gradient-based approach to avoid saddle points 基于确定性梯度的避鞍点方法
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-11-09 DOI: 10.1017/s0956792522000316
L. M. Kreusser, S. J. Osher, B. Wang
{"title":"A deterministic gradient-based approach to avoid saddle points","authors":"L. M. Kreusser, S. J. Osher, B. Wang","doi":"10.1017/s0956792522000316","DOIUrl":"https://doi.org/10.1017/s0956792522000316","url":null,"abstract":"<p>Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230705121909977-0335:S0956792522000316:S0956792522000316_inline1.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$lfloor (n-1)/2rfloor$\u0000</span></span>\u0000</span>\u0000</span>, and hence it is significantly smaller than that of GD whose dimension is <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230705121909977-0335:S0956792522000316:S0956792522000316_inline2.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$n-1$\u0000</span></span>\u0000</span>\u0000</span>.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"22 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539663","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
Time-dependent modelling of thin poroelastic films drying on deformable plates 多孔弹性薄膜在可变形板上干燥的时间相关模型
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-10-31 DOI: 10.1017/s0956792523000062
M. Hennessy, R. Craster, O. Matar
{"title":"Time-dependent modelling of thin poroelastic films drying on deformable plates","authors":"M. Hennessy, R. Craster, O. Matar","doi":"10.1017/s0956792523000062","DOIUrl":"https://doi.org/10.1017/s0956792523000062","url":null,"abstract":"\u0000 Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the film during drying are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Föppl-von Kármán (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from \u0000 \u0000 \u0000 \u0000$t$\u0000\u0000 \u0000 to \u0000 \u0000 \u0000 \u0000$t^{1/2}$\u0000\u0000 \u0000 , in agreement with experiments.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44569311","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
Modelling, simulation and optimisation of parabolic trough power plants 抛物线槽式电站的建模、仿真与优化
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-10-11 DOI: 10.1017/S0956792522000274
H. Bakhti, I. Gasser, Stefan Dipl.-Ing. Schuster, E. Parfenov
{"title":"Modelling, simulation and optimisation of parabolic trough power plants","authors":"H. Bakhti, I. Gasser, Stefan Dipl.-Ing. Schuster, E. Parfenov","doi":"10.1017/S0956792522000274","DOIUrl":"https://doi.org/10.1017/S0956792522000274","url":null,"abstract":"We present a mathematical model built to describe the fluid dynamics for the heat transfer fluid in a parabolic trough power plant. Such a power plant consists of a network of tubes for the heat transport fluid. In view of optimisation tasks in the planning and in the operational phase, it is crucial to find a compromise between a very detailed description of many possible physical phenomena and a necessary simplicity needed for a fast and robust computational approach. We present the model, a numerical approach, simulation for single tubes and also for realistic network settings. In addition, we optimise the power output with respect to the operational parameters.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"592 - 615"},"PeriodicalIF":1.9,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47570795","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
Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions 电磁学中的Friedlander-Keller射线展开：来自三维任意表面的单色辐射
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-10-10 DOI: 10.1017/s0956792522000249
A. Radjen, R. Tew, G. Gradoni
{"title":"Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions","authors":"A. Radjen, R. Tew, G. Gradoni","doi":"10.1017/s0956792522000249","DOIUrl":"https://doi.org/10.1017/s0956792522000249","url":null,"abstract":"The standard approach to applying ray theory to solving Maxwell’s equations in the large wave-number limit involves seeking solutions that have (i) an oscillatory exponential with a phase term that is linear in the wave-number and (ii) has an amplitude profile expressed in terms of inverse powers of that wave-number. The Friedlander–Keller modification includes an additional power of this wave-number in the phase of the wave structure, and this additional term is crucial when analysing certain wave phenomena such as creeping and whispering gallery wave propagation. However, other wave phenomena necessitate a generalisation of this theory. The purposes of this paper are to provide a ‘generalised’ Friedlander–Keller ray ansatz for Maxwell’s equations to obtain a new set of field equations for the various phase terms and amplitude of the wave structure; these are then solved subject to boundary data conforming to wave-fronts that are either specified or general. These examples specifically require this generalisation as they are not amenable to classic ray theory.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46519439","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信