European Journal of Applied Mathematics最新文献_第8页

On a class of nonlocal continuity equations on graphs 图上一类非局部连续性方程

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-09-30 DOI: 10.1017/S0956792523000128

A. Esposito, F. Patacchini, A. Schlichting

引用次数: 5

Characterising small objects in the regime between the eddy current model and wave propagation 描述小物体在涡流模型和波传播之间的状态

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-09-27 DOI: 10.1017/s0956792523000207

P. Ledger, W. Lionheart

{"title":"Characterising small objects in the regime between the eddy current model and wave propagation","authors":"P. Ledger, W. Lionheart","doi":"10.1017/s0956792523000207","DOIUrl":"https://doi.org/10.1017/s0956792523000207","url":null,"abstract":"\u0000 Being able to characterise objects at low frequencies, but in situations where the modelling error in the eddy current approximation of the Maxwell system becomes large, is important for improving current metal detection technologies. Importantly, the modelling error becomes large as the frequency increases, but the accuracy of the eddy current model also depends on the object topology and on its materials, with the error being much larger for certain geometries compared to others of the same size and materials. Additionally, the eddy current model breaks down at much smaller frequencies for highly magnetic conducting materials compared to non-permeable objects (with similar conductivities, sizes and shapes) and, hence, characterising small magnetic objects made of permeable materials using the eddy current at typical frequencies of operation for a metal detector is not always possible. To address this, we derive a new asymptotic expansion for permeable highly conducting objects that is valid for small objects and holds not only for frequencies where the eddy current model is valid but also for situations where the eddy current modelling error becomes large and applying the eddy approximation would be invalid. The leading-order term we derive leads to new forms of object characterisations in terms of polarizability tensor object descriptions where the coefficients can be obtained from solving vectorial transmission problems. We expect these new characterisations to be important when considering objects at greater stand-off distance from the coils, which is important for safety critical applications, such as the identification of landmines, unexploded ordnance and concealed weapons. We also expect our results to be important when characterising artefacts of archaeological and forensic significance at greater depths than the eddy current model allows and to have further applications parking sensors and improving the detection of hidden, out-of-sight, metallic objects.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42144949","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

Projective invariants of images 图像的投影不变量

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-09-26 DOI: 10.1017/S0956792522000298

P. Olver

引用次数: 1

Symmetry actions and brackets for adjoint-symmetries. II: Physical examples 伴随对称的对称作用和括号。II：物理示例

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-08-22 DOI: 10.1017/S0956792522000328

S. Anco

引用次数: 1

Convergence to a self-similar solution for a one-phase Stefan problem arising in corrosion theory 腐蚀理论中单相Stefan问题自相似解的收敛性

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-08-09 DOI: 10.1017/s0956792522000250

M. Bouguezzi, D. Hilhorst, Y. Miyamoto, J. Scheid

引用次数: 0

Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies 两个非均匀弹性体接触的赫兹和粘着平面模型

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-07-25 DOI: 10.1017/s0956792522000237

Y. Antipov, S. Mkhitaryan

{"title":"Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies","authors":"Y. Antipov, S. Mkhitaryan","doi":"10.1017/s0956792522000237","DOIUrl":"https://doi.org/10.1017/s0956792522000237","url":null,"abstract":"Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterised by the Young modulus varying with depth as a power function. This paper models Hertzian and adhesive contact of two elastic inhomogeneous power-law graded bodies with different exponents. The problem is governed by an integral equation with two different power kernels. A nonstandard method of Gegenbauer orthogonal polynomials for its solution is proposed. It leads to an infinite system of linear algebraic equations of a special structure. The integral representations of the system coefficients are evaluated, and the properties of the system are studied. It is shown that if the exponents coincide, the infinite system admits a simple exact solution that corresponds to the case when the Young moduli are different but the exponents are the same. Formulas for the length of the contact zone, the pressure distribution and the surface normal displacements of the contacting bodies are obtained in the form convenient for computations. Effects of the mismatch in the Young moduli exponents are studied. A comparative analysis of the Hertzian and adhesive contact models clarifies the effects of the surface energy density on the contact pressure, the contact zone size and the profile of the contacting bodies outside the contact area.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45831338","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

Profiling ponded soil surface in saturated seepage into drain-line sink: Kalashnikov’s method of lateral leaching revisited 在饱和渗流进入排水管水槽的情况下对积水土壤表面进行剖面分析：卡拉什尼科夫侧向浸出法的重新审视

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-07-12 DOI: 10.1017/s0956792522000171

A. Kacimov, Y. Obnosov

引用次数: 3

Resilient tracking consensus over dynamic random graphs: A linear system approach 动态随机图上的弹性跟踪一致性：一种线性系统方法

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-07-12 DOI: 10.1017/s0956792522000225

Y. Shang

引用次数: 8

Fluctuation response patterns of network dynamics – An introduction 网络动力学的波动响应模式——导论

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-07-11 DOI: 10.1017/S0956792522000201

Xiaozhu Zhang, M. Timme

{"title":"Fluctuation response patterns of network dynamics – An introduction","authors":"Xiaozhu Zhang, M. Timme","doi":"10.1017/S0956792522000201","DOIUrl":"https://doi.org/10.1017/S0956792522000201","url":null,"abstract":"Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to pandemics spreading across continents. Most of such systems are driven by irregular and distributed fluctuating input signals from the environment. Yet how networked dynamical systems collectively respond to such fluctuations depends on the location and type of driving signal, the interaction topology and several other factors and remains largely unknown to date. As a key example, modern electric power grids are undergoing a rapid and systematic transformation towards more sustainable systems, signified by high penetrations of renewable energy sources. These in turn introduce significant fluctuations in power input and thereby pose immediate challenges to the stable operation of power grid systems. How power grid systems dynamically respond to fluctuating power feed-in as well as other temporal changes is critical for ensuring a reliable operation of power grids yet not well understood. In this work, we systematically introduce a linear response theory (LRT) for fluctuation-driven networked dynamical systems. The derivations presented not only provide approximate analytical descriptions of the dynamical responses of networks, but more importantly, also allow to extract key qualitative features about spatio-temporally distributed response patterns. Specifically, we provide a general formulation of a LRT for perturbed networked dynamical systems, explicate how dynamic network response patterns arise from the solution of the linearised response dynamics, and emphasise the role of LRT in predicting and comprehending power grid responses on different temporal and spatial scales and to various types of disturbances. Understanding such patterns from a general, mathematical perspective enables to estimate network responses quickly and intuitively, and to develop guiding principles for, e.g., power grid operation, control and design.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"429 - 466"},"PeriodicalIF":1.9,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49595347","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

Integration of the modified double layer potential of the vector boundary element method for eddy current problems 涡电流问题的修正双层势矢量边界元积分法

IF 1.9 4区数学

European Journal of Applied Mathematics Pub Date : 2022-06-16 DOI: 10.1017/s0956792522000183

S. Sivak, I. Stupakov, M. Royak, S. Royak

{"title":"Integration of the modified double layer potential of the vector boundary element method for eddy current problems","authors":"S. Sivak, I. Stupakov, M. Royak, S. Royak","doi":"10.1017/s0956792522000183","DOIUrl":"https://doi.org/10.1017/s0956792522000183","url":null,"abstract":"The boundary element method for the eddy current problem (BEM-ECP) was proposed in a number of papers and is applicable to important tasks such as the problem of inductive heating and transmission of electromagnetic energy. BEM-ECP requires the construction of a system of linear algebraic equations in which the matrix is inherently dense and is constructed out of element matrices. For the process of the element matrix computation, two cases are normally considered: far-field interaction and near-field interaction, because the construction of element matrices requires integration of a singular function. In this article, we suggest a transform that allows computing the matrix components of the near-singular interaction part while implementing only the single and double layer potentials. The previously suggested modified double layer potential (MDLP) can be integrated by means of this transform, which simplifies the program implementation of BEM-ECP significantly. Solving model problems, we analyse the drawbacks of the previously suggested approach. This analysis includes the proof of the MDLP singularity that makes the integration of this potential a rather difficult task without the help of our transform. The previously suggested approach does not work well with surfaces that are not smooth. Our approach does consider such cases, which is its main advantage. We demonstrate this on the model problems with known analytical solutions.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45209602","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