{"title":"Scattering of water waves by an inclined porous plate submerged in ocean with ice cover","authors":"D. Mondal, S. Banerjea","doi":"10.1093/QJMAM/HBW004","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW004","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"195-213"},"PeriodicalIF":0.9,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analytical solutions for Hele-Shaw moving boundary flows in the presence of a circular cylinder","authors":"Jonathan S. Marshall","doi":"10.1093/QJMAM/HBV019","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV019","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"1-33"},"PeriodicalIF":0.9,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The first author’s work and the second author’s visit to Brunel University were partly supported by Brunel University’s ‘BRIEF’ award scheme.
第一作者的工作和第二作者对布鲁内尔大学的访问得到了布鲁内尔大学“BRIEF”奖励计划的部分支持。
{"title":"Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids","authors":"A. V. Pichugin, D. Prikazchikov","doi":"10.1093/QJMAM/HBV017","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV017","url":null,"abstract":"The first author’s work and the second author’s visit to Brunel University were partly supported by \u0000Brunel University’s ‘BRIEF’ award scheme.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"14 1","pages":"67-81"},"PeriodicalIF":0.9,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61240070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact solutions for Hele-Shaw free boundary flows around a flat plate of finite length","authors":"Jonathan S. Marshall","doi":"10.1093/QJMAM/HBV018","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV018","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"35-66"},"PeriodicalIF":0.9,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we address the phenomenon of temporal, self-sustained oscillations for a solid oxide fuel cell which utilises a humidified methane fuel stream. Our objective is to uncover the fundamental mechanisms giving rise to current oscillations that have been observed experimentally. To this end, we develop a model based on the fundamental chemical kinetics and transfer processes which take place within the fuel cell. This leads to a three-dimensional dynamical system, which, under typical operating conditions, is rationally reducible to a planar dynamical system. This planar dynamical system was studied in (Sands et al., Proc. R. Soc. Lond. A 470 (2014)) for the case where the parameter c̄0 1, corresponding with a weakly humidified fuel stream. In the present article, the structural dynamics of the planar dynamical system for the case where the parameter c̄0 = O(1), which corresponds with a humidified fuel stream, are studied in detail. Self-sustained oscillations are shown to arise through Hopf bifurcations in this planar dynamical system, and the key parameter ranges for the occurrence of such oscillations are identified. Fuel stream humidification is also shown to significantly alter the fuel cell dynamics, leading to hysteresis.
在这篇文章中，我们解决了一个固体氧化物燃料电池的时间，自我持续振荡的现象，它利用加湿甲烷燃料流。我们的目标是揭示引起电流振荡的基本机制，这些振荡是通过实验观察到的。为此，我们开发了一个基于燃料电池内发生的基本化学动力学和转移过程的模型。这导致了一个三维动力系统，在典型的操作条件下，可以合理地归结为一个平面动力系统。这种平面动力系统在(Sands et al.， Proc. R. Soc)中进行了研究。Lond。A 470(2014))的情况下，参数c′0′1，对应于弱加湿燃料流。在本文中，详细研究了参数c < 0 = O(1)的平面动力系统的结构动力学，这与加湿燃料流相对应。该平面动力系统通过Hopf分岔产生了自持续振荡，并确定了产生自持续振荡的关键参数范围。燃料流加湿也显示出显著改变燃料电池动力学，导致滞后。
{"title":"A fundamental model exhibiting non-linear oscillatory dynamics in solid oxide fuel cells—the effects of fuel stream humidification","authors":"J. Sands, J. Uddin, D. Needham","doi":"10.1093/QJMAM/HBV020","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV020","url":null,"abstract":"In this article, we address the phenomenon of temporal, self-sustained oscillations for a solid oxide fuel cell which utilises a humidified methane fuel stream. Our objective is to uncover the fundamental mechanisms giving rise to current oscillations that have been observed experimentally. To this end, we develop a model based on the fundamental chemical kinetics and transfer processes which take place within the fuel cell. This leads to a three-dimensional dynamical system, which, under typical operating conditions, is rationally reducible to a planar dynamical system. This planar dynamical system was studied in (Sands et al., Proc. R. Soc. Lond. A 470 (2014)) for the case where the parameter c̄0 1, corresponding with a weakly humidified fuel stream. In the present article, the structural dynamics of the planar dynamical system for the case where the parameter c̄0 = O(1), which corresponds with a humidified fuel stream, are studied in detail. Self-sustained oscillations are shown to arise through Hopf bifurcations in this planar dynamical system, and the key parameter ranges for the occurrence of such oscillations are identified. Fuel stream humidification is also shown to significantly alter the fuel cell dynamics, leading to hysteresis.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"83-113"},"PeriodicalIF":0.9,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generation of long waves by an oscillating line source above a flat beach of angle α=π/2M,M∈Z: the 3-d Case","authors":"U. Ehrenmark","doi":"10.1093/QJMAM/HBV015","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV015","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"421-460"},"PeriodicalIF":0.9,"publicationDate":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61240062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Maxwell concept of equivalent inhomogeneity is re-examined in the context of elastic composite, porous or micro-cracked materials of periodic structure. It is demonstrated that accurate estimates for the effective elastic properties can be obtained by the modified Maxwell approach that employs the proper shape of the equivalent inhomogeneity and explicitly accounts for the geometry of the cluster and for the interactions between its constituents. In addition, it is shown that regular polygonal and some other symmetric inhomogeneities possess ‘strange’and remarkable properties. Under the action of uniform far-field loads, the averages of certain combinations of stresses inside these inhomogeneities are constant and coincide with those for a circular inhomogeneity.
{"title":"The shape of Maxwell's equivalent inhomogeneity and ‘strange’ properties of regular polygons and other symmetric domains","authors":"S. Mogilevskaya, D. Nikolskiy","doi":"10.1093/QJMAM/HBV012","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV012","url":null,"abstract":"The Maxwell concept of equivalent inhomogeneity is re-examined in the context of elastic composite, porous or micro-cracked materials of periodic structure. It is demonstrated that accurate estimates for the effective elastic properties can be obtained by the modified Maxwell approach that employs the proper shape of the equivalent inhomogeneity and explicitly accounts for the geometry of the cluster and for the interactions between its constituents. In addition, it is shown that regular polygonal and some other symmetric inhomogeneities possess ‘strange’and remarkable properties. Under the action of uniform far-field loads, the averages of certain combinations of stresses inside these inhomogeneities are constant and coincide with those for a circular inhomogeneity.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"363-385"},"PeriodicalIF":0.9,"publicationDate":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass' quasiperodic functions for representation of the potential that considerably facilitates the problem and allows us to find an exact expression for the effective tensor. For weakly interacting tubes we obtain Maxwell-like approximation of the effective parameter which is in very good agreement with experimental results in considered examples.
{"title":"Effective properties of periodic tubular structures","authors":"Y. Godin","doi":"10.1093/qjmam/hbw003","DOIUrl":"https://doi.org/10.1093/qjmam/hbw003","url":null,"abstract":"A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass' quasiperodic functions for representation of the potential that considerably facilitates the problem and allows us to find an exact expression for the effective tensor. For weakly interacting tubes we obtain Maxwell-like approximation of the effective parameter which is in very good agreement with experimental results in considered examples.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"181-193"},"PeriodicalIF":0.9,"publicationDate":"2015-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbw003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary A three-dimensional deformation problem for articular cartilage layer is considered in the framework of the linear biphasic poroviscoelastic theory. The solid matrix of biphasic layer is assumed to be transversely isotropic. A short-time leading-order asymptotic solution is obtained for a relatively thin biphasic poroviscoelastic layer bonded to a rigid impermeable substrate.
{"title":"An asymptotic model for a thin biphasic poroviscoelastic layer","authors":"I. Argatov, Gennady Mishuris","doi":"10.1093/QJMAM/HBV008","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV008","url":null,"abstract":"Summary A three-dimensional deformation problem for articular cartilage layer is considered in the framework of the linear biphasic poroviscoelastic theory. The solid matrix of biphasic layer is assumed to be transversely isotropic. A short-time leading-order asymptotic solution is obtained for a relatively thin biphasic poroviscoelastic layer bonded to a rigid impermeable substrate.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"45 1","pages":"289-297"},"PeriodicalIF":0.9,"publicationDate":"2015-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of oblique wave scattering of a Rayleigh wave by a cylindrical cavity in an elastic half-space is solved using the multipole expansion method. Whereas in the analogous water-wave problem a single scalar field is expressed as an infinite multipole expansion, and in the Rayleigh wave case with normal incidence two scalar fields suffice, here we require three coupled scalar multipole expansions. The focus of our numerical results is on the energy scattered by the cavity and in particular the proportion of the incident wave energy that is reflected and transmitted in the form of Rayleigh waves and the proportion that is transformed into cylindrical bulk waves which propagate into the half-space.
{"title":"Oblique rayleigh wave scattering by a cylindrical cavity","authors":"C. Linton, I. Thompson","doi":"10.1093/QJMAM/HBV006","DOIUrl":"https://doi.org/10.1093/QJMAM/HBV006","url":null,"abstract":"The problem of oblique wave scattering of a Rayleigh wave by a cylindrical cavity\u0000in an elastic half-space is solved using the multipole expansion method. Whereas in the\u0000analogous water-wave problem a single scalar field is expressed as an infinite multipole\u0000expansion, and in the Rayleigh wave case with normal incidence two scalar fields suffice,\u0000here we require three coupled scalar multipole expansions. The focus of our numerical\u0000results is on the energy scattered by the cavity and in particular the proportion of the\u0000incident wave energy that is reflected and transmitted in the form of Rayleigh waves\u0000and the proportion that is transformed into cylindrical bulk waves which propagate\u0000into the half-space.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"68 1","pages":"235-261"},"PeriodicalIF":0.9,"publicationDate":"2015-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBV006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61239831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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