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A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori-Zwanzig formalism. 基于Mori-Zwanzig形式的非线性系统降阶模型记忆效应的先验估计。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2017-09-01 Epub Date: 2017-09-27 DOI: 10.1098/rspa.2017.0385
Ayoub Gouasmi, Eric J Parish, Karthik Duraisamy
{"title":"<i>A priori</i> estimation of memory effects in reduced-order models of nonlinear systems using the Mori-Zwanzig formalism.","authors":"Ayoub Gouasmi,&nbsp;Eric J Parish,&nbsp;Karthik Duraisamy","doi":"10.1098/rspa.2017.0385","DOIUrl":"https://doi.org/10.1098/rspa.2017.0385","url":null,"abstract":"<p><p>Reduced models of nonlinear dynamical systems require closure, or the modelling of the unresolved modes. The Mori-Zwanzig procedure can be used to derive formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the time history of the resolved variables. While this procedure does not reduce the complexity of the original system, these equations can serve as a mathematically consistent basis to develop closures based on memory approximations. In this scenario, knowledge of the memory kernel is paramount in assessing the validity of a memory approximation. Unravelling the memory kernel requires solving the orthogonal dynamics, which is a high-dimensional partial differential equation that is intractable, in general. A method to estimate the memory kernel <i>a priori</i>, using full-order solution snapshots, is proposed. The key idea is to solve a pseudo orthogonal dynamics equation, which has a convenient Liouville form, instead. This ersatz arises from the assumption that the semi-group of the orthogonal dynamics is a composition operator for one observable. The method is exact for linear systems. Numerical results on the Burgers and Kuramoto-Sivashinsky equations demonstrate that the proposed technique can provide valuable information about the memory kernel.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170385"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0385","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 52
The problem of camouflaging via mirror reflections. 通过镜子反射来伪装的问题。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2017-09-01 Epub Date: 2017-09-27 DOI: 10.1098/rspa.2017.0147
Alexander Plakhov
{"title":"The problem of camouflaging via mirror reflections.","authors":"Alexander Plakhov","doi":"10.1098/rspa.2017.0147","DOIUrl":"https://doi.org/10.1098/rspa.2017.0147","url":null,"abstract":"<p><p>This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is, therefore, natural to search for bodies that are, in a sense, close to invisible. We introduce a <i>visibility index</i> of a body measuring the mean angle of deviation of incident light rays, and derive a lower estimate for this index. This estimate is a function of the body's volume and of the minimal radius of a ball containing the body. This result is far from being final and opens a possibility for further research.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170147"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0147","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35581890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Homogenized boundary conditions and resonance effects in Faraday cages. 法拉第笼中的均匀边界条件和共振效应。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2016.0062
D P Hewett, I J Hewitt
{"title":"Homogenized boundary conditions and resonance effects in Faraday cages.","authors":"D P Hewett,&nbsp;I J Hewitt","doi":"10.1098/rspa.2016.0062","DOIUrl":"https://doi.org/10.1098/rspa.2016.0062","url":null,"abstract":"<p><p>We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called 'Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20160062"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2016.0062","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34624490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids. 非稀软复合固体的表面张力和Mori-Tanaka理论。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2015.0853
Francesco Mancarella, Robert W Style, John S Wettlaufer
{"title":"Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids.","authors":"Francesco Mancarella,&nbsp;Robert W Style,&nbsp;John S Wettlaufer","doi":"10.1098/rspa.2015.0853","DOIUrl":"https://doi.org/10.1098/rspa.2015.0853","url":null,"abstract":"<p><p>Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, <i>R</i>, to an elastocapillary lengthscale, <i>L</i>. Interfacial tension substantially impacts the effective elastic moduli of the composite when [Formula: see text]. When <i>R</i><3<i>L</i>/2 (<i>R</i>=3<i>L</i>/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20150853"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2015.0853","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34562164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
The pulsating orb: solving the wave equation outside a ball. 脉动球:解球外的波动方程。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2016.0037
P A Martin
{"title":"The pulsating orb: solving the wave equation outside a ball.","authors":"P A Martin","doi":"10.1098/rspa.2016.0037","DOIUrl":"https://doi.org/10.1098/rspa.2016.0037","url":null,"abstract":"<p><p>Transient acoustic waves are generated by the oscillations of an object or are scattered by the object. This leads to initial-boundary value problems (IBVPs) for the wave equation. Basic properties of this equation are reviewed, with emphasis on characteristics, wavefronts and compatibility conditions. IBVPs are formulated and their properties reviewed, with emphasis on weak solutions and the constraints imposed by the underlying continuum mechanics. The use of the Laplace transform to treat the IBVPs is also reviewed, with emphasis on situations where the solution is discontinuous across wavefronts. All these notions are made explicit by solving simple IBVPs for a sphere in some detail.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20160037"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2016.0037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34624488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Submesoscale currents in the ocean. 海洋中的亚中尺度洋流。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2016.0117
James C McWilliams
{"title":"Submesoscale currents in the ocean.","authors":"James C McWilliams","doi":"10.1098/rspa.2016.0117","DOIUrl":"https://doi.org/10.1098/rspa.2016.0117","url":null,"abstract":"<p><p>This article is a perspective on the recently discovered realm of submesoscale currents in the ocean. They are intermediate-scale flow structures in the form of density fronts and filaments, topographic wakes and persistent coherent vortices at the surface and throughout the interior. They are created from mesoscale eddies and strong currents, and they provide a dynamical conduit for energy transfer towards microscale dissipation and diapycnal mixing. Consideration is given to their generation mechanisms, instabilities, life cycles, disruption of approximately diagnostic force balance (e.g. geostrophy), turbulent cascades, internal-wave interactions, and transport and dispersion of materials. At a fundamental level, more questions remain than answers, implicating a programme for further research.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20160117"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2016.0117","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34624493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 611
Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method. 基于边缘单元的三维电磁波拓扑优化有限元方法。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2015.0835
Yongbo Deng, Jan G Korvink
{"title":"Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.","authors":"Yongbo Deng,&nbsp;Jan G Korvink","doi":"10.1098/rspa.2015.0835","DOIUrl":"https://doi.org/10.1098/rspa.2015.0835","url":null,"abstract":"<p><p>This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20150835"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2015.0835","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34562163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 36
Extended non-local games and monogamy-of-entanglement games. 扩展非局部博弈和纠缠一夫一妻制博弈。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2016.0003
Nathaniel Johnston, Rajat Mittal, Vincent Russo, John Watrous
{"title":"Extended non-local games and monogamy-of-entanglement games.","authors":"Nathaniel Johnston,&nbsp;Rajat Mittal,&nbsp;Vincent Russo,&nbsp;John Watrous","doi":"10.1098/rspa.2016.0003","DOIUrl":"https://doi.org/10.1098/rspa.2016.0003","url":null,"abstract":"<p><p>We study a generalization of non-local games-which we call <i>extended non-local games</i>-in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on the outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the <i>monogamy-of-entanglement</i> games introduced by Tomamichel, Fehr, Kaniewski and Wehner, which they also generalize. We prove that a natural extension of the Navascués-Pironio-Acín hierarchy of semidefinite programmes converges to the optimal commuting measurement value of extended non-local games, and we prove two extensions of results of Tomamichel <i>et al.</i> concerning monogamy-of-entanglement games.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20160003"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2016.0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34624486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Proteins as templates for complex synthetic metalloclusters: towards biologically programmed heterogeneous catalysis. 蛋白质作为复杂合成金属簇的模板:迈向生物编程的异质催化。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2016.0078
Charlie Fehl, Benjamin G Davis
{"title":"Proteins as templates for complex synthetic metalloclusters: towards biologically programmed heterogeneous catalysis.","authors":"Charlie Fehl,&nbsp;Benjamin G Davis","doi":"10.1098/rspa.2016.0078","DOIUrl":"https://doi.org/10.1098/rspa.2016.0078","url":null,"abstract":"<p><p>Despite nature's prevalent use of metals as prosthetics to adapt or enhance the behaviour of proteins, our ability to programme such architectural organization remains underdeveloped. Multi-metal clusters buried in proteins underpin the most remarkable chemical transformations in nature, but we are not yet in a position to fully mimic or exploit such systems. With the advent of copious, relevant structural information, judicious mechanistic studies and the use of accessible computational methods in protein design coupled with new synthetic methods for building biomacromolecules, we can envisage a 'new dawn' that will allow us to build de novo metalloenzymes that move beyond mono-metal centres. In particular, we highlight the need for systems that approach the multi-centred clusters that have evolved to couple electron shuttling with catalysis. Such hybrids may be viewed as exciting mid-points between homogeneous and heterogeneous catalysts which also exploit the primary benefits of biocatalysis.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20160078"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2016.0078","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34624492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Nonlinear stability analysis of Darcy's flow with viscous heating. 粘性加热条件下达西流动的非线性稳定性分析。
IF 3.5
Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2016-05-01 DOI: 10.1098/rspa.2016.0036
Michele Celli, Leonardo S de B Alves, Antonio Barletta
{"title":"Nonlinear stability analysis of Darcy's flow with viscous heating.","authors":"Michele Celli,&nbsp;Leonardo S de B Alves,&nbsp;Antonio Barletta","doi":"10.1098/rspa.2016.0036","DOIUrl":"https://doi.org/10.1098/rspa.2016.0036","url":null,"abstract":"<p><p>The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20160036"},"PeriodicalIF":3.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2016.0036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34624487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
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