Proceedings. Mathematical, physical, and engineering sciences最新文献_第2页

A new approach to integrable evolution equations on the circle. 圆上可积演化方程的一种新方法。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-06 DOI: 10.1098/rspa.2020.0605

A S Fokas, J Lenells

引用次数: 11

First-order convergence of Milstein schemes for McKean-Vlasov equations and interacting particle systems. McKean-Vlasov方程和相互作用粒子系统的Milstein格式的一阶收敛性。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-06 DOI: 10.1098/rspa.2020.0258

Jianhai Bao, Christoph Reisinger, Panpan Ren, Wolfgang Stockinger

引用次数: 28

Granular size segregation in silos with and without inserts. 在有或没有插入物的筒仓中粒度分离。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-20 DOI: 10.1098/rspa.2020.0242

A Cliff, L A Fullard, E C P Breard, J Dufek, C E Davies

{"title":"Granular size segregation in silos with and without inserts.","authors":"A Cliff, L A Fullard, E C P Breard, J Dufek, C E Davies","doi":"10.1098/rspa.2020.0242","DOIUrl":"https://doi.org/10.1098/rspa.2020.0242","url":null,"abstract":"The storage of granular materials is a critical process in industry, which has driven research into flow in silos. Varying material properties, such as particle size, can cause segregation of mixtures. This work seeks to elucidate the effects of size differences and determine how using a flow-correcting insert mitigates segregation during silo discharge. A rotating table was used to collect mustard seeds discharged from a three-dimensional (3D)-printed silo. This was loaded with bidisperse mixtures of varying proportions. A 3D-printed biconical insert was suspended near the hopper exit to assess its effect on the flow. Samples were analysed to determine the mass fractions of small particle species. The experiments without the insert resulted in patterns consistent with segregation. Introducing the insert into the silo eliminated the observed segregation during discharge. Discrete element method simulations of silo discharge were performed with and without the insert. These results mirrored the physical experiment and, when complimented with coarse graining analysis, explained the effect of the insert. Most of the segregation occurs at the grain-air free surface and is driven by large velocity gradients. In the silo with an insert, the velocity gradient at the free surface is greatly reduced, hence, so is the degree of segregation.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200242"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897646/pdf/rspa20200242.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414293","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: 3

Nonlinear viscoelasticity of strain rate type: an overview. 应变率型非线性粘弹性:综述。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2020.0715

Yasemin Şengül

{"title":"Nonlinear viscoelasticity of strain rate type: an overview.","authors":"Yasemin Şengül","doi":"10.1098/rspa.2020.0715","DOIUrl":"https://doi.org/10.1098/rspa.2020.0715","url":null,"abstract":"There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200715"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897644/pdf/rspa20200715.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25407097","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

A super Degasperis-Procesi equation and related integrable systems. 一类超Degasperis-Procesi方程及相关可积系统。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2020.0780

Binfang Gao, Kai Tian, Qing Ping Liu

引用次数: 3

Topological mode switching in modulated structures with dynamic encircling of an exceptional point. 具有异常点动态环绕的调制结构拓扑模式切换。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2020.0766

Linlin Geng, Weixuan Zhang, Xiangdong Zhang, Xiaoming Zhou

{"title":"Topological mode switching in modulated structures with dynamic encircling of an exceptional point.","authors":"Linlin Geng, Weixuan Zhang, Xiangdong Zhang, Xiaoming Zhou","doi":"10.1098/rspa.2020.0766","DOIUrl":"https://doi.org/10.1098/rspa.2020.0766","url":null,"abstract":"Exceptional points are special degeneracies occurring in non-Hermitian systems at which both eigenfrequencies and eigenmodes coalesce simultaneously. Fascinating phenomena, including topological, non-reciprocal and chiral energy transfer between normal modes, have been envisioned in optical and photonic systems with the exceptional point dynamically encircled in the parameter space. However, it has remained an open question of whether and how topological mode switching relying on exceptional points could be achieved in mechanical systems. The present paper studies a two-mode mechanical system with an exceptional point and implements the dynamic encircling of such a point using dynamic modulation mechanisms with time-driven elasticity and viscosity. Topological mode switching with robustness against the input state and loop trajectories has been demonstrated numerically. It is found that the dynamical encircling of an exceptional point with the starting point near the symmetric phase leads to chiral mode transfer controlled mainly by the encircling direction, while non-chiral dynamics is observed for the starting point near the broken phase. Analyses also show that minor energy input is required in the process of encircling the exceptional point, demonstrating the intrinsically motivated behaviour of topological mode switching.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200766"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897639/pdf/rspa20200766.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414762","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: 8

A stable, unified model for resonant Faraday cages. 谐振法拉第笼的稳定统一模型。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2020.0668

B Delourme, E Lunéville, J-J Marigo, A Maurel, J-F Mercier, K Pham

{"title":"A stable, unified model for resonant Faraday cages.","authors":"B Delourme, E Lunéville, J-J Marigo, A Maurel, J-F Mercier, K Pham","doi":"10.1098/rspa.2020.0668","DOIUrl":"https://doi.org/10.1098/rspa.2020.0668","url":null,"abstract":"We study some effective transmission conditions able to reproduce the effect of a periodic array of Dirichlet wires on wave propagation, in particular when the array delimits an acoustic Faraday cage able to resonate. In the study of Hewett & Hewitt (2016 Proc. R. Soc. A 472, 20160062 (doi:10.1098/rspa.2016.0062)) different transmission conditions emerge from the asymptotic analysis whose validity depends on the frequency, specifically the distance to a resonance frequency of the cage. In practice, dealing with such conditions is difficult, especially if the problem is set in the time domain. In the present study, we demonstrate the validity of a simpler unified model derived in Marigo & Maurel (2016 Proc. R. Soc. A 472, 20160068 (doi:10.1098/rspa.2016.0068)), where unified means valid whatever the distance to the resonance frequencies. The effectiveness of the model is discussed in the harmonic regime owing to explicit solutions. It is also exemplified in the time domain, where a formulation guaranteeing the stability of the numerical scheme has been implemented.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200668"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897637/pdf/rspa20200668.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414759","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: 4

Numerical calculation of N-periodic wave solutions to coupled KdV-Toda-type equations. 耦合kdv - toda型方程n周期波解的数值计算。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-13 DOI: 10.1098/rspa.2020.0752

Yingnan Zhang, Xingbiao Hu, Jianqing Sun

引用次数: 2

Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states. 通过LSTM神经网络学习函数预测极端海况下船舶动态。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2019.0897

J Del Águila Ferrandis, M S Triantafyllou, C Chryssostomidis, G E Karniadakis

{"title":"Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states.","authors":"J Del Águila Ferrandis, M S Triantafyllou, C Chryssostomidis, G E Karniadakis","doi":"10.1098/rspa.2019.0897","DOIUrl":"https://doi.org/10.1098/rspa.2019.0897","url":null,"abstract":"Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. IEEE Trans. Neural Netw. 4, 910-918 (doi:10.1109/72.286886)), and it is the first implementation of such theory to realistic engineering problems.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20190897"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897645/pdf/rspa20190897.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414292","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: 40

The Polycentric Dynamics of Melbourne and Sydney: suburb attractiveness divides a city at the home ownership level. 墨尔本和悉尼的多中心动态:郊区吸引力在住房拥有率水平上划分城市。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2020.0514

Emanuele Crosato, Mikhail Prokopenko, Michael S Harré

{"title":"The Polycentric Dynamics of Melbourne and Sydney: suburb attractiveness divides a city at the home ownership level.","authors":"Emanuele Crosato, Mikhail Prokopenko, Michael S Harré","doi":"10.1098/rspa.2020.0514","DOIUrl":"https://doi.org/10.1098/rspa.2020.0514","url":null,"abstract":"Urban dynamics in large metropolitan areas result from complex interactions across social, economic and political factors, including population distribution, flows of wealth and infrastructure requirements. We develop a Census-calibrated model of urban dynamics for the Greater Sydney and Melbourne areas for 2011 and 2016, highlighting the evolution of population distributions and the housing market structure in these two cities in terms of their mortgage and rent distributions. We show that there is a tendency to homophily between renters and mortgage holders: renters tend to cluster nearer commercial centres, whereas mortgagors tend to populate the outskirts of these centres. We also identify a critical threshold at which the long-term evolution of these two cities will bifurcate between a 'sprawling' and a 'polycentric' configuration, showing that both cities lie on the polycentric side of the critical point in the long-run. Importantly, there is a divergence of these centric tendencies between the renters and mortgage holders. The polycentric patterns characterizing the mortgagors are focused around commercial centres, and we show that the emergent housing patterns follow the major transport routes through the cities.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200514"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897640/pdf/rspa20200514.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414758","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