Philosophical Transactions of the Royal Society A最新文献_第10页

Living with Ramanujan for 40 years 和拉马努金一起生活了40年

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-09 DOI: 10.1098/rsta.2018.0437

B. Berndt

{"title":"Living with Ramanujan for 40 years","authors":"B. Berndt","doi":"10.1098/rsta.2018.0437","DOIUrl":"https://doi.org/10.1098/rsta.2018.0437","url":null,"abstract":"As was customary at that time, Srinivasa Ramanujan was born in the home of his maternal grandparents on 22 December 1887 in the south Indian town of Erode. After a few months, his mother brought him home to Kumbakonam (figure 1), approximately 120 miles east of Erode and 160 miles south-southwest of Madras (now Chennai). A brother, sister and brother were born in 1889, 1891 and 1894, respectively, but each died within a few months of birth. The two surviving younger brothers (1898–1946; 1905–1978) wrote an interesting but somewhat disconnected account of Ramanujan’s life that contains personal information that we would not have known otherwise [1]. At the time of Ramanujan’s birth, Kumbakonam had a population of about 53 000. The family was quite poor; Ramanujan’s father worked for 20 rupees a month as a clerk for a cloth merchant in Kumbakonam, and his mother took in student boarders from the local high school and government college. Ramanujan’s family home was small and humble, much like the other houses on the dirt street in front of their home. It had essentially one room flanked by a very small kitchen at the back of the home and a small storage room at the front. When the author visited the home in 1984, the only visible sign that this was once the home of the most famous mathematician in Indian history was a picture of Ramanujan cut from a newspaper and taped above the home’s entrance behind a small porch in front of the home. Although the author did not ask how many lived in the home, it appeared to him that a set of grandparents, two parents and seven children lived there. Facing Ramanujan’s home and turning to the left, one sees the famous Sarangapani Temple only about two blocks away. Kumbakonam is famous for its many temples. Ramanujan’s home has now been converted into a museum dedicated to the memory of Ramanujan.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83702880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

First-principle description of acoustic radiation of shear flows 剪切流声辐射的第一性原理描述

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-02 DOI: 10.1098/rsta.2019.0077

Xuesong Wu, Zhongyu Zhang

{"title":"First-principle description of acoustic radiation of shear flows","authors":"Xuesong Wu, Zhongyu Zhang","doi":"10.1098/rsta.2019.0077","DOIUrl":"https://doi.org/10.1098/rsta.2019.0077","url":null,"abstract":"As a methodology complementary to acoustic analogy, the asymptotic approach to aeroacoustics seeks to predict aerodynamical noise on the basis of first principles by probing into the physical processes of acoustic radiation. The present paper highlights the principal ideas and recent developments of this approach, which have shed light on some of the fundamental issues in sound generation in shear flows. The theoretical work on sound wave emission by nonlinearly modulated wavepackets of supersonic and subsonic instability modes in free shear flows identifies the respective physical sources or emitters. A wavepacket of supersonic modes is itself an efficient emitter, radiating directly intensive sound in the form of a Mach wave beam, the frequencies of which are in the same band as those of the modes in the packet. By contrast, a wavepacket of subsonic modes radiates very weak sound directly. However, the nonlinear self-interaction of such a wavepacket generates a slowly modulated mean-flow distortion, which then emits sound waves with low frequencies and long wavelengths on the scale of the wavepacket envelope. In both cases, the acoustic waves emitted to the far field are explicitly expressed in terms of the amplitude function of the wavepacket. The asymptotic approach has also been applied to analyse generation of sound waves in wall-bounded shear flows on the triple-deck scale. Several subtleties have been found. The near-field approximation has to be worked out to a sufficiently higher order in order just to calculate the far-field sound at leading order. The back action of the radiated sound on the flow in the viscous sublayer and the main shear layer is accounted for by an impedance coefficient. This effect is of higher order in the subsonic regime, but becomes a leading order in the transonic and supersonic regimes. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91027543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Strongly anisotropic surface elasticity and antiplane surface waves 强各向异性表面弹性和反平面表面波

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0100

V. Eremeyev

引用次数: 25

Fault-tolerant elastic–plastic lattice material 容错弹塑性点阵材料

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0107

M. Ryvkin, V. Slesarenko, A. Cherkaev, S. Rudykh

{"title":"Fault-tolerant elastic–plastic lattice material","authors":"M. Ryvkin, V. Slesarenko, A. Cherkaev, S. Rudykh","doi":"10.1098/rsta.2019.0107","DOIUrl":"https://doi.org/10.1098/rsta.2019.0107","url":null,"abstract":"The paper describes a fault-tolerant design of a special two-dimensional beam lattice. The morphology of such lattices was suggested in the theoretical papers (Cherkaev and Ryvkin 2019 Arch. Appl. Mech. 89, 485–501; Cherkaev and Ryvkin 2019 Arch. Appl. Mech. 89, 503–519), where its superior properties were found numerically. The proposed design consists of beam elements with two different thicknesses; the lattice is macro-isotropic and stretch dominated. Here, we experimentally verify the fault-tolerant properties of these lattices. The specimens were three-dimensional-printed from the VeroWhite elastoplastic material. The lattice is subjected to uniaxial tensile loading. Due to its morphology, the failed beams are evenly distributed in the lattice at the initial stage of damage; at this stage, the material remains intact, preserves its bearing ability, and supports relatively high strains before the final failure. At the initial phase of damage, the thinner beams buckle; then another group of separated thin beams plastically yield and rupture. The fatal macro-crack propagates after the distributed damage reaches a critical level. This initial distributed damage stage allows for a better energy absorption rate before the catastrophic failure of the structure. The experimental results are supported by simulations which confirm that the proposed fault-tolerant material possesses excellent energy absorption properties thanks to the distributed damage stage phenomenon. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81149415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

Internal resonances and relaxation memory kernels in composites 复合材料的内部共振和弛豫记忆核

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0106

E. Cherkaev

引用次数: 2

Applying an iterative method numerically to solve n × n matrix Wiener–Hopf equations with exponential factors 应用迭代法数值求解n × n矩阵指数因子Wiener-Hopf方程

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0241

Matthew J. Priddin, A. Kisil, Lorna J. Ayton

引用次数: 9

Equilibration of energies in a two-dimensional harmonic graphene lattice 二维谐波石墨烯晶格中的能量平衡

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0114

I. Berinskii, V. Kuzkin

{"title":"Equilibration of energies in a two-dimensional harmonic graphene lattice","authors":"I. Berinskii, V. Kuzkin","doi":"10.1098/rsta.2019.0114","DOIUrl":"https://doi.org/10.1098/rsta.2019.0114","url":null,"abstract":"We study dynamical phenomena in a harmonic graphene (honeycomb) lattice, consisting of equal particles connected by linear and angular springs. Equations of in-plane motion for the lattice are derived. Initial conditions typical for molecular dynamic modelling are considered. Particles have random initial velocities and zero displacements. In this case, the lattice is far from thermal equilibrium. In particular, initial kinetic and potential energies are not equal. Moreover, initial kinetic energies (and temperatures), corresponding to degrees of freedom of the unit cell, are generally different. The motion of particles leads to equilibration of kinetic and potential energies and redistribution of kinetic energy among degrees of freedom. During equilibration, the kinetic energy performs decaying high-frequency oscillations. We show that these oscillations are accurately described by an integral depending on dispersion relation and polarization matrix of the lattice. At large times, kinetic and potential energies tend to equal values. Kinetic energy is partially redistributed among degrees of freedom of the unit cell. Equilibrium distribution of the kinetic energies is accurately predicted by the non-equipartition theorem. Presented results may serve for better understanding of the approach to thermal equilibrium in graphene. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88193680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 15

Modelling strain localization in Ti–6Al–4V at high loading rate: a phenomenological approach 高加载速率下Ti-6Al-4V的应变局部化建模:一种现象学方法

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0105

R. Zhou, K. Pang, A. Bisht, A. Roy, S. Suwas, V. Silberschmidt

{"title":"Modelling strain localization in Ti–6Al–4V at high loading rate: a phenomenological approach","authors":"R. Zhou, K. Pang, A. Bisht, A. Roy, S. Suwas, V. Silberschmidt","doi":"10.1098/rsta.2019.0105","DOIUrl":"https://doi.org/10.1098/rsta.2019.0105","url":null,"abstract":"A phenomenological approach, based on a combination of a damage mechanism and a crystal plasticity model, is proposed to model a process of strain localization in Ti–6AI–4V at a high strain rate of 103 s−1. The proposed model is first calibrated employing a three-dimensional representative volume element model. The calibrated parameters are then employed to investigate the process of onset of strain localization in the studied material. A suitable mesh size is chosen for the proposed model by implementing a mesh-sensitivity study. The influence of boundary conditions on the initiation of the strain localization is also studied. A variation of crystallographic orientation in the studied material after the deformation process is characterized, based on results for different boundary conditions. The study reveals that the boundary conditions significantly influence the formation of shear bands as well as the variation of crystallographic orientation in the studied material. Results also indicate that the onset of strain localization can affect considerably the material's behaviour. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74496394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

One-way interfacial waves in a flexural plate with chiral double resonators 具有手性双谐振器的弯曲板中的单向界面波

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-25 DOI: 10.1098/rsta.2019.0350

G. Carta, D. Colquitt, A. Movchan, N. Movchan, I. Jones

{"title":"One-way interfacial waves in a flexural plate with chiral double resonators","authors":"G. Carta, D. Colquitt, A. Movchan, N. Movchan, I. Jones","doi":"10.1098/rsta.2019.0350","DOIUrl":"https://doi.org/10.1098/rsta.2019.0350","url":null,"abstract":"In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85440891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 15

Point mass dynamics on spherical hypersurfaces 球面超曲面上的点质量动力学

Philosophical Transactions of the Royal Society A Pub Date : 2019-11-18 DOI: 10.1098/rsta.2018.0349

D. Dritschel

引用次数: 1