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

Three-manifold quantum invariants and mock theta functions 三流形量子不变量和模拟函数

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-09 DOI: 10.1098/rsta.2018.0439

Miranda C. N. Cheng, Francesca Ferrari, G. Sgroi

引用次数: 15

How Ramanujan may have discovered the mock theta functions 拉马努金是如何发现模拟函数的

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-09 DOI: 10.1098/rsta.2018.0436

G. Andrews

引用次数: 1

The Ramanujan conjecture and its applications 拉马努金猜想及其应用

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-09 DOI: 10.1098/rsta.2018.0441

Wen-Ching Winnie Li

引用次数: 6

Srinivasa Ramanujan: in celebration of the centenary of his election as FRS Srinivasa Ramanujan:庆祝他当选FRS一百周年

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-09 DOI: 10.1098/rsta.2019.0386

K. Ono

{"title":"Srinivasa Ramanujan: in celebration of the centenary of his election as FRS","authors":"K. Ono","doi":"10.1098/rsta.2019.0386","DOIUrl":"https://doi.org/10.1098/rsta.2019.0386","url":null,"abstract":"Srinivasa Ramanujan, the so-called Man Who Knew Infinity, was one of the most influential, as well as most enigmatic, mathematicians in the recent history of mathematics. With a letter written to G. H. Hardy in 1913, the impoverished Hindu college dropout, self-taught in mathematics, reaching for worlds beyond the shores of India, introduced himself to the history of science. He had spent his youth sitting on cool stone floors in the neighbourhood temple, surrounded by Hindu deities, his mind wandering the world of mathematics. After absorbing the mysterious equations in the letter, Hardy invited Ramanujan to study in England, an extraordinary offer for an Indian under colonial rule. Together they innovated vast tracts of mathematics, before Ramanujan returned to India in fragile health. Tragically, he died at 32 from a misdiagnosed illness, leaving behind three enigmatic notebooks. Ramanujan’s notebooks and research papers have continued to inspire developments in modern mathematics and physics. His formulae and observations now play central roles in fields extending well beyond the realm of pure mathematics. For these reasons, we felt the need to honour the legacy of this great man. To celebrate the centenary of Srinivasa Ramanujan’s election as a Fellow of the Royal Society,1 we organized a public discussion meeting at which leading scientists spoke about Ramanujan’s legacy to mathematics and science. This meeting was held on 15–16 October 2018 at Carlton House. Fifteen distinguished scientists spoke about Ramanujan’s mathematics and his extraordinary legacy across Computer Science, Electrical Engineering, Mathematics and Physics. They were:","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87107054","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

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":null,"pages":null},"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

Analysis of fan-stage gap-flow data to inform simulation of fan broadband noise. 分析风扇级间隙流量数据，为模拟风扇宽带噪声提供依据。

Philosophical Transactions of the Royal Society A Pub Date : 2019-12-02 Epub Date: 2019-10-14 DOI: 10.1098/rsta.2019.0080

Sheryl Grace, Ignacio Gonzalez-Martino, Damiano Casalino

{"title":"Analysis of fan-stage gap-flow data to inform simulation of fan broadband noise.","authors":"Sheryl Grace, Ignacio Gonzalez-Martino, Damiano Casalino","doi":"10.1098/rsta.2019.0080","DOIUrl":"10.1098/rsta.2019.0080","url":null,"abstract":"<p><p>Time-resolved simulations present a new opportunity for studying the disturbances responsible for the broadband interaction noise created by the fan stage. In this paper, two vane configurations from the source diagnostic test at the approach rotor speed were computed with PowerFLOW's very large-eddy simulation (VLES) method using two solution strategies: a coarser mesh near the rotor and a trip to trigger turbulent transition on the rotor; and a much finer mesh near the rotor with no trip. The simulated data allow for an investigation of the potential effect from the vane configuration and an in-depth study of the mean and turbulent flow in the interstage gap. A challenge related to post-processing of high-resolution simulations is discussed. Comparison of the flow quantities with previously obtained Reynolds Averaged Navier-Stokes simulation results indicates that little advantage is gained by running a lattice Boltmann method (LBM)/VLES to simply recover the gap flow parameters for use with a lower-order fan broadband interaction noise calculation method. The true benefit of the LBM/VLES is that the noise calculation can be directly and simultaneously completed with the flow simulation. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.</p>","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6801395/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78782220","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: 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":null,"pages":null},"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":null,"pages":null},"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