Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences最新文献

Plankton 浮游生物

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2019-11-11 DOI: 10.1525/abt.2016.78.1.80

R. Lord

引用次数: 0

Spectral concentrations and resonances of a second–order block operator matrix and an associated λ–rational Sturm-Liouville problem 二阶块算子矩阵的谱浓度和共振及相关的λ有理Sturm-Liouville问题

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2003.1272

B. M. Brown, M. Langer, M. Marletta

引用次数: 5

Rotational transformations of the sum of the squares of the flux Jacobians of the Navier–Stokes equations Navier-Stokes方程的通量雅可比矩阵平方和的旋转变换

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1365

Chittur S. Venkatasubban

{"title":"Rotational transformations of the sum of the squares of the flux Jacobians of the Navier–Stokes equations","authors":"Chittur S. Venkatasubban","doi":"10.1098/rspa.2004.1365","DOIUrl":"https://doi.org/10.1098/rspa.2004.1365","url":null,"abstract":"We report the discovery of a new mathematical identity for the Navier–Stokes equations, which model the flow of a viscous compressible gas. The identity relates the sum of the squares of the viscous flux Jacobians in rotated coordinate systems, and takes the form of a remarkably compact similarity transformation: ∑ i=1 3 A * i d =G{ ∑ i=1 3 A i d A i d } G T . The proof of an analogous relationship for the sum of the squares of the Euler flux Jacobians appeared in Venkatasubban (Proc. R. Soc. Lond. (2001) A457, 1111–1114). At that time, the extension to the Navier–Stokes equations was not evident, given that this requires a separate and detailed derivation. It may be remarked that these relationships possess an elegant simplicity that the flux Jacobians themselves do not have. In developing numerical algorithms for flow solvers based on the Navier–Stokes equations, it is often necessary or advantageous to work in a rotated coordinate frame. This relation thus has potential applications in the development of new and improved algorithms for Navier–Stokes computer codes used to solve industrial problems in aerodynamics and fluid dynamics.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":"33 1","pages":"3499 - 3503"},"PeriodicalIF":0.0,"publicationDate":"2004-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87106749","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

Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximation 轴对称体在水平面上旋转的动力学。稳定性和陀螺仪近似

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1329

H. K. Moffatt, Y. Shimomura, M. Branicki

{"title":"Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximation","authors":"H. K. Moffatt, Y. Shimomura, M. Branicki","doi":"10.1098/rspa.2004.1329","DOIUrl":"https://doi.org/10.1098/rspa.2004.1329","url":null,"abstract":"The general spinning motion of an axisymmetric rigid body on a horizontal table is analysed, allowing for slip and friction at the point of contact P. Attention is focused on the case of spheroids (prolate or oblate), and particularly on spheroids whose density distribution is such that the centre–of–mass and centre–of–volume coincide. Four classes of fixed points (i.e. steady states) are identified, and the linear stability properties in each case are determined, assuming viscous friction at P. The governing dynamical system is six–dimensional. Trajectories of the system are computed, and are shown in projection in a three–dimensional subspace; these start near unstable fixed points and (in the case of viscous friction) end at stable fixed points. It is shown inter alia that a uniform prolate spheroid set in sufficiently rapid spinning motion with its axis horizontal is unstable, and its axis rises to a stable steady state, at either an intermediate angle or the vertical, depending on the initial angular velocity. These computations allow an assessment of the circumstances under which the condition described as ‘gyroscopic balance’ is realized. Under this condition, the evolution from an unstable to a stable state is greatly simplified, being described by a first–order differential equation. Oscillatory modes which are stable on linear analysis may be destabilized during this evolution, with consequential oscillations in the normal reaction R at the point of support. The computations presented here are restricted to circumstances in which R remains positive.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":"61 1","pages":"3643 - 3672"},"PeriodicalIF":0.0,"publicationDate":"2004-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87400887","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: 44

Mechanical field fluctuations in polycrystals estimated by homogenization techniques 用均质化技术估计多晶的力学场波动

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1278

R. Brenner, O. Castelnau, L. Badea

{"title":"Mechanical field fluctuations in polycrystals estimated by homogenization techniques","authors":"R. Brenner, O. Castelnau, L. Badea","doi":"10.1098/rspa.2004.1278","DOIUrl":"https://doi.org/10.1098/rspa.2004.1278","url":null,"abstract":"The fluctuation of mechanical fields arising in polycrystals is investigated. These materials are viewed as composites of the Hashin–Shtrikman type with a large number of anisotropic phases and a ‘granular’ topology. We show that the estimation of the intra–phase stress and strain (rate) second moments comes down to the resolution of a linear system of equations. Applied to a linear viscous face–centred cubic (FCC) polycrystal, it is observed that significant local slip rates are estimated even when the corresponding Schmid factor vanishes, due to the intergranular interactions. For the application to viscoplastic polycrystals, the secant and affine nonlinear extensions of the self–consistent scheme are compared. At large stress sensitivity (n = 30), it is observed that the secant linearization leads to almost uniform slip rates for all slip systems in every phase, whereas the affine approach predicts a much larger spread. Furthermore, there is no one–to–one relation between the phase–average stress (or strain rate) and the corresponding second moment. It is emphasized that intra–phase strain–rate heterogeneities should be accounted for when dealing with microstructure evolution.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":"106 1","pages":"3589 - 3612"},"PeriodicalIF":0.0,"publicationDate":"2004-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76087719","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: 41

Correction for Linton and Barnett, Efficient computation of Schlömilch-type series 对Linton和Barnett的修正，Schlömilch-type级数的有效计算

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/RSPA.2004.2000

C. Linton, D. C. Barnett

引用次数: 0

Diffraction by a plane sector 平面扇形的衍射

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1322

B. Budaev, D. Bogy

引用次数: 10

Rigorous bounds of Stokes constants for some nonlinear ordinary differential equations at rank-one irregular singularities 一类非线性常微分方程在秩一不规则奇点处Stokes常数的严格界

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1310

O. Costin, R. Costin, M. Kohut

引用次数: 6

A computational framework for agglomeration in thermochemically reacting granular flows 热化学反应颗粒流中团聚的计算框架

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1277

T. Zohdi

引用次数: 58

Hamel coefficients for the rotational motion of an N–dimensional rigid body n维刚体旋转运动的哈默尔系数

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-12-08 DOI: 10.1098/rspa.2004.1320

J. Hurtado, A. Sinclair

引用次数: 22