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Three-dimensional separated flow structure over prolate spheroids 长形球体上的三维分离流结构
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0052
K. Wang, H. Zhou, C. H. Hû, S. Harrington
{"title":"Three-dimensional separated flow structure over prolate spheroids","authors":"K. Wang, H. Zhou, C. H. Hû, S. Harrington","doi":"10.1098/rspa.1990.0052","DOIUrl":"https://doi.org/10.1098/rspa.1990.0052","url":null,"abstract":"Colour poster paints were used for water-tunnel visualization of the surface flow patterns over prolate spheroids of axis-ratios b/a = ½, ⅓ and ¼ at incidence from 0-90°. Results display the surface flow pattern over the entire body presumably for the first time in terms of completeness and clarify unsettled questions in the literature.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86136257","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: 34
Tension-field theory 张力场理论
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0055
D. Steigmann
{"title":"Tension-field theory","authors":"D. Steigmann","doi":"10.1098/rspa.1990.0055","DOIUrl":"https://doi.org/10.1098/rspa.1990.0055","url":null,"abstract":"A general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations. The principal contribution is a partial differential equation describing a geometrical property of tension trajectories. This is one of a system of two equations which describes the state of stress independently of the deformation. This system is strongly elliptic at any stable solution, whereas the deformation is described by a system of parabolic type. Controllable solutions, i. e. those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone, are obtained. The general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples. Existing small strain theories are shown to correspond to a singular limit of the general theory, at which the underlying system changes from elliptic to parabolic type.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85218049","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: 309
A mode III crack at the interface between two nonlinear materials 两种非线性材料界面处的III型裂纹
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0059
C. Champion, C. Atkinson
{"title":"A mode III crack at the interface between two nonlinear materials","authors":"C. Champion, C. Atkinson","doi":"10.1098/rspa.1990.0059","DOIUrl":"https://doi.org/10.1098/rspa.1990.0059","url":null,"abstract":"The stress singularity at the tip of a crack at the interface between two different power-law materials under mode III loading (longitudinal shear) is considered. By considering expansions at the crack tip in each region, and matching across the interface ahead of the crack, it is found that the stress singularities are the same in each material, and correspond to that for a crack in a homogeneous material with hardening exponent equal to the maximum of the hardening exponents of the two materials. The displacements near the crack tip are found to be of different orders in the two materials, and it is shown that all the crack tip energy is concentrated in the material with the largest hardening exponent. The results are illustrated by means of an example involving a displacement loaded bimaterial strip.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73474397","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: 25
Obstacle drag in stratified flow 分层流中的障碍阻力
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0054
I. Castro, W. Snyder, P. Baines
{"title":"Obstacle drag in stratified flow","authors":"I. Castro, W. Snyder, P. Baines","doi":"10.1098/rspa.1990.0054","DOIUrl":"https://doi.org/10.1098/rspa.1990.0054","url":null,"abstract":"This paper describes an experimental study of the drag of two- and three-dimensional bluff obstacles of various cross-stream shapes when towed through a fluid having a stable, linear density gradient with Brunt-Vaisala frequency, N. Drag measurements were made directly using a force balance, and effects of obstacle blockage (h/D, where h and D are the obstacle height and the fluid depth, respectively) and Reynolds number were effectively eliminated. It is shown that even in cases where the downstream lee waves and propagating columnar waves are of large amplitude, the variation of drag with the parameter K ( = ND/πU) is qualitatively close to that implied by linear theories, with drag minima existing at integral values of K. Under certain conditions large, steady, periodic variations in drag occur. Simultaneous drag measurements and video recordings of the wakes show that this unsteadiness is linked directly with time-variations in the lee and columnar wave amplitudes. It is argued that there are, therefore, situations where the inviscid flow is always unsteady even for large times; the consequent implications for atmospheric motions are discussed.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86243591","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
Hydrogenolysis and related reactions of hydrocarbons (C3 to C5) on silica-supported Rh-Pt bimetallic catalysts 硅负载铑铂双金属催化剂上碳氢化合物(C3 ~ C5)的氢解及相关反应
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0049
J. A. Oliver, C. Kemball
{"title":"Hydrogenolysis and related reactions of hydrocarbons (C3 to C5) on silica-supported Rh-Pt bimetallic catalysts","authors":"J. A. Oliver, C. Kemball","doi":"10.1098/rspa.1990.0049","DOIUrl":"https://doi.org/10.1098/rspa.1990.0049","url":null,"abstract":"The reactions with hydrogen of propane, butane, 2-methylpropane, pentane, 2-methylbutane, 2, 2-dimethylpropane and cyclopentane have been studied in a static reactor using a series of highly dispersed rhodium-platinum catalysts supported on high-area silica. The main reaction over all catalysts was hydrogenolysis involving the breaking of a single carbon-carbon bond. Most of the compounds reacted at similar rates over platinum with activation energies in the range 132-144 kJ mol-1. With rhodium, rates varied with hydrocarbon structure by factors of more than 102. The selectivities for the formation of the various products showed that the relative rates of breaking different carbon-carbon bonds over rhodium were S-S > P-S > S-T > P-T > P-Q (P = primary, Q = quaternary, S = secondary and T = tertiary). At temperatures above 455 K, there was evidence of a change of rate-determining step over rhodium with the overall reaction becoming controlled by the rate of desorption of methane. Probable mechanisms over platinum and rhodium are discussed. Rhodium was more active than platinum by factors of about 200 for branched hydrocarbons and of 103 or more for straight-chain compounds. Patterns of activity with metal composition are interpreted in terms of active sites consisting of ensembles of about six metal atoms. But an alternative description of the active site as a single metal atom with properties influenced by a number of nearest neighbours cannot be excluded.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89727570","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: 5
On the interpretation of electron diffraction patterns from materials containing planar boundaries: the intergrowth tungsten bronzes 含平面边界材料的电子衍射图解释:共生钨青铜
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0053
G. Harburn, R. Tilley, R. Williams
{"title":"On the interpretation of electron diffraction patterns from materials containing planar boundaries: the intergrowth tungsten bronzes","authors":"G. Harburn, R. Tilley, R. Williams","doi":"10.1098/rspa.1990.0053","DOIUrl":"https://doi.org/10.1098/rspa.1990.0053","url":null,"abstract":"Materials containing planar boundaries are of general interest and complete understanding of their structures is important. When direct imaging of the boundaries by, for instance, high-resolution electron microscopy, is impracticable, details of their structure and arrangement may be obtained from electron diffraction patterns. Such patterns are discussed in terms of those from intergrowth tungsten bronzes as specific examples. Fourier-transform calculations for proposed structures have been made to establish, in conjunction with optical-diffraction analogues, the features of the far-field diffraction patterns. These results have been compared with diffraction patterns obtained experimentally by transmission electron microscopy. The aim of the study, to show that the arrangement of the boundaries in these complicated phases can be deduced from their diffraction patterns without the need for high-resolution imaging, has been achieved. The steps to be taken to make these deductions are set out.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89739664","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: 1
Stieltjes transforms and the Stokes phenomenon Stieltjes变换和Stokes现象
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0058
W. Boyd
{"title":"Stieltjes transforms and the Stokes phenomenon","authors":"W. Boyd","doi":"10.1098/rspa.1990.0058","DOIUrl":"https://doi.org/10.1098/rspa.1990.0058","url":null,"abstract":"Recently, Berry, Olver and Jones have found uniform asymptotic expansions for the exponentially small remainder terms that result when asymptotic expansions are optimally truncated. These uniform expansions describe the rapid change in the behaviour of the remainders as a Stokes line is crossed. We show how such uniform expansions may be found when a function can be expressed as a Stieltjes transform. Such an approach has the following advantages: the uniform expansion is calculated directly, non-uniform expansions away from the Stokes line are readily found, and explicit error bounds may be established. We illustrate the method by application to the modified Bessel function Kv(z).","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79813568","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: 42
Deformation and microstructure of rutile 金红石的变形与显微组织
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0056
M. Blanchin, L. Bursill, C. Lafage
{"title":"Deformation and microstructure of rutile","authors":"M. Blanchin, L. Bursill, C. Lafage","doi":"10.1098/rspa.1990.0056","DOIUrl":"https://doi.org/10.1098/rspa.1990.0056","url":null,"abstract":"Studies of the mechanical properties of rutiles are described, in particular the behaviour of the elastic limit under compression with respect to variations in temperature (pure rutile), intrinsic non-stoichiometry (pure rutile reduced under low oxygen pressure) and extrinsic non-stoichiometry (rutile doped with chromia and alumina). A wide range of values is obtained, which may be understood in terms of the interaction of dislocations belonging to the slip systems {101} <1̄01> and {110} <001> with impurities, non-stoichiometric small and extended defects and precipitates. Transmission electron microscopy at medium resolution as well as high-resolution electron microscopy have been used to relate mechanical behaviour with microstructure.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81887357","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: 17
The antiphon. II. The exact evaluation of memory capacity 轮流吟唱的歌。2记忆容量的精确评估
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0050
P. Whittle
{"title":"The antiphon. II. The exact evaluation of memory capacity","authors":"P. Whittle","doi":"10.1098/rspa.1990.0050","DOIUrl":"https://doi.org/10.1098/rspa.1990.0050","url":null,"abstract":"An improved analysis is given of the antiphon: the device proposed in Whittle (1989) to achieve reliable memory from unreliable components. It is shown that for large systems of N such components one can reliably store KN + o(N) nats of information, and the supremum value of K (the capacity, C) is determined. It is moreover shown that a positive capacity (which is evaluated) can be achieved with the number M of processing units of no more than order N.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76529779","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: 3
Scattering by a surface inhomogeneity on an elastic half-space, with application to fluid-structure interaction noise 弹性半空间表面非均匀性散射，并应用于流固相互作用噪声
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-05-08 DOI: 10.1098/rspa.1990.0057
M. S. Howe
{"title":"Scattering by a surface inhomogeneity on an elastic half-space, with application to fluid-structure interaction noise","authors":"M. S. Howe","doi":"10.1098/rspa.1990.0057","DOIUrl":"https://doi.org/10.1098/rspa.1990.0057","url":null,"abstract":"A harmonic point source is situated in fluid bounded by a nominally plane interface with an elastic half-space. The source is close to a small protrusion of the elastic medium into the fluid, and it is required to determine the interaction (‘diffraction’) radiation, i. e. the acoustic, elastic-body and surface (Scholte) waves produced by the scattering of the near field of the source by the protrusion. The solution of this canonical problem is applied to the prediction of acoustic and structural noise generated by low Mach number turbulent flow over an inhomogeneity on the boundary of an elastic solid. Estimates are presented of the frequency spectra of the power delivered to the various wave modes and their dependence on the elastic properties of the solid, and a comparison is made with empirical predictions of excitation of the same modes in the absence of the inhomogeneity. The scattered radiation can be significant even when the surface inhomogeneity does not penetrate beyond the viscous sublayer into the turbulent flow.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80090534","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
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