Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences最新文献_第8页

Comparison of the minimum plastic spin and rate sensitive slip theories for loading of symmetrical crystal orientations 对称晶体取向加载的最小塑性自旋和速率敏感滑移理论的比较

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0008

L. Toth, J. Jonas, K. Neale

{"title":"Comparison of the minimum plastic spin and rate sensitive slip theories for loading of symmetrical crystal orientations","authors":"L. Toth, J. Jonas, K. Neale","doi":"10.1098/rspa.1990.0008","DOIUrl":"https://doi.org/10.1098/rspa.1990.0008","url":null,"abstract":"The plastic loading of face-centred cubic crystals along directions of symmetry leads to ambiguities in slip system selection. A solution to this problem has been proposed (Fuh & Havner, Proc. R. Soc. Lond. A 427, 193-239 (1989)) by postulating that the operating slip combination is the one which corresponds to the minimum plastic spin (MPS). A comparison is made between the MPS and rate-dependent slip theories. The predictions obtained are identical for the following cases: (i) (110) loading in channel die compression (with one exception) and (ii) all the multiple slip orientations in uniaxial tension. In the case of [100] pure plane strain compression, there is agreement for the four slip-system orientations, but not when six systems are required in the MPS analysis. It is shown that the symmetry of the slip distributions called for by the MPS and rate sensitive approaches is responsible for the broad equivalence between the predictions of the two theories. In each of the examples discussed, the number of operating slip systems is determined by symmetry considerations, leading to the operation of two, four, six or eight slip-systems, rather than by the number of prescribed constraints.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"20 1","pages":"201 - 219"},"PeriodicalIF":0.0,"publicationDate":"1990-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81732080","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: 18

Emendations to a proof in the general three-dimensional theory of oscillating sources of waves 对一般三维振荡波源理论中一个证明的修正

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0003

M. Lighthill

{"title":"Emendations to a proof in the general three-dimensional theory of oscillating sources of waves","authors":"M. Lighthill","doi":"10.1098/rspa.1990.0003","DOIUrl":"https://doi.org/10.1098/rspa.1990.0003","url":null,"abstract":"Asymptotic forms far from the source region of waves generated by oscillating sources in a linear homogeneous anisotropic system were derived by a method of proof that requires emendation although the final conclusions remain unchanged. An intermediate asymptotic result, in the form of an integral over that part S+ of the whole real wavenumber surface S on which a certain inequality (related to the radiation condition) is satisfied, needs modification as described in §2; but, as shown in §3, it is the modified form that is correctly estimated as in the final conclusions. Thus the proof is given two necessary emendations that cancel out. A careful analysis in §4 of why they cancel shows that the original intermediate result regains validity if S+, besides including that part of the real wavenumber surface S on which the inequality ∂ω/∂k1 > 0 is satisfied (where ω is frequency and k1 the component of wavenumber in the direction chosen for wave estimation), is considered as being continued on the complex wavenumber surface S, beyond the curve C on which ∂ω/∂k1 = 0, in the negative pure-imaginary k1-direction. This change is required to ensure the proper application of Cauchy’s theorem. Furthermore, the removal of any discontinuity at C prevents the appearance of an additional asymptotic term that would be unavoidably associated with such a singularity. I am grateful to Professor V. A. Borovikov for stimulating me to make these necessary clarifications.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"15 17 1","pages":"31 - 42"},"PeriodicalIF":0.0,"publicationDate":"1990-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79428788","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: 7

Quantum theory and the brain 量子理论和大脑

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0004

Matthew J. Donald

引用次数: 70

Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations 特征初值问题转化为柯西问题及其在爱因斯坦方程中的应用

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-08 DOI: 10.1098/rspa.1990.0009

A. Rendall

引用次数: 242

A distributional theory for asymptotic expansions 渐近展开式的一个分布理论

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-01 DOI: 10.1098/rspa.1990.0041

Ricardo Estrada, R. Kanwal

{"title":"A distributional theory for asymptotic expansions","authors":"Ricardo Estrada, R. Kanwal","doi":"10.1098/rspa.1990.0041","DOIUrl":"https://doi.org/10.1098/rspa.1990.0041","url":null,"abstract":"We present various techniques for the asymptotic expansions of generalized functions. We show that the moment asymptotic expansions hold for a very wide variety of kernels such as generalized functions of rapid decay and rapid oscillations. We do not use Mellin transform techniques as done by previous authors in the field. Instead, we introduce a direct approach that not only solves the one-dimensional problems but also applies to various multidimensional integrals and oscillatory kernels as well. This approach also helps in the development of various asymptotic series arising in diverse fields of mathematics and physics. We find that the asymptotic expansions of generalized functions depend on the selection of suitable spaces of test functions. Accordingly, we have exercised special care in classifying the spaces and the distributions defined on them. Furthermore, we use the theory of topological tensor products to obtain the expansions of vector-valued distributions. We present several examples to illustrate that many classical results follow in a simple manner. For instance, we derive from our results the asymptotic expansions of certain series considered by Ramanujan.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"15 1","pages":"399 - 430"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91251366","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: 49

Static and dynamic behaviour of soils: a rational approach to quantitative solutions. II. Semi-saturated problems 土壤的静态和动态行为:定量解决方案的合理方法。2Semi-saturated问题

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-01 DOI: 10.1098/rspa.1990.0062

O. Zienkiewicz, Y. Xie, B. Schrefler, A. Ledesma, N. Bićanić

引用次数: 101

The structure and dynamics of bubble-type vortex breakdown 气泡型涡旋击穿的结构与动力学

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-01 DOI: 10.1098/rspa.1990.0076

R. Spall, T. Gatski, R. Ash

引用次数: 70

Fractal control boundaries of driven oscillators and their relevance to safe engineering design 驱动振荡器的分形控制边界及其与安全工程设计的关系

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-01-01 DOI: 10.1098/rspa.1990.0022

J. Thompson, M. Soliman

{"title":"Fractal control boundaries of driven oscillators and their relevance to safe engineering design","authors":"J. Thompson, M. Soliman","doi":"10.1098/rspa.1990.0022","DOIUrl":"https://doi.org/10.1098/rspa.1990.0022","url":null,"abstract":"When a metastable, damped oscillator is driven by strong periodic forcing, the catchment basin of constrained motions in the space of the starting conditions {x(0),ẋ(0)} develops a fractal boundary associated with a homoclinic tangling of the governing invariant manifolds. The four-dimensional basin in the phase-control space spanned by {x(0), ẋ)(0), F, ω}, where F is the magnitude and ω the frequency of the excitation, will likewise acquire a fractal boundary, and we here explore the engineering significance of the control cross section corresponding, for example, to x(0) = ẋ(0) = 0. The fractal boundary in this section is a failure locus for a mechanical or electrical system subjected, while resting in its ambient equilibrium state, to a sudden pulse of excitation. We assess here the relative magnitude of the uncertainties implied by this fractal structure for the optimal escape from a universal cubic potential well. Absolute and transient basins are examined, giving control-space maps analogous to familiar pictures of the Mandelbrot set. Generalizing from this prototype study, it is argued that in engineering design, against boat capsize or earthquake damage, for example, a study of safe basins should augment, and perhaps entirely replace, conventional analysis of the steady-state attracting solutions.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"11 1","pages":"1 - 13"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88667338","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: 87

A numerical investigation of the Schaeffer homotopy in the problem of Taylor‒Couette flows Taylor-Couette流问题中Schaeffer同伦的数值研究

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1989-12-08 DOI: 10.1098/rspa.1989.0128

D. K. Anson, K. Cliffe

引用次数: 6

Several products of distributions on Rm Rm上分布的几个乘积

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1989-12-08 DOI: 10.1098/rspa.1989.0133

C. Zhi, B. Fisher

引用次数: 17