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

Some examples of Penrose’s quasi-local mass construction 彭罗斯的准局部大规模建筑的一些例子

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 2015-09-24 DOI: 10.1098/rspa.1983.0092

K. Tod

引用次数: 106

The influence of diffusion on the current-voltage curve in a flame ionization detector 扩散对火焰电离检测器电流-电压曲线的影响

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1992-08-08 DOI: 10.1098/rspa.1989.0089

H. Bolton, P. Halbherr

引用次数: 1

Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I 多孔介质中自然对流对热点火的影响。2集总热模型1

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0073

V. Balakotaiah, P. Pourtalet

{"title":"Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I","authors":"V. Balakotaiah, P. Pourtalet","doi":"10.1098/rspa.1990.0073","DOIUrl":"https://doi.org/10.1098/rspa.1990.0073","url":null,"abstract":"In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t/ln t + t/(t - 1) (1 < t ≼ 3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{ - B Ls + B Ls/t} ln t, where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single-valued, isola, inverse S, mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78306418","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

On the existence of interfacial (Stoneley) waves in bonded piezoelectric half-spaces 结合压电半空间中界面波的存在性

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0075

M. Abbudi, D. Barnett

引用次数: 33

Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition 狄利克雷条件下奇摄动双稳定势的极小值和梯度流

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0071

Nicholas C. Owen, J. Rubinstein, P. Sternberg

引用次数: 77

A theoretical analysis of electrochemical arc machining 电化学电弧加工的理论分析

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0067

J. McGeough, H. Rasmussen

{"title":"A theoretical analysis of electrochemical arc machining","authors":"J. McGeough, H. Rasmussen","doi":"10.1098/rspa.1990.0067","DOIUrl":"https://doi.org/10.1098/rspa.1990.0067","url":null,"abstract":"Electrochemical arc machining (ECAM) involves the removal of metal from an anodically polarized workpiece by both erosion arising from discharges produced in an aqueous electrolyte and electrolytic dissolution. A theoretical model is derived for the process and analysed for two specific applications, fine-hole drilling and the finishing of components by smoothing of their initially rough surfaces. In the second of these examples, a perturbation procedure for obtaining approximate solutions is used; the model so developed encorporates the effects of current density on current efficiency which are known from experimental electrochemical machining (ECM) studies to influence the rate and mode of smoothing. For fine-hole drilling by ECAM, the analysis predicts that the interelectrode gap width increases with the applied voltage and inversely with the square root of the mechanically driven anode. In the case of smoothing, ECAM is found to remove the surface irregularities at a much faster rate and with lower loss of stock metal than ECM alone, when electrolytes such as sodium chloride solution yielding 100% current efficiency are used for the latter process. The analysis shows that an electrolyte solution with a current density-dependent current efficiency is needed if parent metal loss by ECM is to approach that of ECAM, and even then, machining by the latter is still much faster. Attention is drawn to experimental evidence in support of these predictions of ECAM behaviour. Finally, results from the model are used to verify the practical use of ECM for rapid finishing of the surfaces of components left rough by electrodischarge machining.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83699578","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

On the solutions of a class of dual integral equations occurring in diffraction problems 衍射问题中一类对偶积分方程的解

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0066

K. Eswaran

{"title":"On the solutions of a class of dual integral equations occurring in diffraction problems","authors":"K. Eswaran","doi":"10.1098/rspa.1990.0066","DOIUrl":"https://doi.org/10.1098/rspa.1990.0066","url":null,"abstract":"It is shown that there exists a category of two-dimensional diffraction problems, which can be put into a ‘standard form‘ of dual integral equations. These diffraction problems include: diffraction of electromagnetic waves by a finite strip, a finite slit, the diffraction of scalar or vector elastic waves by a rigid strip or crack, etc. A general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions. The sufficient conditions for a given dual integral equations to be solvable in this manner are also determined. Hence, the method forms a complement to the Weiner-Hopf method. To illustrate the method solutions are obtained for a bench-mark problem : the diffraction of light by a finite perfectly conducting strip (or equivalently the diffraction of SH waves by a crack). Comparison with results obtained by others for low, intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies. Both the near field and the far field are obtained, the latter is shown to correspond to the Fraunhoffer diffraction pattern for high frequency. It is also shown that for the equivalent crack problem the stress intensity factor (SIF) fluctuates rapidly with changes in the angle of incidence for high frequencies, thus making the SIF especially sensitive to angle of incidence at high frequencies.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77337919","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

Computer simulation studies of anisotropic systems. XVIII. Re-entrant phase separation in nematogenic mixtures of cylindrical and spherical particles 各向异性系统的计算机模拟研究。十八。圆柱形和球形颗粒致线虫混合物的再入相分离

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0063

R. Hashim, G. R. Luckhurst, S. Romano

{"title":"Computer simulation studies of anisotropic systems. XVIII. Re-entrant phase separation in nematogenic mixtures of cylindrical and spherical particles","authors":"R. Hashim, G. R. Luckhurst, S. Romano","doi":"10.1098/rspa.1990.0063","DOIUrl":"https://doi.org/10.1098/rspa.1990.0063","url":null,"abstract":"Addition of a solute composed of quasi-spherical molecules to a nematic liquid crystal is known to depress the nematic–isotropic transition temperature. A biphasic régime, consisting of coexisting nematic and isotropic phases, is also created at the transition. A molecular field theory of such mixtures, developed by Humphries and Luckhurst, predicts, in addition, the appearance of a re-entrant biphasic region following the nematic phase for a narrow range of compositions. This unusual re-entrant phase separation has not been observed for real nematogenic mixtures, presumably because the system freezes before the re-entrant phases can be formed. Here we report the observation of this biphasic régime for a model nematogenic mixture, formed from cylindrical and spherical particles, which was studied using the Monte Carlo technique of computer simulation. The particles are confined to the sites of a simple cubic lattice but still retain their rotational freedom; in consequence the mixture is unable to freeze in the conventional sense. The temperature variation of the heat capacity and the solute–solute radial distribution function reveal the predicted transition to the re-entrant biphasic régime. The internal energy and the second-rank orientational order parameter were also determined as a function of temperature. The predictions of the Humphries–Luckhurst theory are found to be in good qualitative accord with the results of the simulation.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84948924","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

Analysis of chemical kinetic systems over the entire parameter space. III. A wet combustion system 整个参数空间的化学动力学系统分析。3湿式燃烧系统

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0068

B. F. Gray

引用次数: 14

Finite deformation of flexible composites 柔性复合材料的有限变形

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences Pub Date : 1990-06-08 DOI: 10.1098/rspa.1990.0074

S. Luo, T. Chou

引用次数: 29