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

{"title":"Non-factorizable separable systems and higher-order symmetries of the Dirac operator","authors":"M. Fels, N. Kamran","doi":"10.1098/rspa.1990.0032","DOIUrl":"https://doi.org/10.1098/rspa.1990.0032","url":null,"abstract":"It is shown that there exist separable systems for the Dirac operator on four-dimensional lorentzian spin manifolds that are not factorizable in the sense of Miller. The symmetry operators associated to these new separable systems are of higher order than the Dirac operator. They are characterized in the second-order case in terms of quadratic first integrals of the geodesic flow satisfying additional invariant conditions.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75041469","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}

{"title":"Calibrating an area-detector diffractometer: integral response","authors":"David J. Thomas","doi":"10.1098/rspa.1990.0030","DOIUrl":"https://doi.org/10.1098/rspa.1990.0030","url":null,"abstract":"The quality of diffraction data measured with electronic area-detectors is improved by correcting for non-uniformities in the response of the detector. Many detectors are actually much more uniform than they appear because much of the perceived non-uniformity is an artefact of the distortions in their imaging geometry and of the methods of illumination during calibration. Indeed, every known correction reduces the perceived non-uniformity. Our inability to illuminate the detector uniformly with radiation of the same wavelength as is used during data-collection is a particular worry because of differential absorption. The tails of the point-spread function also perturb the apparent response, particularly near to the edges of the imaging area. These problems are difficult to compensate, so there is no completely satisfactory method of determining the true response of real detectors. However, this does not prevent us from making calibrations of usable accuracy. Although this paper applies to all types of area-detector, the discussion is centred mainly on the ENRAF-NONIUS fast system, which is a commercially available television diffractometer, calibrated using software written by the present author. Calibrating the response of imaging detectors is a general problem, and many of the techniques expounded here are of wide applicability.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76014351","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}

{"title":"Velocity and size characteristics of liquid-fuelled flames stabilized by a swirl burner","authors":"Y. Hardalupas, A. M. Taylor, J. Whitelaw","doi":"10.1098/rspa.1990.0028","DOIUrl":"https://doi.org/10.1098/rspa.1990.0028","url":null,"abstract":"Velocity and droplet size characteristics of an unconfined quarl burner, of 16 mm quarl inlet diameter, have been measured with a phase-Doppler anemometer at a swirl number of about 0.29: the Reynolds number of the flow was 30000, based on the cold bulk velocity of 30.4 m s-1 and the hydraulic diameter. The atomization was achieved by shear between the swirling air and six radial kerosene jets and the resulting Sauter and arithmetic mean diameters were about 70 and 50 μm respectively after injection: velocity characteristics are presented for three 5 μm-wide size classes, 10, 30 and 60 μm. The flows correspond to no combustion and combustion of natural gas with a heat release of 8 kW supplemented by liquid kerosene flow rates sufficient to generate 21.6 and 37.2 kW : the gas equivalence ratio was 0.45 and atomized kerosene at two flow rates increased the overall ratios to 1.64 and 2.53. In non-reacting flow, droplets 30 μm and smaller are sufficiently small to be entrained by the mean air velocity towards the central part of the flow and into the swirl-induced recirculating air bubble. The 60 μm droplets are able to travel through the bubble uninfluenced by turbulent fluctuations in the air and are ‘centrifuged’ away from the centreline, through acquisition of a mean swirl velocity component, so that a large proportion of the kerosene volume flow rate lies at the edge of the swirling jet. Because larger droplets are centrifuged to the outer part of the flow, whereas the smaller are entrained towards the centreline, the Sauter and arithmetic mean diameters are, by 1.22 quarl exit diameters downstream of the quarl, approximately 65 and 36 μm at the outer part of the flow and 35 and 12 μm near the centreline in the inert flow. In reacting flow, droplets evaporate rapidly in regions of elevated temperatures and hence no droplets are found within the flame brush and recirculation region. The aerodynamic response of each size class to the air velocity is similar to inert flow so that the majority of the kerosene flow is centrifuged away from the flame. On exit from the quarl, the evaporation and burning rates cause the Sauter and arithmetic mean diameters to be about 70 and 50 μm and 60 and 30 μm at the inner and outer edges of the spray respectively. By 1.22 quarl exit-diameters from the exit of the quarl, the air motion entrains droplets smaller than about 30 μm towards the flame, at the inner edge of the spray, so that the Sauter and arithmetic mean diameters are 60 and 40 μm at the outer edge of the jet. There is comparatively little effect of changing the flow rate of kerosene because the combustion is controlled by the low available number of smaller droplets, although the Group combustion number corresponds to ‘cloud’ burning. The relative response of droplets to the mean and turbulent components of air motion, including the ‘centrifuging’ effect, can be scaled to other flows through dimensionless numbers defined in the text.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83597465","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}

{"title":"Acoustic scattering by parallel plates with periodic connectors","authors":"E. Skelton","doi":"10.1098/rspa.1990.0021","DOIUrl":"https://doi.org/10.1098/rspa.1990.0021","url":null,"abstract":"The scattering of a plane sound wave by two infinite, elastic, parallel plates constrained by equally spaced, identical, mechanical line connectors, which can support only compressional motion and which are simply hinged to both plates, is investigated using Fourier transforms. A formally exact solution is obtained and investigated asymptotically when the only fluid present occupies the half-space from which the sound wave is incident and provides heavy fluid loading to the plate, and likewise when this fluid also occupies the space between the plates. Conditions for resonant behaviour are also examined in these limits.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75971486","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}

{"title":"The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction","authors":"D. Ruelle","doi":"10.1098/rspa.1990.0010","DOIUrl":"https://doi.org/10.1098/rspa.1990.0010","url":null,"abstract":"Under the name of chaos the mathematical ideas of differentiable dynamics have had a profound impact on physics. Some success stories are discussed. Attention is also directed to the excessive optimism of some currently attempted applications. It is shown how and why they should fail.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82900628","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}

{"title":"Electro-optic observations of electrodynamic band formation in colloidal suspensions","authors":"B. Jennings, M. Stankiewicz","doi":"10.1098/rspa.1990.0015","DOIUrl":"https://doi.org/10.1098/rspa.1990.0015","url":null,"abstract":"In static and low-frequency electric fields, colloidal particles in suspension tend to associate into ‘strings’ or ‘pearl chains’ along the field lines. A phenomenon has been observed in which, under long duration alternating electric fields, colloidal particles in aqueous or conducting media exhibit an electrodynamic instability in which they gather into high concentration ‘bands’ which run essentially perpendicular to the applied field vector. A detailed study is catalogued herein for aqueous suspensions of the discotic mineral kaolinite. A theory has been developed, which embraces the ‘pearl chain’ and ‘band’ formations, demonstrating that one can be formed from the other with increasing frequency and field strength and illustrating the dependence of band formation on electrophoretic mobility as observed in related electro-optical experiments. The value of the phenomenon as a mechanism for concentrating dispersed colloidal particles into regions of very high local density is apparent.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89182841","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}

{"title":"Algebras of genetic self-incompatibility systems","authors":"P. Holgate","doi":"10.1098/rspa.1990.0017","DOIUrl":"https://doi.org/10.1098/rspa.1990.0017","url":null,"abstract":"To every system of inheritance there corresponds a genetic algebra, generally non-associative, that describes its structure. The genetic algebras of a large number of breeding systems have been studied, but they have all been non-selective, and mostly random mating. The object of this paper is to investigate the genetic algebras of a number of systems involving a very strong form of differential fertility, where some pairs of individuals cannot produce viable offspring at all. For these, none of the classical properties of genetic algebra hold. In §2, the phenomenon of pollen incompatibility with m alleles is studied. The case m = 3 occurs in nature in Nicotiana alata For this, but not when m > 3, the genetic algebra is found to be Lie admissible, and some detailed relations consequent on this are obtained. Section 3 is devoted to two systems of style height self-incompatibility, Lythrum salicaria and Oxalis rosea. For these, described essentially by 6- and 26- dimensional genetic algebras respectively, the idempotents are listed, and full and outline descriptions respectively are given of the lattices of subalgebras. In the last section a class of algebras is defined corresponding to a multilocus generalization of the Lythrum mechanism. It is shown that this mechanism always leads to an isoplethic equilibrium.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80691384","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}

{"title":"Waves near Stokes lines","authors":"M. Berry","doi":"10.1098/rspa.1990.0013","DOIUrl":"https://doi.org/10.1098/rspa.1990.0013","url":null,"abstract":"The large-k asymptotics of d2u(z)/dz2 = k2R2(z) u(z) are studied near a Stokes line (ω ≡ ∫z z0 R dz real, where z0 is a zero of R2(z), of any order), on which there is greatest disparity between the dominant and subdominant exponential waves in the phase-integral (WKB) approximations. The aim is to establish precisely how the multiplier b_ of the subdominant wave varies across the Stokes line. Although b_ always has a total change proportional to i times the multiplier of the dominant wave (the Stokes phenomenon), the form of the change depends on the convention used to define the two waves. The optimal convention, for which the variation is maximally compact and smooth, is to define them by the phase-integral approximation truncated at its least term, whose order is proportional to k and therefore large (‘asymptotics of asymptotics’). Then the variation of b_ is proportional to the error function of the natural Stokes-crossing variable Im ω √(k/Re ω). This result is obtained without resumming divergent series (thereby avoiding ‘asymptotics of asymptotics of asymptotics’). An application is given, to the birth of exponentially weak reflected waves in media with smoothly varying refractive index.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85120380","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}

{"title":"Nonlinear stability of rotating pseudo-rigid bodies","authors":"D. Lewis, J. Simo","doi":"10.1098/rspa.1990.0014","DOIUrl":"https://doi.org/10.1098/rspa.1990.0014","url":null,"abstract":"A rigorous nonlinear stability analysis of rotating homogeneous elastic bodies is presented, which exploits the hamiltonian structure and symmetries inherent to homogeneous elasticity by means of the energy-momentum method. It is shown that stability of a relative equilibrium is implied by the definiteness of the second variation of a modified hamiltonian restricted to an appropriate subspace. The analysis makes crucial use of a special parametrization of the constrained space of admissible variations, which results in a nearly diagonal second variation. The stability conditions obtained by this method include the conditions for stability of the equilibrium configuration as a rigid body and satisfaction of the Baker-Ericksen inequalities. As an application of our results, we obtain complete, explicit stability conditions for a particular form of relative equilibria for three classes of materials: for two of these, Ciarlet-Geymonat and St Venant-Kirchhoff materials, these equilibria are always stable; for the third, a compressible Mooney-Rivlin material, both stable and unstable equilibria exist.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88598452","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}

{"title":"Acoustic scattering by parallel plates with a single connector","authors":"E. Skelton","doi":"10.1098/rspa.1990.0020","DOIUrl":"https://doi.org/10.1098/rspa.1990.0020","url":null,"abstract":"A plane sound wave is incident upon one of two infinite parallel plates that are constrained along a line by a mechanical connector, which is simply hinged to both plates and which can support compressional motion. A formal solution is obtained and investigated for the cases where the plate upon which the sound wave is incident is subjected to heavy fluid loading while the parallel plate is subjected to light fluid loading and the fluid between the plates is either light or heavy. When the plates are separated by heavy fluid the additional limits of large and small plate spacing are used.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1990-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89506332","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}