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

{"title":"Construction of Lagrangians in continuum theories","authors":"M. Scholle","doi":"10.1098/rspa.2004.1354","DOIUrl":"https://doi.org/10.1098/rspa.2004.1354","url":null,"abstract":"For physical systems the dynamics of which is formulated within the framework of Lagrange formalism, the dynamics is completely defined by only one function, namely the Lagrangian. For instance, the whole conservative Newtonian mechanics has been successfully embedded into this methodical concept. In continuum theories, however, the situation is different: no generally valid construction rule for the Lagrangian has been established in the past. In this paper general properties of Lagrangians in non–relativistic field theories are derived by considering universal symmetries, namely space– and time–translations, rigid rotations and Galilei boosts. These investigations discover the dual structure, i.e. the coexistence of two complementary representations of the Lagrangian. From the dual structure, relevant restrictions for the analytical form of the Lagrangian are derived which eventually result in a general scheme for Lagrangians. For two examples, namely Schrödinger's theory and the flow of an ideal fluid, the compatibility of the Lagrangian with the general scheme is demonstrated. The dual structure also has consequences for the balances which result from the respective symmetries by Noether's theorem: universally valid constitutive relations between the densities and the flux densities of energy, momentum, mass and centre of mass are derived. By an inverse treatment of these constitutive relations a Lagrangian for a given physical system can be constructed. This procedure is demonstrated for an elastically deforming body.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84248022","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":"On the propagation of plane waves in type–III thermoelastic media","authors":"P. Puri, P. Jordan","doi":"10.1098/rspa.2004.1341","DOIUrl":"https://doi.org/10.1098/rspa.2004.1341","url":null,"abstract":"The propagation of plane waves in infinite, three–dimensional, type–III thermoelastic media is investigated. Exact dispersion relation solutions are determined and several characterizations of the wavefield are examined. Low– and high–frequency asymptotic expressions are given, small–coupling limit results are derived, and special/limiting cases, including those corresponding to thermoelastic media of types II and I, are noted. Computational tools are used to illustrate the analytical findings and to study the effects of varying the physical parameters. Of the findings presented, the following are most significant: (i) the determination of critical values of the physical parameters and their impact on the wavefields; (ii) ascertaining that type–III media behave, essentially, like type–II (respectively, type–I) media with respect to low– (respectively, high–) frequency plane waves; (iii) establishing the Whitham stability of plane waves in type–III media; and (iv) the determination of the dispersion characteristics of type–III media.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83423574","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":"Structural development of vortical flows around a square jet in cross-flow","authors":"A. Sau, T. Sheu, S. Tsai, R. Hwang, T. Chiang","doi":"10.1098/rspa.2004.1324","DOIUrl":"https://doi.org/10.1098/rspa.2004.1324","url":null,"abstract":"The present computational study is devoted to unfolding the complex process of three–dimensional flow interaction around a square jet in cross–flow. The aim is to provide a clear understanding about the structural development of the entire vortical flow field, which may immensely enhance our knowledge regarding mutual interaction among various vortical structures that takes place around the jet. Careful attempts have been made to capture the detailed mechanism of formation of the near–field horseshoe–vortex system and the roll–up process of the hovering vortices. The rolled–up shear–layer hovering vortices, which wrap around the front and the lateral jet–cross–flow interface, are observed to initiate the Kelvin–Helmholtz–like instability. The present study also clearly displays the inception process of the counter–rotating vortex pair (CVP) from the shear layers that develop on the two lateral side walls of the jet pipe. In order to better understand the complete flow–interaction process and the governing flow physics, the simulation was performed for a moderate value of the Reynolds number (Re = 225), and for a jet–to–free–stream velocity ratio of 2.5. The interaction process between the streamwise wall vortices and the developed upright (or spin–off, or zipper) vortices in the downstream boundary layer is observed to contribute substantially in the structural development of the jet wake. The upright vortices were seen to originate from the tornado–like critical points on the channel floor shear layer, and subsequently the vortices lift themselves away from the channel floor to merge ultimately with the evolving CVP. Importantly, such merging processes are observed to locally enhance the CVP strength. Following the topological theory of Legendre, the depicted map of computed critical points and the separation lines helps to provide additional insight into the flow mechanism. The computed results clearly demonstrate the entire vortical flow–interaction process to its totality, including all the recent experimental predictions that are made for such flows. Notably, as it was experimentally verified for round jets in cross–flow, in the present configuration too, the flow separation on the channel floor is found to be the basic source of inception of the wall and the upright vortices. The separated flow in the vicinity of different wall vortical corelines joins to form the upright vortices.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77173422","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":"Iterated function system models of digital channels","authors":"D. Broomhead, J. Huke, M. Muldoon, J. Stark","doi":"10.1098/rspa.2004.1336","DOIUrl":"https://doi.org/10.1098/rspa.2004.1336","url":null,"abstract":"This paper introduces a new class of models of digital communications channels. Physically, these models take account of the digital nature of the input. Mathematically, they are iterated function systems. As a consequence of making explicit assumptions about the role of discreteness in the models, it is possible to make general statements about the behaviour of these channels without needing to assume that they are linear. We provide the mathematical background necessary to understand the behaviour of these models and prove a number of results about their observability. We also provide a number of examples intended to demonstrate their connection with linear state–space models, and to suggest how the nonlinear theory might be developed towards applications.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90265135","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":"Double–link expandohedra: a mechanical model for expansion of a virus","authors":"Flórián Kovács, Tibor Tarnai, S. Guest, Patrick W. Fowler","doi":"10.1098/rspa.2004.1344","DOIUrl":"https://doi.org/10.1098/rspa.2004.1344","url":null,"abstract":"Double–link expandohedra are introduced: each is constructed from a parent polyhedron by replacing all faces with rigid plates, adjacent plates being connected by a pair of spherically jointed bars. Powerful symmetry techniques are developed for mobility analysis of general double–link expandohedra, and when combined with numerical calculation and physical model building, they demonstrate the existence of generic finite breathing expansion motions in many cases. For icosahedrally symmetric trivalent parents with pentagonal and hexagonal faces only (fullerene polyhedra), the derived expandohedra provide a mechanical model for the experimentally observed swelling of viruses such as cowpea chlorotic mottle virus (CCMV). A fully symmetric swelling motion (a finite mechanism) is found for systems based on icosahedral fullerene polyhedra with odd triangulation number, T ⩽ 31, and is conjectured to exist for all odd triangulation numbers.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82556657","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":"Upstream–propagating solitary waves and forced internal–wave breaking in stratified flow over a sill","authors":"M. Stastna, W. Peltier","doi":"10.1098/rspa.2004.1316","DOIUrl":"https://doi.org/10.1098/rspa.2004.1316","url":null,"abstract":"We discuss numerical simulations of the flow of an inviscid, density stratified fluid over a broad obstacle of high elevation relative to the finite depth of the fluid layer. The density stratification and topography are chosen to be consistent with recent observations of the flow in Knight Inlet, a fjord in British Columbia, Canada. We find that under certain physically realized conditions the response of the fluid includes large–amplitude, resonantly generated internal solitary waves that propagate upstream, and in some cases break. The post–breaking structures consist of a nearly steady wave envelope and a highly unsteady core that is focused near the surface. The response of the fluid on the lee slope of the topography and further downstream can be understood in terms of the breaking of topographically forced internal waves. The qualitative features of the flow depend to a large degree on whether internal-wave breaking initially occurs in the strong near–surface pycnocline or in the underlying weakly stratified main part of the water column. We discuss the analogy between the oceanic flow and the extensively studied intense downslope windstorms that occur in the atmosphere when internal waves break over the topography that generates them.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78954276","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":"On the complete model with stochastic volatility by Hobson and Rogers","authors":"M. Di Francesco, A. Pascucci","doi":"10.1098/rspa.2004.1370","DOIUrl":"https://doi.org/10.1098/rspa.2004.1370","url":null,"abstract":"In the complete model with stochastic volatility by Hobson and Rogers, preference independent options prices are solutions to degenerate partial differential equations obtained by including additional state variables describing the dependence on past prices of the underlying. In this paper, we aim to emphasize the mathematical tractability of the model by presenting analytical and numerical results comparable with the known ones in the classical Black–Scholes environment.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75755852","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":"Efficient face detection by a cascaded support–vector machine expansion","authors":"Sami Romdhani, P. Torr, Bernhard Schölkopf, Andrew Blake","doi":"10.1098/rspa.2004.1333","DOIUrl":"https://doi.org/10.1098/rspa.2004.1333","url":null,"abstract":"We describe a fast system for the detection and localization of human faces in images using a nonlinear ‘support–vector machine’. We approximate the decision surface in terms of a reduced set of expansion vectors and propose a cascaded evaluation which has the property that the full support–vector expansion is only evaluated on the face–like parts of the image, while the largest part of typical images is classified using a single expansion vector (a simpler and more efficient classifier). As a result, only three reduced–set vectors are used, on average, to classify an image patch. Hence, the cascaded evaluation, presented in this paper, offers a thirtyfold speed–up over an evaluation using the full set of reduced–set vectors, which is itself already thirty times faster than classification using all the support vectors.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80807568","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":"Rayleigh wave with a transverse structure","authors":"A. Kiselev","doi":"10.1098/rspa.2004.1359","DOIUrl":"https://doi.org/10.1098/rspa.2004.1359","url":null,"abstract":"A new simple closed–form solution describing a surface wave propagating along a free, plane surface of a homogeneous solid half–space is presented. The solution, in which in–plane and antiplane motions are combined, linearly depends on the transverse variable. The wave speed is the same as that of the classical Rayleigh wave.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87437378","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":"Pattern analysis and metrology: the extraction of stable features from observable measurements","authors":"P. Scott","doi":"10.1098/rspa.2004.1291","DOIUrl":"https://doi.org/10.1098/rspa.2004.1291","url":null,"abstract":"To extract patterns from observable measurements we need to be able to define and identify stable features in observable measurements that persist in the presence of small artificial features such as noise, measurement errors, etc. The representational theory of measurement is used to define the stability of a measurement procedure. A technique, ‘motif analysis’, is defined to identify and remove ‘insignificant’ features while leaving ‘significant’ features. This technique is formalized and three properties identified that ensure stability. The connection of motif analysis with morphological closing filters is established and used to prove the stability of motif analysis. Finally, a practical metrology example is given of motif analysis in surface texture. Here motif analysis is used to segment a surface into its significant features.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76100339","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}