Poster 1. Assessing ° ood risk for canals Robert Arrowsmith British Waterways, Brindley Suite, Willow Grange, Church Road, Watford, Hertfordshire WD17 4QA, UK British Waterways manages 3000 km of canal and river navigations. A methodology for estimating ®ood risk in canals has been developed over the last three years. Flood risk is assessed in two stages. Initial screening uses estimates of catchment in®ow derived from ®ood-studies report (FSR) methods. If the ®ood risk is above a threshold value a more detailed assessment is undertaken using the Flood estimation handbook, following a detailed on-site assessment of the catchment and canal. For both stages all ®ows into the canal are estimated, together with the potential for out®ow over ®ood weirs, etc. The inherent storage within the canal is also taken into account. The methodology provides a basis for prioritizing engineering works to improve the level of protection for the canal. The methodology is ®exible enough to allow changes in ®ood risk to be incorporated as the e¬ects of climate change are better understood.
{"title":"Posters exhibited at The Royal Society Discussion Meeting ‘Flood risk in a changing climate’","authors":"H. Wheater, D. Cox, J. Hunt, P. Mason, Peter Wolf","doi":"10.1098/rsta.2002.1019","DOIUrl":"https://doi.org/10.1098/rsta.2002.1019","url":null,"abstract":"Poster 1. Assessing ° ood risk for canals Robert Arrowsmith British Waterways, Brindley Suite, Willow Grange, Church Road, Watford, Hertfordshire WD17 4QA, UK British Waterways manages 3000 km of canal and river navigations. A methodology for estimating ®ood risk in canals has been developed over the last three years. Flood risk is assessed in two stages. Initial screening uses estimates of catchment in®ow derived from ®ood-studies report (FSR) methods. If the ®ood risk is above a threshold value a more detailed assessment is undertaken using the Flood estimation handbook, following a detailed on-site assessment of the catchment and canal. For both stages all ®ows into the canal are estimated, together with the potential for out®ow over ®ood weirs, etc. The inherent storage within the canal is also taken into account. The methodology provides a basis for prioritizing engineering works to improve the level of protection for the canal. The methodology is ®exible enough to allow changes in ®ood risk to be incorporated as the e¬ects of climate change are better understood.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2002-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87088347","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}
Correction for ‘Integrative models of the heart: achievements and limitations’ by P. J. Hunter, P. Kohl and D. Noble (Phil. Trans. R. Soc. Lond. A 359, 1049–1054. (doi: 10.1098/rsta.2001.0816)). The following two references should be inserted on p. 1054.
{"title":"Correction for Hunter et al., Integrative models of the heart: achievements and limitations","authors":"P. Hunter, P. Kohl, D. Noble","doi":"10.1098/RSTA.2001.2003","DOIUrl":"https://doi.org/10.1098/RSTA.2001.2003","url":null,"abstract":"Correction for ‘Integrative models of the heart: achievements and limitations’ by P. J. Hunter, P. Kohl and D. Noble (Phil. Trans. R. Soc. Lond. A 359, 1049–1054. (doi: 10.1098/rsta.2001.0816)). The following two references should be inserted on p. 1054.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77703960","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}
Highly nonlinear, unilateral effects on interfaces are accurately modelled within the framework of non–smooth mechanics. Unilateral contact and friction interactions are prototypes of the above–mentioned effects. Like all boundary–only nonlinearities, unilateral interfaces are most suitable candidates for the application of boundary–element techniques. Another, possibly more significant, reason for using this approach is the high accuracy of approximation for both boundary displacements and boundary tractions which is attained. Typical cases of unilateral interfaces are studied in this paper by the boundaryelement method. Among them, a unilateral contact interface which leads to LCPBEM (linear complementarity problem–boundary–element method) problems related to variational inequalities, a frictional contact interface which leads to ICP–BEM (implicit complementarity problem–boundary–element method) problems related to implicit variational inequalities, or quasi–variational inequalities and an adhesive interface which leads to CP–BEM (critical–point–boundary–element method) problems related to hemi–variational inequalities. Appropriate extensions and relevant theoretical questions are briefly discussed in a short appendix.
{"title":"Transient dynamic analysis in layered structures with unilateral interfaces","authors":"G. Stavroulakis, H. Antes","doi":"10.1098/rsta.2001.0907","DOIUrl":"https://doi.org/10.1098/rsta.2001.0907","url":null,"abstract":"Highly nonlinear, unilateral effects on interfaces are accurately modelled within the framework of non–smooth mechanics. Unilateral contact and friction interactions are prototypes of the above–mentioned effects. Like all boundary–only nonlinearities, unilateral interfaces are most suitable candidates for the application of boundary–element techniques. Another, possibly more significant, reason for using this approach is the high accuracy of approximation for both boundary displacements and boundary tractions which is attained. Typical cases of unilateral interfaces are studied in this paper by the boundaryelement method. Among them, a unilateral contact interface which leads to LCPBEM (linear complementarity problem–boundary–element method) problems related to variational inequalities, a frictional contact interface which leads to ICP–BEM (implicit complementarity problem–boundary–element method) problems related to implicit variational inequalities, or quasi–variational inequalities and an adhesive interface which leads to CP–BEM (critical–point–boundary–element method) problems related to hemi–variational inequalities. Appropriate extensions and relevant theoretical questions are briefly discussed in a short appendix.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85613481","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}
The paper reviews the frictionless collision problem in rigid–body dynamics. After having established the contact kinematical equations and the impact equations, Newton's and Poisson's impact laws are stated in inequality form for one collision point. This situation is extended by superposition to multi–contact configurations. The concept of superposition together with the equations for a single contact defines the mechanical impact theory. It is valid only within a certain restricted framework specified by several physical assumptions, which are discussed to some extent.
{"title":"On frictionless impact models in rigid-body systems","authors":"C. Glocker","doi":"10.1098/rsta.2001.0857","DOIUrl":"https://doi.org/10.1098/rsta.2001.0857","url":null,"abstract":"The paper reviews the frictionless collision problem in rigid–body dynamics. After having established the contact kinematical equations and the impact equations, Newton's and Poisson's impact laws are stated in inequality form for one collision point. This situation is extended by superposition to multi–contact configurations. The concept of superposition together with the equations for a single contact defines the mechanical impact theory. It is valid only within a certain restricted framework specified by several physical assumptions, which are discussed to some extent.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84783664","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}
The present temporal analysis of impact between two rough and compliant hard bodies employs a lumped–parameter model of the small region of contact that suffers significant deformations. This model represents effects of both normal and tangential compliance by means of discrete elements. By employing specific compliance relations one obtains smooth dynamics of the time–dependent processes of stick and sliding that take place in the contact region during an oblique collision. Effects of compliance and friction on the contact process in an eccentric impact configuration are obtained for planar changes in relative motion and for energy dissipation during impact. The solutions are compared with results obtained with the assumption of negligible compliance in order to determine the range of impact velocities and structural parameters wherein tangential compliance significantly affects the results.
{"title":"Oblique impact with friction and tangential compliance","authors":"W. Stronge, R. James, B. Ravani","doi":"10.1098/rsta.2001.0903","DOIUrl":"https://doi.org/10.1098/rsta.2001.0903","url":null,"abstract":"The present temporal analysis of impact between two rough and compliant hard bodies employs a lumped–parameter model of the small region of contact that suffers significant deformations. This model represents effects of both normal and tangential compliance by means of discrete elements. By employing specific compliance relations one obtains smooth dynamics of the time–dependent processes of stick and sliding that take place in the contact region during an oblique collision. Effects of compliance and friction on the contact process in an eccentric impact configuration are obtained for planar changes in relative motion and for energy dissipation during impact. The solutions are compared with results obtained with the assumption of negligible compliance in order to determine the range of impact velocities and structural parameters wherein tangential compliance significantly affects the results.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87535470","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}
Correction for ‘The infrared predissociation spectrum of H3+’ by F. Kemp, C. E. Kirk and I. R. McNab (Phil. Trans. R. Soc. Lond. A 358, 2403–2418. (doi: 10.1098/rsta.2000.0656)). On p. 2411 the statement ‘An important conclusion to be drawn from theory (Miller et al. 1989), which was largely verified, was that the intense lines in the clumps arose from transitions with small kinetic energy releases’ contains an incorrect reference.
F. Kemp, C. E. Kirk和I. R. McNab对“H3+的红外预解离光谱”的修正。反式。r . Soc。Lond。358, 2403-2418。(doi: 10.1098 / rsta.2000.0656))。在第2411页，“从理论(Miller et al. 1989)得出的一个重要结论是，团块中的强谱线是由小动能释放的跃迁引起的，这一结论在很大程度上得到了验证”，其中包含了一个不正确的引用。
{"title":"Correction for Kemp et al., The infrared predissociation spectrum of H3+","authors":"F. Kemp, C. Kirk, I. Mcnab","doi":"10.1098/RSTA.2001.2000","DOIUrl":"https://doi.org/10.1098/RSTA.2001.2000","url":null,"abstract":"Correction for ‘The infrared predissociation spectrum of H3+’ by F. Kemp, C. E. Kirk and I. R. McNab (Phil. Trans. R. Soc. Lond. A 358, 2403–2418. (doi: 10.1098/rsta.2000.0656)). On p. 2411 the statement ‘An important conclusion to be drawn from theory (Miller et al. 1989), which was largely verified, was that the intense lines in the clumps arose from transitions with small kinetic energy releases’ contains an incorrect reference.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86927400","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}
From the standpoint of mechanics all moving objects, like machines and mechanisms in engineering or animals in biology, are characterized by the kinematics and kinetics of the movable rigid or elastic bodies and by certain constraints, which might be bilateral or unilateral. A complete set of constraints may be interpreted as an abstract mapping of a machine, because constraints are responsible for the functional realization of the designed machine motion. Classical multibody theory includes bilateral constraints. Only recently has multibody theory been extended to unilateral constraints. The consideration of multiple contact processes was outside the domain of solution possibility in the past. Since then potential applications have exploded. This paper gives a survey of these applications.
{"title":"Applications of unilateral multibody dynamics","authors":"F. Pfeiffer","doi":"10.1098/rsta.2001.0912","DOIUrl":"https://doi.org/10.1098/rsta.2001.0912","url":null,"abstract":"From the standpoint of mechanics all moving objects, like machines and mechanisms in engineering or animals in biology, are characterized by the kinematics and kinetics of the movable rigid or elastic bodies and by certain constraints, which might be bilateral or unilateral. A complete set of constraints may be interpreted as an abstract mapping of a machine, because constraints are responsible for the functional realization of the designed machine motion. Classical multibody theory includes bilateral constraints. Only recently has multibody theory been extended to unilateral constraints. The consideration of multiple contact processes was outside the domain of solution possibility in the past. Since then potential applications have exploded. This paper gives a survey of these applications.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74318873","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}
Correction for ‘Frictional chatter in orthogonal metal cutting’ by M. Wiercigroch and A. M. Krivtsov (Phil. Trans. R. Soc. Lond. A 359, 713–738. (doi: 10.1098/rsta.2000.0752)). In l. 4 below eqn (3.4) on p. 717, the equation is incorrect.
{"title":"Correction for Wiercigroch and Krivtsov, Frictional chatter in orthogonal metal cutting","authors":"M. Wiercigroch, A. Krivtsov","doi":"10.1098/rsta.2001.2001","DOIUrl":"https://doi.org/10.1098/rsta.2001.2001","url":null,"abstract":"Correction for ‘Frictional chatter in orthogonal metal cutting’ by M. Wiercigroch and A. M. Krivtsov (Phil. Trans. R. Soc. Lond. A 359, 713–738. (doi: 10.1098/rsta.2000.0752)). In l. 4 below eqn (3.4) on p. 717, the equation is incorrect.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75506988","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}
Hopf bifurcation for smooth systems is characterized by a crossing of a pair of complex conjugate eigenvalues of the linearized problem through the imaginary axis. Since this approach is not at hand for non-smooth systems, we use the geometrical characterization given by the change from an unstable to a stable focus through a centre for a basic (piecewise) linear system. In that way we find two mechanisms for the destabilizing of the basic stationary solution and for the generation of bifurcating periodic orbits: a generation switch of the stability properties or the influence of the unstable subsystem measured by the time of duration spent in the subsystem. The switch between stable and unstable subsystems seems to be a general source of destabilization observed in several mechanical systems. We expect that the features analysed for planar systems will help us to understand higher-dimensional systems as well.
{"title":"Generalized Hopf bifurcation for non-smooth planar systems","authors":"T. Küpper, S. Moritz","doi":"10.1098/rsta.2001.0905","DOIUrl":"https://doi.org/10.1098/rsta.2001.0905","url":null,"abstract":"Hopf bifurcation for smooth systems is characterized by a crossing of a pair of complex conjugate eigenvalues of the linearized problem through the imaginary axis. Since this approach is not at hand for non-smooth systems, we use the geometrical characterization given by the change from an unstable to a stable focus through a centre for a basic (piecewise) linear system. In that way we find two mechanisms for the destabilizing of the basic stationary solution and for the generation of bifurcating periodic orbits: a generation switch of the stability properties or the influence of the unstable subsystem measured by the time of duration spent in the subsystem. The switch between stable and unstable subsystems seems to be a general source of destabilization observed in several mechanical systems. We expect that the features analysed for planar systems will help us to understand higher-dimensional systems as well.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74849872","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}
A. Yodh, Keng-hui Lin, J. Crocker, A. Dinsmore, R. Verma, P. Kaplan
Correction for ‘Entropically driven self-assembly and interaction in suspension’ by A. G. Yodh, K.-H. Lin, J. C. Crocker, A. D. Dinsmore, R. Verma and P. D. Kaplan (Phil. Trans. R. Soc. Lond. A 359, 921–937. (doi: 10.1098/rsta.2000.0810)). On p. 921, the Digital Object Identifier should read 10.1098/rsta.2000.0810.
{"title":"Correction for Yodh et al., Entropically driven self-assembly and interaction in suspension","authors":"A. Yodh, Keng-hui Lin, J. Crocker, A. Dinsmore, R. Verma, P. Kaplan","doi":"10.1098/RSTA.2001.2002","DOIUrl":"https://doi.org/10.1098/RSTA.2001.2002","url":null,"abstract":"Correction for ‘Entropically driven self-assembly and interaction in suspension’ by A. G. Yodh, K.-H. Lin, J. C. Crocker, A. D. Dinsmore, R. Verma and P. D. Kaplan (Phil. Trans. R. Soc. Lond. A 359, 921–937. (doi: 10.1098/rsta.2000.0810)). On p. 921, the Digital Object Identifier should read 10.1098/rsta.2000.0810.","PeriodicalId":20023,"journal":{"name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85264612","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}
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