The mathematics of deforming surfaces : based on the proceedings of a Conference on the Mathematics and Computation of Deforming Surfaces, organized by the Institute of Mathematics and its Applications and held at the University of Cambridge in December 1988
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書誌事項
The mathematics of deforming surfaces : based on the proceedings of a Conference on the Mathematics and Computation of Deforming Surfaces, organized by the Institute of Mathematics and its Applications and held at the University of Cambridge in December 1988
（The Institute of Mathematics and its Applications conference series, new ser.,
Clarendon Press, 1996
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内容説明・目次
内容説明
The mathematics of deformable surfaces covers a wide range of mathematical ideas and techniques and has applications to all kinds of surfaces from those of textile fabrics, to sheet metal, the deformation of balloons, the shape of water waves and air bubbles in water, the shape of flame fronts and density interfaces in turbulent flows, and the effects of turbulent diffusion. The interesting variety of topics discussed included the following: Le M 'e haut 'e and Correc (France) considered the pressure loading and buckling of cyclindrical sheets, and showed how this can be modelled using LF-splines. Lloyd (UK) showed how the special characteristics of textiles can make it difficult to use conventional Finite Element techniques. Peregrine (Bristol) discusses a surface that is an interface between two regions with different physical properties, so that the shape is determined entirely by dynamical processes within two regions. The main section within the conference were: Modelling Deforming Surfaces, The Deformation of Notional Surfaces, and Techniques for Analysing Deforming Interfaces.
This book is intended for research mathematicians and engineers interested in the motion and deformation of surfaces such as changes in the shape of metals and fabrics, the shape of water waves, the effects of turbulent diffusion.
目次
1: Modelling Deforming Surfaces. 2: Modelling axisymmetric thin shells with LF-splines. 3: Approaches to modelling the mechanical properties of fabrics and the representation of fabrics as flexible surfaces using differential geometry. 4: The complex buckling of textile fabrics. 5: Stability of steep unsteady water waves. 6: Deforming surfaces and viscous sintering. 7: The Deformation of Notional Surfaces:. 8: Contour dynamics/surgery. 9: Stretching of line and surface elements in random velocity fields. 10: Moving surfaces in turbulent flows. 11: Techniques for Analysing Deforming Interfaces:. 12: Fourier descriptions for measuring bubble motion and deformation. 13: Extraction of spatial statistics from experimentally visualised cross-sections of a turbulent flame. 14: Geometrical observations of turbulent density interfaces
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