Boundaries, interfaces, and transitions
著者
書誌事項
Boundaries, interfaces, and transitions
（CRM proceedings & lecture notes, v. 13）
American Mathematical Society, c1998
- : pbk
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注記
Includes bibliographical references
内容説明・目次
内容説明
There is currently considerable mathematical interest and very real potential for applications in using geometry in the design, identification and control of technological processes. Geometry plays the role of a design variable in the shape optimization of mechanical parts. It also appears as a control variable in optimal swimming, shape control of aircraft wings or stabilization of membranes and plates by periodic variations of the boundary. As it is used as a design or control variable, it often undergoes 'mutations' as in the microstructures of materials, crystal growth, image processing or the texture of objects which involve relaxations of classical geometry and geometrical entities. In other areas, such as free and moving boundary problems, the understanding of the underlying phenomena is very much related to the geometric properties of the fronts and the nature of the nonlinearities involved.This book brings together tools that have been developed in a priori distant areas of mathematics, mechanics and physics. It provides coverage of selected contemporary problems in the areas of optimal design, mathematical models in material sciences, hysteresis, superconductivity, phase transition, crystal growth, moving boundary problems, thin shells and some of the associated numerical issues.
目次
The transition to turbulence via turbulent bursts by K. Coughlin Intrinsic differential geometric methods in the asymptotic analysis of linear thin shells by M. C. Delfour Shape analysis via distance functions: Local theory by M. C. Delfour and J.-P. Zolesio Six lectures on shape memory by I. Muller Six lectures on superconductivity by J. Rubinstein Front propagation by H. M. Soner Six talks on hysteresis by A. Visintin Dynamic metastability and singular perturbations by M. J. Ward Dendrites, fingers, interfaces and free boundaries by J.-J. Xu.
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