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Differential Geometry and Continuum Mechanics

  • Gui-Qiang G. Chen
  • Michael Grinfeld
  • R. J. Knops

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 137)

Table of contents

  1. Front Matter
    Pages i-viii
  2. General

    1. Front Matter
      Pages 1-1
  3. Differential Geometry

  4. Defects and Microstructure

    1. Front Matter
      Pages 121-121
    2. G. Capriz, R. J. Knops
      Pages 167-201
  5. Solids

    1. Front Matter
      Pages 253-253
    2. Cristinel Mardare
      Pages 307-342
  6. Fluids and Liquid Crystals

    1. Front Matter
      Pages 343-343
    2. Epifanio G. Virga
      Pages 363-380
  7. Back Matter
    Pages 381-387

About these proceedings

Introduction

This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated.

The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students.

These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.

Keywords

Compensated Compactness Defects Differential Geometry Elasticity Isometric Embeddings Liquid Crystals Microstructure Nonlinear Mechanics Partial Differential Equations Phase Boundaries Riemannian Manifolds Surface Energies (Lipid Bilayer)

Editors and affiliations

  • Gui-Qiang G. Chen
    • 1
  • Michael Grinfeld
    • 2
  • R. J. Knops
    • 3
  1. 1.Radcliffe Observatory QuarterMathematical InstituteOxfordUnited Kingdom
  2. 2.Department of Mathematics and Statistics Livingstone TowerUniversity of StrathclydeGlasgowUnited Kingdom
  3. 3.School of Mathem. and Computer ScienceHeriot-Watt UniversityEdinburghUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-18573-6
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-18572-9
  • Online ISBN 978-3-319-18573-6
  • Series Print ISSN 2194-1009
  • Series Online ISSN 2194-1017
  • Buy this book on publisher's site