Bridging the Scales Between Discrete and Continuum Dislocation Models

  • Patrick van MeursEmail author
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 26)


We prove the many-particle limit passage of interacting particle systems described by gradient flows . The limiting equation is a gradient flow which describes the evolution of the particle density. Our proof methods rely on variational techniques such as \(\varGamma \) -convergence of the particle configuration energies and stability of gradient flows. The interacting particle systems under consideration model the motion of dislocations in metals. Since the collective motion of dislocations is the main driving force of plastic deformation of metals, we aim to contribute with our analysis to the current understanding of plasticity.


Gradient Flow Interact Particle System Dislocation Wall Discrete Dislocation Finite Borel Measure 
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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Kanazawa UniversityKanazawaJapan

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