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Hybrid models of dislocations

Adrian P. Sutton

in Physics of Elasticity and Crystal Defects

Published in print:
2020
Published Online:
August 2020
ISBN:
9780198860785
eISBN:
9780191893001
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198860785.003.0007
Subject:
Physics, Condensed Matter Physics / Materials, Crystallography: Physics

In a Volterra dislocation the relative displacement by the Burgers vector appears abruptly in the dislocation core so that the core has no width. This leads to divergent stresses and strains, which ... More


Action-Minimizing Curves for Tonelli Lagrangians

Alfonso Sorrentino

in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical ... More


Weak KAM Theory and Forcing Equivalence

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes weak Kolmogorov-Arnold-Moser (KAM) theory and forcing relation. One change from the standard presentation is that one needs to modify the definition of Tonelli Hamiltonians to ... More


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