Dislocations are line defects which act as quantised carriers of plastic slip in crystalline materials. Understanding their behaviour in a given crystalline material is therefore key to providing predictive models of plasticity. While the existence of dislocations was postulated in 1934, and confirmed experimentally in the 1950s, much work is still needed to connect our knowledge of the mechanisms at the atomistic scale with plastic processes observed at the centimetre scale. In this talk, I will present a mathematical perspective on recent progress in transferring information between atomistic and continuum theories which model dislocations. Topics I plan to discuss include boundary conditions for atomistic simulation, mobility laws for dislocation motion at finite temperature, and semi-discrete continuum models of dislocation dynamics.
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