This thesis is concerned with establishing a rigorous, modern
theory of the stochastic and dissipative forces on crystal defects,
which remain poorly understood despite their importance in any
temperature dependent micro-structural process such as the ductile
to brittle transition or irradiation damage. The author first
uses novel molecular dynamics simulations to parameterise an
efficient, stochastic and discrete dislocation model that allows
access to experimental time and length scales. Simulated
trajectories are in excellent agreement with experiment. The author
also applies modern methods of multiscale analysis to extract novel
bounds on the transport properties of these many body systems.
Despite their successes in coarse graining, existing theories are
found unable to explain stochastic defect dynamics. To
resolve this, the author defines crystal defects through projection
operators, without any recourse to elasticity. By rigorous
dimensional reduction, explicit analytical forms are
derived for the stochastic forces acting on crystal defects,
allowing new quantitative insight into the role of thermal
fluctuations in crystal plasticity.
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