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Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics
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Stochastic Dynamics of Crystal Defects (Hardcover, 1st ed. 2015)
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Stochastic Dynamics of Crystal Defects (Hardcover, 1st ed. 2015)
Series: Springer Theses
Expected to ship within 10 - 15 working days
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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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