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Systems with competing energy scales are widespread and exhibit
rich and subtle behaviour, although their systematic study is a
relatively recent activity. This text presents lectures given at a
NATO Advanced Study Institute reviewing the current knowledge and
understanding of the subject, particularly with regard to phase
transitions and dynamics, at an advanced tutorial level. Both
general and specific aspects are considered, with competitions
having several origins; differences in intrinsic interactions,
interplay between intrinsic and extrinsic effects, such as geometry
and disorder; irreversibility and non-equilibration. Among the
specific physical application areas are supercooled liquids and
glasses, high-temperature superconductors, flux or vortex pinning
and motion, charge density waves, domain growth and coarsening, and
electron solidification.
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