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LMS Invited Lecturer
Professor Knobloch will deliver ten 45 minute lecures on spatially localised structures. The content of these will be as follows:
Introduces observations of: Ferrofluid peaks, spot formation in chemical systems, vortices, oscillons, etc and discusses defects, holes and fronts as localized structures (LS).
The Swift-Hohenberg equation (SH23): numerics of the snaking region, origin of pinning re- gion/analogy with phase transitions, geometrical explanation of snaking and its relation to pinning, other inhabitants of the pinning region (multipulse states etc), wavenumber selection, depinning and front motion. Swift-Hohenberg equation (SH35): brief discus- sion, including collapsed snaking.
Bifurcations in spatially reversible systems, 1:1 re- versible Hopf bifurcation, exponential asymptotics, termination of the snaking branches and finite domain effects.
Stripes, targets vs spots, localized hexagons and lozenge-like structures (worms).
Broken translation invariance: finite domain effects; Broken reversibility: drifting pulses; Broken variational structure.
Oscillons, holes and the forced complex Ginzburg-Landau equation for the 1:1 and 2:1 temporal resonance, higher order resonances, defect-mediated snaking.
Doubly diffusive sys- tems, Binary fluid convection, Marangoni convection, Plane Couette flow, Generalized Korteweg-de Vries equation.
Reaction-diffusion systems, Grey-Scott model, spots and spot replication in 1D and 2D, snaking of stationary and traveling pulses.
Solitons in nonlinear optics, melting of soliton lattices, writing and erasing solitons, and buckling in structural mechanics. Novel applications: liquid films, vortices, defects etc.