Localised Patterns

Spatially localised patches of pattern can arise spontaneously in experiments in a wide variety of nonlinear media including liquid crystals, autocatalytic chemical reactions, gas discharge systems, optical crystals and in solidification. Perhaps the most intriguing examples of such patterns are small circularly symmetric spatially localised subharmonic excitations (dubbed oscillons) that occur in vertically vibrated granular materials, viscous fluids and plasmas. Recently developed theory predicts the nucleation and pattern selection of multi-dimensional localised structures in quite general continuous media, via the interplay between linear instability and nonlinear bistability, and explains experimental results showing competition between different localised patterns.

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Members

Daniele Avitabile
David Lloyd

Collaborators

Edgar Knobloch (UC, Berkeley)
Bjorn Sandstede (Brown University)