05.02.2019 (Tuesday)

Mode interactions in complex and disordered patterns

Regular Seminar Alastair Rucklidge (Leeds)

15:00 City U.
room BLG07

Why do some systems organise themselves into well ordered patterns with astonishing symmetry and regularity, while other superficially similar systems produce defects and disorder? In systems where two different length scales are unstable, the nonlinear interaction between the different modes is key: steady complex patterns can be stabilised when the modes act together to reinforce each other. But, if the two types of pattern compete with each other, the outcome can be considerably more complicated: a time-dependent disordered mixture of patterns constantly shifting and changing. In a small domain, the nature of the interaction between a small number of modes on each length scale can readily be computed. In a large domain, each mode can interact with hundreds of other modes, but the overall behaviour still appears to be guided by small-domain considerations.