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Karhunen-Loeve analysis for pattern description in phase separated lipid bilayer systems.

Karhunen-Loeve analysis, a special variant of principal component analysis, is used to describe and analyze the dynamics of self-assembled pattern formation in a mixed phospholipid bilayer. The dominant modes of the evolving heterogeneities in density and dynamics are elucidated. At low temperatures the evolution of patterns can be followed by the principal modes of the systems. We find that the higher modes only evolve after the dominant modes have been established. At high temperatures no such dominant modes are found. So, a clear descriptor of an evolving self-assembled pattern can be identified and its time evolution can be monitored. This analysis suggests, additionally, a new way of determining the equilibration decision in complex systems.