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In this talk I will address some of our recent results on modelling the excited state dynamics and the resulting optical response of Frenkel excitons in self-assembled molecular J-aggregates. The focus will be on linear and tubular aggregates. Effects of disorder, weak interactions with vibrations in the host medium, as well as vibronic effects will be addressed. Throughout the talk connections with experiment will be made. I will discuss specific (nonlinear) optical spectroscopies to probe particular aspects of the energetics and the dynamics of the Frenkel excitons in these supramolecular systems. |