Inter-Intra Molecular Dynamics as an Iterated Function System

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  • Kaneko Kunihiko
    Department of Basic Science, University of Tokyo and ERATO Complex Systems Biology, JST

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Several extensions of an iterated function system (IFS) are discussed as possible applications to abstract dynamics of units (molecules) with slowly relaxing internal states under frequent collisional interactions. It is found that an increase in the collision frequency leads to successive discrete states that can be analyzed as partial steps to form a Cantor set. By considering the interactions among the units, a self-consistent IFS is derived, which leads to the formation and stabilization of multiple such discrete states. The proposed mechanism, if it exists in a complex polymer under a crowded condition, allows for the kinetically induced formation of multiple states.

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