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Care is needed with algorithms for computer simulations of the Brownian motion of complex systems, such as colloidal and macromolecular systems which have internal degrees of freedom describing changes in configuration. Problems can arise when the diffusivity or the inertia changes with the configuration of the system. There are some problems in replacing very stiff bonds by rigid constraints. These problems and their resolution are illustrated by some artificial models; firstly in one dimension, then in the neighbourhood of an ellipse in two dimensions and finally for the trimer polymer molecule.
Grassia et al. (Tue,) studied this question.
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