Damping function example problem

Firstly, it has been shown that there may be many experimental problems in a direct determination of the experimental fimction. In shear, damping functions obtained from step strain and from step strain rate experiments do not match each other. This poses an important question on the validity of the separability assumption in the short time rai e. Significant departures from this factorization have already been observed in the case of narrow polystyrene fractions by Takahashi et al. [54]. These authors found that time-strain superposition of the linear and nonlinear relaxation moduli was only possible above a cert2un characteristic time. It is interesting to note that this is predicted by the Doi-Edwards theory [10] and according to this theory, this phenomena is attributed to an additional decrease of the modulus connected to a tube contraction process and time-strain separability may hold after this equilibration process has been completed. Other examples of non-separability were also reported by Einaga et al. [55] and more recently by Venerus et al. [56] for solutions. 

The sine form of the damping function leads to another major problem, which lays in the occurrence of undesirable oscillations in transient shear flows (Figure 11). This phenomenon may be misleading for example when modelling instabilities in complex flows, since it is then hardly possible to distinguish between real phenomena and those generated by the model itself. 

For standard problems in the physics and chemistry of condensed matter, such as simple fluids containing rare gas atoms or diatomic molecules, etc., computer simulation considers a small region of matter in full atomistic detail. " For example, for a simple fluid it often is sufficient to simulate a small box containing of the order of 10 atoms, which interact with each other with chemically realistic forces. These methods work because simple fluids are homogeneous on a scale of 10 A already the oscillations in the pair distribution function then are damped out under most circumstances. Also reliable models for the effective forces are usually available from quantum chemistry methods. 

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