Polymers and manifolds in static random flows: a renormalization group study

Details Polymers and manifolds in static random flows: a renormalization group study Polymers and manifolds in static random flows: a renormalization group study

1998-08-30

arxiv.org/abs/cond-mat/9808330v2

Nucl.Phys.B552:529-598,1999

Physics

Condensed Matter

Final version, some explications added and misprints corrected (69 pages latex, 40 eps-figures included)

Scientific paper

10.1016/S0550-3213(99)00179-0

We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for directed polymers (each monomer sees a different flow) and for d < 6 for isotropic polymers (each monomer sees the same flow) and more generally for d2 and the velocity versus applied force characteristics is sublinear, i.e. at small forces v(f) f^phi with phi > 1. It indicates that this new state is glassy, with dynamically generated barriers leading to trapping, even by a divergenceless (transversal) flow. For random flows with long-range (LR) correlations, we find continuously varying exponents with the ratio gL/gT of potential to transversal disorder, and interesting crossover phenomena between LR and SR behavior. For isotropic polymers new effects (e.g. a sign change of zeta - zeta_0) result from the competition between localization and stretching by the flow. In contrast to purely potential disorder, where the dynamics gets frozen, here the dynamical exponent z is not much larger than 2, making it easily accessible by simulations. The phenomenon of pinning by transversal disorder is further demonstrated using a two monomer ``dumbbell'' toy model.

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