1 research outputs found
Polymers and manifolds in static random flows: a renormalization group study
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
d<d_c(D) in the case of a manifold. This leads to new large scale behavior,
which we analyze using field theoretical methods. We show that all divergences
can be absorbed in multilocal counter-terms which we compute to one loop order.
We obtain the non trivial roughness zeta, dynamical z and transport exponents
phi in a dimensional expansion. For directed polymers we find zeta about 0.63
(d=3), zeta about 0.8 (d=2) and for isotropic polymers zeta about 0.8 (d=3). In
all cases z>2 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.Comment: Final version, some explications added and misprints corrected (69
pages latex, 40 eps-figures included