4,724 research outputs found
Intra-chain correlation functions and shapes of homopolymers with different architectures in dilute solution
We present results of Monte Carlo study of the monomer-monomer correlation
functions, static structure factor and asphericity characteristics of a single
homopolymer in the coil and globular states for three distinct architectures of
the chain: ring, open and star. To rationalise the results we introduce the
dimensionless correlation functions rescaled via the corresponding mean-squared
distances between monomers. For flexible chains with some architectures these
functions exhibit a large degree of universality by falling onto a single or
several distinct master curves. In the repulsive regime, where a stretched
exponential times a power law form (de Cloizeaux scaling) can be applied, the
corresponding exponents and have been obtained. The exponent
is found to be universal for flexible strongly repulsive coils
and in agreement with the theoretical prediction from improved higher-order
Borel-resummed renormalisation group calculations. The short-distance exponents
of an open flexible chain are in a good agreement with the
theoretical predictions in the strongly repulsive regime also. However,
increasing the Kuhn length in relation to the monomer size leads to their fast
cross-over towards the Gaussian behaviour. Likewise, a strong sensitivity of
various exponents on the stiffness of the chain, or on the number
of arms in star polymers, is observed. The correlation functions in the
globular state are found to have a more complicated oscillating behaviour and
their degree of universality has been reviewed. Average shapes of the polymers
in terms of the asphericity characteristics, as well as the universal behaviour
in the static structure factors, have been also investigated.Comment: RevTeX 12 pages, 10 PS figures. Accepted by J. Chem. Phy
The effect of noise on the dynamics of a complex map at the period-tripling accumulation point
As shown recently (O.B.Isaeva et al., Phys.Rev E64, 055201), the phenomena
intrinsic to dynamics of complex analytic maps under appropriate conditions may
occur in physical systems. We study scaling regularities associated with the
effect of additive noise upon the period-tripling bifurcation cascade
generalizing the renormalization group approach of Crutchfield et al.
(Phys.Rev.Lett., 46, 933) and Shraiman et al. (Phys.Rev.Lett., 46, 935),
originally developed for the period doubling transition to chaos in the
presence of noise. The universal constant determining the rescaling rule for
the intensity of the noise in period-tripling is found to be
Numerical evidence of the expected scaling is
demonstrated.Comment: 9 pages, 4 figure
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