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Register a new userA scale-free network hidden in the collapsing polymer
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Alkan Kabak\\c{c}io\\u{g}lu
Publication date
2004
fields
Physics
and research's language is
English
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We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $gamma = 1/(2-c)$ up to a cut-off degree $d_c propto L^{2-c}$, where $c$ is the loop exponent for dense polymers ($c=11/8$ in two dimensions) and $L$ is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.
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We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {em anomalous} diffusive behavior even in the {em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $alpha = 2/(2 u +2 - gamma_1)$, where $ u$ is the Flory exponent and $gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $tau propto f^{-1}N^{frac{2}{alpha} -1}$. Also the corresponding time dependent statistical moments, $< s(t) > propto t^{alpha}$ and $< s(t)^2 > propto t^{2alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.
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