Yacov Kantor

Anomalous dynamics of translocation

We study the dynamics of the passage of a polymer through a membrane pore (translocation), focusing on the scaling properties with the number of monomers N. The natural coordinate for translocation is the number of monomers on one side of the hole at a given time. Commonly used models that assume Brownian dynamics for this variable predict a mean (unforced) passage time tau that scales as N2, even in the presence of an entropic barrier. In particular, however, the time it takes for a free polymer to diffuse a distance of the order of its radius by Rouse dynamics scales with an exponent larger than two, and this should provide a lower bound to the translocation time. To resolve this discrepancy, we perform numerical simulations with Rouse dynamics for both phantom (in space dimensions d=1 and 2), and self-avoiding (in d=2) chains. The results indicate that for large N, translocation times scale in the same manner as diffusion times, but with a larger prefactor that depends on the size of the hole. Such scaling implies anomalous dynamics for the translocation process. In particular, the fluctuations in the monomer number at the hole are predicted to be nondiffusive at short times, while the average pulling velocity of the polymer in the presence of a chemical-potential difference is predicted to depend on N.

Anomalous dynamics of forced translocation

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (subdiffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N2 and N1+nu, respectively, where nu is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).

Instabilities of Charged Polyampholytes

We consider polymers formed from a (quenched) random sequence of charged monomers of opposite signs. Such polymers, known as polyampholytes (PAs), are compact when completely neutral and expanded when highly charged. We examine the transition between the two regimes by Monte Carlo simulations, and by analogies to charged drops. We find that the overall excess charge Q is the main determinant of the size of the PAs. A polymer composed of N charges of \ifmmode\pm\else\textpm\fi{}

Improved rigorous bounds on the effective elastic moduli of a composite material

{\mathit{q}}_{0}

Equilibrium shapes of flat knots.

is compact for Q

Pulling knotted polymers

{\mathit{Q}}_{\mathit{c}}

Randomly Charged Polymers: An Exact Enumeration Study

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Polymers with Random Self-Interactions

{\mathit{q}}_{0}

Elastostatic resonances—a new approach to the calculation of the effective elastic constants of composites☆

/ \ensuremath{\surd}N and expanded otherwise. The transition is reminiscent of the Rayleigh shape instability of a charged drop. A uniform excess charge causes the breakup of a fluid drop. We speculate that a uniformly charged polymer stretches out to a necklace shape. The inhomogeneities in charge distort the shape away from an ordered necklace.

Anomalous diffusion with absorbing boundary

Abstract A new method for deriving rigorous bounds on the effective elastic constants of a composite material is presented and used to derive a number of known as well as some new bounds. The new approach is based on a presentation of those constants as a sum of simple poles. The locations and strengths of the poles are treated as variational parameters, while different kinds of available information are translated into constraints on these parameters. Our new results include an extension of the range of validity of the Hashin-Shtrikman bounds to the case of composites made of isotropic materials but with an arbitrary microgeometry. We also use information on the effective elastic constants of one composite in order to obtain improved bounds on the effective elastic constants of another composite with the same or a similar microgeometry.