Forced translocation of a polymer: dynamical scaling vs. MD-simulation

We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of propagating front of tensile force along the chain backbone, suggested recently by T. Sakaue. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation, "trumpet", "stem-trumpet", etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasi-static approximation), we derive an equation of motion for the tensile front position $X(t)$. We show that the scaling law for the average translocation time $$ changes from $\sim N^{2\nu}/f^{1/\nu}$ to $\sim N^{1+\nu}/f$ (for the free-draining case) as the dimensionless force ${\widetilde f}_{R} = a N^{\nu}f /T$ (where $a$, $N$, $\nu$, $f$, $T$ are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by Molecular Dynamics (MD) simulation. Data from our computer experiment indicates indeed that the translocation scaling exponent $\alpha$ grows with the pulling force ${\widetilde f}_{R}$) albeit the observed exponent $\alpha$ stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations which are neglected in the quasi-static approximation.Comment: 17 pages, 8 figures; figure 5 is new; figures 4 and 6-8 are upgrade

Polymer translocation through a nanopore - a showcase of anomalous diffusion

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {\em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $\alpha = 2/(2\nu+2-\gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {\em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $$, and $- < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev.

Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion

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 $\alpha = 2/(2\nu +2 - \gamma_1)$, where $\nu$ 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, $\propto t^{\alpha}$ and $\propto t^{2\alpha}$ 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.Comment: 6 pages, 4 figures, accepted to Europhys. Lett; some references were supplemented; typos were correcte

Effect of External Noise Correlation in Optical Coherence Resonance

Coherence resonance occurring in semiconductor lasers with optical feedback is studied via the Lang-Kobayashi model with external non-white noise in the pumping current. The temporal correlation and the amplitude of the noise have a highly relevant influence in the system, leading to an optimal coherent response for suitable values of both the noise amplitude and correlation time. This phenomenon is quantitatively characterized by means of several statistical measures.Comment: RevTeX, 4 pages, 7 figure

Design and Manufacture of a Large-Bore 10 T Superconducting Dipole for the CERN Cable Test Facility

A large-bore 10 T superconducting dipole magnet was designed and fabricated in close cooperation between CERN and HMA Power Systems. The dipole has a length of about 1.7 m and an aperture of 88 mm and is composed of two two-layer poles wound with NbTi cables cooled to 1.9 K to reach magnetic inductions close to 10 T. This dipole will be installed at the CERN cable test facility and used as a background field magnet to test LHC superconducting cables. In its large aperture up to four cable samples can be tested at the same time. The mechanical design of the magnet is such that coil prestress variations between warm and cold conditions are kept within 20 MPa. A short model was also built and cooled down in order to check and confirm with test results the mechanical behavior of the dipole. Magnetic measurements, at room temperature, were performed upon its arrival at CERN prior to installation in the test facility. The dipole was recently cooled down and tested. This paper will discuss the design, the main manufacturing steps and the initial test results

Design, Fabrication and Initial Testing of a Large Bore Single Aperture 1 m Long Superconducting Dipole Made with Phenolic Inserts

In the framework of the LHC magnet development programme, a large bore single aperture 1-meter long superconducting dipole has been built in collaboration with HOLEC. The magnet features a single layer coil wound using the LHC main dipole outer layer cable, phenolic inserts, and a keyed two part structural iron yoke. This paper presents the magnetic and mechanical design and optimisation of the magnet. We describe the coil winding and curing, and present the construction and assembly procedures. Finally we report on the mechanical behaviour during assembly and cooling, and present the magnet training behaviour

Testing of the large bore single aperture 1-meter superconducting dipoles made with phenolic inserts

Two identical single aperture 1-metre superconducting dipoles have been built in collaboration with HMA Power Systems and tested at CERN. The 87.8 mm aperture magnets feature a single layer coil wound using LHC main dipole outer layer cable, phenolic spacer type collars, and a keyed two part structural iron yoke. The magnets are designed as models of the D1 separation dipole in the LHC experimental insertions, whose nominal field is 4.5 T at 4.5 K. In this report we present the test results of the two magnets at 4.3 K and 1.9 K

Dynamics of forced biopolymer translocation

We present results from our simulations of biopolymer translocation in a solvent which explain the main experimental findings. The forced translocation can be described by simple force balance arguments for the relevant range of pore potentials in experiments and biological systems. Scaling of translocation time with polymer length varies with pore force and friction. Hydrodynamics affects this scaling and significantly reduces translocation times.Comment: Published in: http://www.iop.org/EJ/article/0295-5075/85/5/58006/epl_85_5_58006.htm