Extreme-value statistics of work done in stretching a polymer in a gradient flow

Work distribution for unzipping processes

A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature T and subject to an external force f, which couples to the free length L of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force f_{c}(T) in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature T and force f, the full distribution P(L) of free lengths in the thermodynamic limit and show that it is qualitatively very different for ff_{c}. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained P(L) already allows us to derive an analytical expression for the work distribution P(W) in the zipped phase f Collapse

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Affiliation(s)

Peter Werner Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
Alexander K Hartmann Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
Satya N Majumdar Laboratoire de Physique Théorique et Modèles Statistique, Université Paris-Saclay, 91405 Orsay CEDEX, France

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Large-deviation statistics of vorticity stretching in isotropic turbulence

A key feature of three-dimensional fluid turbulence is the stretching and realignment of vorticity by the action of the strain rate. It is shown in this paper, using the cumulant-generating function, that the cumulative vorticity stretching along a Lagrangian path in isotropic turbulence obeys a large deviation principle. As a result, the relevant statistics can be described by the vorticity stretching Cramér function. This function is computed from a direct numerical simulation data set at a Taylor-scale Reynolds number of Re(λ)=433 and compared to those of the finite-time Lyapunov exponents (FTLE) for material deformation. As expected, the mean cumulative vorticity stretching is slightly less than that of the most-stretched material line (largest FTLE), due to the vorticity's preferential alignment with the second-largest eigenvalue of strain rate and the material line's preferential alignment with the largest eigenvalue. However, the vorticity stretching tends to be significantly larger than the second-largest FTLE, and the Cramér functions reveal that the statistics of vorticity stretching fluctuations are more similar to those of the largest FTLE. In an attempt to relate the vorticity stretching statistics to the vorticity magnitude probability density function in statistically stationary conditions, a model Kramers-Moyal equation is constructed using the statistics encoded in the Cramér function. The model predicts a stretched-exponential tail for the vorticity magnitude probability density function, with good agreement for the exponent but significant difference (35%) in the prefactor.