# Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions Source: [Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions]() Collection index: [llms.txt]() Data updated: 2025-10-27T03:44:48.332Z Authors: Nicolas Levernier, Maxim Dolgushev, Olivier B\\'enichou, Alexander Blumen, Thomas Gu\\'erin, Rapha\\"el Voituriez Published: 2017-01-31T12:05:23.000Z ## Abstract This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete non linear dynamics. It is found that Markovian treatments, based on a Wilemski-Fixman approximation, significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size $N$ and capture radius $b$, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large $N$ is given by $T\\sim N^{3/2}\\ln (N/b^2)$, which differs from the case of the Rouse dynamics where $T\\sim N^{2}$. The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()