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Numerical simulations of confined Brownian-yet-non-Gaussian motion

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Abstract

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.

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Data produced for this article are available upon reasonable request to the authors.

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Acknowledgements

The authors thank Arthur Alexandre, Nicolas Fares, Yann Louyer, Thomas Guérin and David Dean, for interesting discussions. They acknowledge financial support from the European Union through the European Research Council under EMetBrown (ERC-CoG-101039103) grant. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. The authors also acknowledge financial support from the Agence Nationale de la Recherche under EMetBrown (ANR-21-ERCC-0010-01), Softer (ANR-21-CE06-0029), and Fricolas (ANR-21-CE06-0039) grants. Finally, they thank the Soft Matter Collaborative Research Unit, Frontier Research Center for Advanced Material and Life Science, Faculty of Advanced Life Science at Hokkaido University, Sapporo, Japan.

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  1. E. Millan and M. Lavaud have equally contributed to this work.

Authors and Affiliations

  1. Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France

    Elodie Millan, Maxime Lavaud, Yacine Amarouchene & Thomas Salez

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  1. Elodie Millan
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Contributions

Y.A. and T.S. conceived the study. E.M. and M.L. performed the research. E.M. wrote the first draft of the manuscript. All the authors discussed the data and contributed to the writing of the manuscript.

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Correspondence to Thomas Salez.

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Millan, E., Lavaud, M., Amarouchene, Y. et al. Numerical simulations of confined Brownian-yet-non-Gaussian motion. Eur. Phys. J. E 46, 24 (2023). https://doi.org/10.1140/epje/s10189-023-00281-y

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