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Pré-Publication, Document De Travail Année : 2022

Numerical simulations of confined Brownian motion

Elodie Millan
  • Fonction : co premier-auteur
  • PersonId : 1146374
Maxime Lavaud
  • Fonction : co premier-auteur
  • PersonId : 750901
  • IdHAL : maxime-lavaud

Résumé

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. Here, we present efficient, broadrange and quantitative numerical simulations of a such a problem. Specifically, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant spherical colloid within a viscous fluid confined by 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 first moments. In particular, we propose a convenient method to compute high-order cumulants by reducing convergence problems, and employ it to characterize the inherent non-Gaussianity of the process.
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Dates et versions

hal-03832770 , version 1 (27-10-2022)
hal-03832770 , version 2 (06-03-2023)

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Elodie Millan, Maxime Lavaud, Yacine Amarouchene, Thomas Salez. Numerical simulations of confined Brownian motion. 2022. ⟨hal-03832770v1⟩
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