Intermittent Brownian dynamics over a rigid strand: Heavily tailed relocation statistics in a simple geometry

Pierre Levitz (1) , Michel Zinsmeister (2) , Patrick Davidson (3) , Doru Constantin (3) , Olivier Poncelet (4)

1 LPMC - Laboratoire de physique de la matière condensée
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 LPS - Laboratoire de Physique des Solides
4 LITEN - Laboratoire d'Innovation pour les Technologies des Energies Nouvelles et les nanomatériaux

We analyze the intermittent Brownian dynamics (a succession of adsorption and bulk relocation steps) of a test particle over a single strand. We propose an analytic expression of the relocation time distribution at all times. We show that this distribution has a nontrivial heavily tailed statistics at long time with a diverging average relocation time. In order to experimentally probe this first passage statistics, we follow the intermittent Brownian dynamics of water molecules over long and stiff imogolite mineral strands, using a field cycling NMR dispersion technique. Our analytic derivation is found to be in good agreement with experimental data on a large domain of observation. Implications for the efficiency of a search strategy on a single filament are then discussed and the importance of the confinement and/or the finite size effect is emphasized.

Domaines: Matière Molle [cond-mat.soft]

Pierre Levitz, Michel Zinsmeister, Patrick Davidson, Doru Constantin, Olivier Poncelet. Intermittent Brownian dynamics over a rigid strand: Heavily tailed relocation statistics in a simple geometry. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78, pp.030102(R). ⟨10.1103/PhysRevE.78.030102⟩. ⟨hal-00430263⟩