Intermittent Brownian dynamics over a rigid strand: heavily tailed relocation statistics in a simple geometry.
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.
Physique de la Matière Condensée, Ecole Polytechnique, CNRS 91128 Palaiseau, France. pierre.levitz@polytechnique.edu
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P
Levitz
M
M
Zinsmeister
P
P
Davidson
D
D
Constantin
O
O
Poncelet