article · 16/07/2013
Active Transport in Dense Diffusive Single-File Systems
Résumé
We study a minimal model of active transport in crowded single-file environments which generalizes the emblematic model of single-file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is biased by an external force, while all other particles of the environment (bath) perform unbiased diffusions. We derive explicit expressions, valid in the limit of high density of bath particles, of the full distribution P-(n)(X) of the TP position and of all its cumulants, for arbitrary values of the bias f and for any time n. Our analysis reveals striking features, such as the anomalous scaling proportional to root n of all cumulants, the equality of cumulants of the same parity characteristic of a Skellam distribution and a convergence to a Gaussian distribution in spite of asymmetric density profiles of bath particles. Altogether, our results provide the full statistics of the TP position and set the basis for a refined analysis of real trajectories of active particles in crowded single-file environments.
Citer cet article
Illien, P., Benichou, O., Mejia-Monasterio, C., Oshanin, G., & Voituriez, R. (2013). Active Transport in Dense Diffusive Single-File Systems. PHYSICAL REVIEW LETTERS, 111(3). https://doi.org/10.1103/PhysRevLett.111.038102@article{Illien2013_233,
author = {Illien, P. and Benichou, O. and Mejia-Monasterio, C. and Oshanin, G. and Voituriez, R.},
year = {2013},
month = {7},
title = {Active Transport in Dense Diffusive Single-File Systems},
journal = {PHYSICAL REVIEW LETTERS},
volume = {111},
number = {3},
abstract = {We study a minimal model of active transport in crowded single-file environments which generalizes the emblematic model of single-file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is biased by an external force, while all other particles of the environment (bath) perform unbiased diffusions. We derive explicit expressions, valid in the limit of high density of bath particles, of the full distribution P-(n)(X) of the TP position and of all its cumulants, for arbitrary values of the bias f and for any time n. Our analysis reveals striking features, such as the anomalous scaling proportional to root n of all cumulants, the equality of cumulants of the same parity characteristic of a Skellam distribution and a convergence to a Gaussian distribution in spite of asymmetric density profiles of bath particles. Altogether, our results provide the full statistics of the TP position and set the basis for a refined analysis of real trajectories of active particles in crowded single-file environments.},
url = {http://www.dx.doi.org/10.1103/PhysRevLett.111.038102},
doi = {10.1103/PhysRevLett.111.038102},
issn = {0031-9007},
}TY - JOUR
AU - Illien, P.
AU - Benichou, O.
AU - Mejia-Monasterio, C.
AU - Oshanin, G.
AU - Voituriez, R.
PY - 2013
DA - 2013/07/16
TI - Active Transport in Dense Diffusive Single-File Systems
JO - PHYSICAL REVIEW LETTERS
VL - 111
IS - 3
SN - 0031-9007
AB - We study a minimal model of active transport in crowded single-file environments which generalizes the emblematic model of single-file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is biased by an external force, while all other particles of the environment (bath) perform unbiased diffusions. We derive explicit expressions, valid in the limit of high density of bath particles, of the full distribution P-(n)(X) of the TP position and of all its cumulants, for arbitrary values of the bias f and for any time n. Our analysis reveals striking features, such as the anomalous scaling proportional to root n of all cumulants, the equality of cumulants of the same parity characteristic of a Skellam distribution and a convergence to a Gaussian distribution in spite of asymmetric density profiles of bath particles. Altogether, our results provide the full statistics of the TP position and set the basis for a refined analysis of real trajectories of active particles in crowded single-file environments.
DO - 10.1103/PhysRevLett.111.038102
UR - http://www.dx.doi.org/10.1103/PhysRevLett.111.038102
ER -