Dynamics of heterogeneous hard spheres in a file
Abstract
Normal dynamics in a quasi-one-dimensional channel of length L (→∞) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W∼D-γ for small D , where 0≤γ<1 . The initial spheres’ density ρ is nonuniform and scales with the distance (from the origin) l as ρ∼l-α , 0≤α≤1 . An approximation for the N -particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys ⟨r2⟩∼t(1-γ)/(2c-γ) , where c=1/(1+α) . The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.
- Publication:
-
Physical Review E
- Pub Date:
- September 2010
- DOI:
- 10.1103/PhysRevE.82.031126
- arXiv:
- arXiv:1002.1450
- Bibcode:
- 2010PhRvE..82c1126F
- Keywords:
-
- 05.40.-a;
- 66.30.Pa;
- 87.10.-e;
- Fluctuation phenomena random processes noise and Brownian motion;
- Diffusion in nanoscale solids;
- General theory and mathematical aspects;
- Condensed Matter - Soft Condensed Matter;
- Quantitative Biology - Quantitative Methods
- E-Print:
- Phys. Rev. E 82, 031126 (2010)