- Access by Xinjiang University
Moment expansion for mapping of the confined diffusion
Phys. Rev. E 87, 032143 – Published 20 March, 2013
DOI: https://doi.org/10.1103/PhysRevE.87.032143
Abstract
The mapping of diffusion in a 2D channel with varying cross section onto the longitudinal coordinate is revisited. We present an algorithm based on construction of a specific hierarchy of equations for the transverse moments of the 2D density. Elimination of all the moments but the zeroth one, the 1D density , results in the mapped equation. Our calculation validates the earlier mapping procedure [P. Kalinay and J. K. Percus, Phys. Rev. E 74, 041203 (2006); P. Kalinay and J. K. Percus, Phys. Rev. E 78, 021103 (2008)], presuming existence of the backward mapping operator, and it naturally arrives at the extended Fick-Jacobs equation [D. Reguera and J. M. Rubì, Phys. Rev. E 64, 061106 (2001)] in the stationary flow, without any phenomenological conjectures.
Article Text
References (22)
- M. H. Jacobs, Diffusion Processess (Springer, New York, 1967).
- R. Zwanzig, J. Phys. Chem. 96, 3926 (1992).
- D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001).
- P. Kalinay and J. K. Percus, J. Chem. Phys. 122, 204701 (2005).
- P. Kalinay and J. K. Percus, J. Stat. Phys. 123, 1059 (2006).
- P. Kalinay and J. K. Percus, Phys. Rev. E 74, 041203 (2006).
- N. Laachi, M. Kenward, E. Yariv, and K. D. Dorfman, Europhys. Lett. 80, 50009 (2007).
- E. Yariv and K. D. Dorfman, Phys. Fluids 19, 037101 (2007).
- R. M. Bradley, Phys. Rev. E 80, 061142 (2009).
- S. Martens, G. Schmid, L. Schimansky-Geier, and P. Hänggi, Phys. Rev. E 83, 051135 (2011); Chaos 21, 047518 (2011).
- P. Kalinay and J. K. Percus, Phys. Rev. E 78, 021103 (2008).
- A. M. Berezhkovskii, M. A. Pustovoit, and S. M. Bezrukov, J. Chem. Phys. 126, 134706 (2007).
- I. Pineda, M. V. Vazquez, A. M. Berezhkovskii, and L. Dagdug, J. Chem. Phys. 135, 224101 (2011); L. Dagdug and I. Pineda, ibid. 137, 024107 (2012).
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 2007).
- B- Q. Ai and L-G. Liu, Phys. Rev. E 74, 051114 (2006); J. Chem. Phys. 128, 024706 (2008).
- F. Marchesoni and S. Savel'ev, Phys. Rev. E 80, 011120 (2009).
- P. Kalinay, Phys. Rev. E 80, 031106 (2009).
- D. Reguera, G. Schmid, P. S. Burada, J. M. Rubì, P. Reimann, and P. Hänggi, Phys. Rev. Lett. 96, 130603 (2006).
- P. Kalinay, Phys. Rev. E 84, 011118 (2011).
- P. S. Burada, G. Schmid, D. Reguera, M. H. Vainstein, J. M. Rubì, and P. Hänggi, Phys. Rev. Lett. 101, 130602 (2008).
- P. Kalinay and J. K. Percus, J. Stat. Phys. 148, 1135 (2012).
- G. Wilemski, J. Stat. Phys. 14, 153 (1976).