Entropic particle transport: Higher-order corrections to the Fick-Jacobs diffusion equation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 83, Issue 5, 2011, Pages

  Martens, S ^a   Schmid, G ^b   Schimansky Geier, L ^a   Hanggi P ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN PARTICLES; CHANNEL GEOMETRY; DIFFUSION EQUATIONS; DIFFUSIVE PARTICLES; EXPECTATION VALUES; FINITE ELEMENT CALCULATIONS; HIGHER ORDER; NUMERICAL RESULTS; PARTICLE TRANSPORT; PERIOD LENGTH; PROBABILITY DENSITIES; SIDE WALLS; THREE-DIMENSIONAL CHANNELS; TRANSPORT VELOCITY; UNIFORM FORCE;

ASYMPTOTIC ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION;

DIFFUSION;

EID: 79961058890     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.051135     Document Type: Article

References (49)

1. P. S. Burada, P. Hänggi, F. Marchesoni, G. Schmid, and P. Talkner, ChemPhysChem. 1439-4235 10.1002/cphc.200800526 10, 45 (2009).
2. P. Hänggi and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.387 81, 387 (2009).
3. F. Keil, R. Krishna, and M. Coppens, Rev. Chem. Eng. RCEGD6 0167-8299 10.1515/REVCE.2000.16.2.71 16, 71 (2000).
4. C. Kettner, P. Reimann, P. Hänggi, and F. Müller, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.312 61, 312 (2000).
5. C. Dekker, Nature Nanotech. RCEGD6 1748-3387 10.1038/nnano.2007.27 2, 209 (2007). (Pubitemid 46739810)
6. U. Keyser, B. Koeleman, S. V. Dorp, D. Krapf, R. Smeets, S. Lemay, N. Dekker, and C. Dekker, Nature Phys. RCEGD6 1745-2473 10.1038/nphys344 2, 473 (2006). (Pubitemid 44022563)
7. S. Howorka and Z. Siwy, Chem. Soc. Rev. RCEGD6 0306-0012 10.1039/b813796j 38, 2360 (2009).
8. D. Pedone, M. Langecker, A. M. Muenzer, R. Wei, R. D. Nagel, and U. Rant, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/22/45/454115 22, 454115 (2010).
9. M. Jacobs, Diffusion Processes (Springer, New York, 1967), p. 68.
10. R. Zwanzig, J. Chem. Phys. 0022-3654 10.1021/j100189a004 96, 3926 (1992).
11. D. Reguera, G. Schmid, P. S. Burada, J. M. Rubi, P. Reimann, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.130603 96, 130603 (2006).
12. A. M. Berezhkovskii, M. A. Pustovoit, and S. M. Bezrukov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2719193 126, 134706 (2007). (Pubitemid 46550263)
13. P. S. Burada, G. Schmid, D. Reguera, J. M. Rubi, and P. Hänggi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.051111 75, 051111 (2007). (Pubitemid 47001008)
14. P. S. Burada, G. Schmid, P. Talkner, P. Hänggi, D. Reguera, and J. M. Rubi, BioSystems BSYMBO 0303-2647 10.1016/j.biosystems.2008.03.006 93, 16 (2008).
15. P. Kalinay and J. K. Percus, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.041203 74, 041203 (2006). (Pubitemid 44536617)
16. R. M. Bradley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.061142 80, 061142 (2009).
17. P. Kalinay, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.031106 80, 031106 (2009).
18. W. Riefler, G. Schmid, and P. Hänggi, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/22/45/454109 22, 454109 (2010).
19. D. Mondal and D. S. Ray, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.032103 82, 032103 (2010).
20. F. Marchesoni, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3402779 132, 166101 (2010).
21. M. Borromeo and F. Marchesoni, Chem. Phys. CMPHC2 0301-0104 10.1016/j.chemphys.2010.03.022 375, 536 (2010).
22. P. Hänggi, F. Marchesoni, S. Savel'ev, and G. Schmid, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.041121 82, 041121 (2010).
23. A. M. Berezhkovskii and L. Dagdug, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3489375 133, 134102 (2010).
24. A. M. Berezhkovskii, L. Dagdug, Y. A. Makhnovskii, and V. Y. Zitserman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3451115 132, 221104 (2010).
25. P. Kalinay and J. K. Percus, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.031143 82, 031143 (2010).
26. H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer, Berlin, 1989).
27. P. Hänggi and H. Thomas, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(82)90045-X 88, 207 (1982).
28. H. Brenner and D. A. Edwards, Macrotransport Processes (Butterworth-Heinemann, Boston, 1993).
29. N. Laachi, M. Kenward, E. Yariv, and K. D. Dorfman, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/80/50009 80, 50009 (2007).
30. E. Yariv and K. D. Dorfman, Phys. Fluids PHFLE6 1070-6631 10.1063/1.2710894 19, 037101 (2007). (Pubitemid 46534406)
31. P. Kalinay and J. K. Percus, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1899150 122, 204701 (2005). (Pubitemid 40858514)
32. A. Groisman and S. R. Quake, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.094501 92, 094501 (2004).
33. T. M. Squires and S. R. Quake, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77.977 77, 977 (2005). (Pubitemid 43272528)
34. M. Oliveira, M. Alves, F. Pinho, and G. McKinley, Exp. Fluids EXFLDU 0723-4864 10.1007/s00348-007-0306-2 43, 437 (2007). (Pubitemid 47293415)
35. F. Marchesoni and S. Savel'ev, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.011120 80, 011120 (2009).
36. P. S. Burada, Y. Li, W. Riefler, and G. Schmid, Chem. Phys. CMPHC2 0301-0104 10.1016/j.chemphys.2010.03.019 375, 514 (2010).
37. R. L. Stratonovich, Radiotekh. Elektron. (Moscow) 3, 497 (1958).
38. P. S. Burada, G. Schmid, D. Reguera, M. H. Vainstein, J. M. Rubi, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.130602 101, 130602 (2008).
39. P. S. Burada, G. Schmid, D. Reguera, J. M. Rubi, and P. Hänggi, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2009-00051-5 69, 11 (2009).
40. D. Reguera and J. M. Rubi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.061106 64, 061106 (2001).
41. P. S. Burada and G. Schmid, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.051128 82, 051128 (2010).
42. X. Wang and G. Drazer, Phys. Fluids PHFLE6 1070-6631 10.1063/1.3226100 21, 102002 (2009).
43. I. M. Sokolov, Eur. J. Phys. EJPHD4 0143-0807 10.1088/0143-0807/31/6/005 31, 1353 (2010).
44. P. Kalinay and J. K. Percus, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.031109 83, 031109 (2011).
45. B. Lindner, M. Kostur, and L. Schimansky-Geier, Fluct. Noise Lett. EJPHD4 0219-4775 10.1142/S0219477501000056 1, R25 (2001).
46. P. S. Burada, G. Schmid, and P. Hänggi, Philos. T. R. Soc. Lond. A PTRMAD 1364-503X 10.1098/rsta.2009.0068 367, 3157 (2009).
47. P. Hänggi and F. Marchesoni, Chaos CHAOEH 1054-1500 10.1063/1.1895505 15, 026101 (2005). (Pubitemid 43127625)
48. S. Lifson and J. Jackson, J. Phys. Chem. JCPSA6 0021-9606 10.1063/1.1732899 36, 2410 (1962).
49. O. Pironneau, F. Hecht, and J. Morice, "freefem++", [www.freefem.org].