Transport and scaling in quenched two- and three-dimensional Lévy quasicrystals

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

Volumn 84, Issue 2, 2011, Pages

  Buonsante, P ^a   Burioni, R ^a,b   Vezzani, A ^a,c  

^a UNIVERSITY OF PARMA   (Italy)

^b INFN SEZIONE DI ROMA   (Italy)

^c CNR   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC BEHAVIORS; DIFFUSION PROPERTIES; GEOMETRIC PARAMETER; GEOMETRICAL DISTRIBUTION; RANDOM SYSTEMS; SCALING ANALYSIS; SELF-SIMILAR; TRANSMISSION PROBABILITIES;

THREE DIMENSIONAL;

PROBABILITY DISTRIBUTIONS;

EID: 80051615045     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.021105     Document Type: Article

References (38)

1. I. M. Sokolov, J. Mai, and A. Blumen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.857 79, 857 (1997).
2. M. A. Lomholt, T. Ambjörnsson, and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.260603 95, 260603 (2005). (Pubitemid 43061524)
3. M. A. Lomholt, B. van den Broek, S.-M. J. Kalisch, G. J. L. Wuite, and R. Metzler, Proc. Nat. Acad. Sci. PNASA6 0027-8424 10.1073/pnas.0903293106 106, 8204 (2009).
4. A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5655 85, 5655 (2000). (Pubitemid 32090288)
5. T. Geisel, J. Nierwetberg, and A. Zacherl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.616 54, 616 (1985).
6. M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature (London) NATUAS 0028-0836 10.1038/363031a0 363, 31 (1993).
7. J. P. Bouchaud, Theory of Financial Risk (Cambridge University Press, Cambridge, England, 2000).
8. M. A. Lomholt, K. Tal, R. Metzler, and K. Joseph, Proc. Natl. Acad. Sci. PNASA6 0027-8424 10.1073/pnas.0803117105 105, 11055 (2008).
9. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.83.81 83, 81 (2011).
10. A. B. Davis and A. Marshak, J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(2002)059<2713:STCOLT>2.0.CO;2 59, 2713 (2002).
11. D. A. Benson, R. Schumer, M. M. Meerschaert, and S. W. Wheatcraft, Transp. Porous Media TPMEEI 0169-3913 10.1023/A:1006733002131 42, 211 (2001). (Pubitemid 32270340)
12. P. Levitz, Europhys. Lett. 0295-5075 10.1209/epl/i1997-00394-5 39, 593 (1997).
13. M. Palombo, A. Gabrielli, S. De Santis, C. Cametti, G. Ruocco, and S. Capuani, J. Chem. Phys. 0021-9606 10.1063/1.3610367 135, 034504 (2011).
14. P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature (London) NATUAS 0028-0836 10.1038/nature06948 453, 495 (2008). (Pubitemid 351733320)
15. A. Blumen, G. Zumofen, and J. Klafter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.3964 40, 3964 (1989).
16. J. Klafter, A. Blumen, G. Zumofen, and M. Shlesinger, Physica A PHYADX 0378-4371 10.1016/0378-4371(90)90416-P 168, 637 (1990).
17. M. Mezard, P. G, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
18. G. Zumofen and J. Klafter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.47.851 47, 851 (1993).
19. A. Zoia, A. Rosso, and M. Kardar, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.021116 76, 021116+ (2007). (Pubitemid 47311842)
20. H. C. Fogedby, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73. 2517 73, 2517 (1994).
21. R. Kutner and P. Maass, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/ 11/010 31, 2603 (1998). (Pubitemid 128042657)
22. M. Schulz, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00474-7 298, 105 (2002).
23. P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.011101 82, 011101 (2010);
24. J. Bartolotti, K. Vynck, and D. S. Wiersma, Phys. Rev. Lett. PLEEE8 1539-3755 10.1103/PhysRevE.82.011101 105, 163902 (2010).
25. E. Barkai, V. Fleurov, and J. Klafter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.1164 61, 1164 (2000).
26. C. W. J. Beenakker, C. W. Groth, and A. R. Akhmerov, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.024204 79, 024204 (2009).
27. R. Burioni, L. Caniparoli, and A. Vezzani, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.060101 81, 060101 (2010).
28. R. Burioni, L. Caniparoli, S. Lepri, and A. Vezzani, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.011127 81, 011127 (2010).
29. A. Vezzani, R. Burioni, L. Caniparoli, and S. Lepri, Philos. Mag. PYLAAG 1478-6435 10.1080/14786435.2010.536179 91, 1987 (2011).
30. D. ben Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, England, 2000).
31. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
32. M. E. Cates, J. Phys. JPRAAJ 0368-3842 10.1051/jphys:019850046070105900 46, 1059 (1985).
33. P. Castiglione, A. Mazzino, P. Muratore-Ginanneschi, and A. Vulpiani, Physica D: Nonlinear Phenom. PDNPDT 0167-2789 10.1016/S0167-2789(99)00031-7 134, 75 (1999).
34. Y. Gefen, B. B. Mandelbrot, and A. Aharony, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45.855 45, 855 (1980).
35. A different average follows from allowing the random walk to start at any lattice coordinate, i.e., within the empty regions as well. However, it is clear that in the thermodynamic limit the starting sites within such regions would dominate the average, and the dynamics would be ballistic.
36. S. Alexander and R. Orbach, J. Phys. Lett. JPSLBO 0302-072X 10.1051/jphyslet:019820043017062500 43, 625 (1982).
37. K. Hattori, T. Hattori, and H. Watanabe, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.92.108 92, 108 (1987).
38. P. Buonsante, R. Burioni, and A. Vezzani (unpublished).