Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems

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

Volumn 81, Issue 2, 2010, Pages

  Yuste, S Bravo ^a   Borrego, R ^a   Abad, E ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORBING BOUNDARIES; ANOMALOUS DIFFUSION; ANOMALOUS DIFFUSION EXPONENT; DECAY MODE; DIFFUSION PROBLEMS; DIFFUSIVE MOTIONS; DIVERGENT SERIES; FRACTIONAL DIFFUSION EQUATION; HIGH DIMENSIONS; INITIAL CONDITIONS; LAPLACE TRANSFORM METHOD; LONG-TIME DECAY; MEAN-SQUARE DISPLACEMENT; MOTION OF PARTICLES; NUMERICAL SIMULATION; RADIAL SYMMETRYS; SEPARATION OF VARIABLES; SOLUTION APPROACH; SPATIAL MODES; STEADY STATE; SUBDIFFUSION; SURVIVAL PROBABILITIES; TIME DOMAIN; TIME REGIME;

COMPUTER SIMULATION; EQUATIONS OF MOTION; LAPLACE TRANSFORMS;

DIFFUSION;

EID: 76649130197     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.021105     Document Type: Article

References (46)

1. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
2. Applications of Fractional Calculus in Physics, edited by, R. Hilfer, (World Scientific, Singapore, 2000).
3. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
4. Anomalous Transport: Foundations and Applications, edited by, R. Klages, G. Radons, and, I. M. Sokolov, (Wiley-VCH, Weinheim, 2008).
5. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
6. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). 10.1088/0305-4470/37/31/R01
7. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E 61, 132 (2000). 10.1103/PhysRevE.61.132
8. E. Barkai, Phys. Rev. E 63, 046118 (2001). 10.1103/PhysRevE.63.046118
9. S. B. Yuste and L. Acedo, Physica A 336, 334 (2004). 10.1016/j.physa. 2003.12.048
10. S. B. Yuste and K. Lindenberg, Phys. Rev. E 72, 061103 (2005). 10.1103/PhysRevE.72.061103
11. S. B. Yuste, J. J. Ruiz-Lorenzo, and K. Lindenberg, Phys. Rev. E 74, 046119 (2006). 10.1103/PhysRevE.74.046119
12. S. B. Yuste and K. Lindenberg, Phys. Rev. E 76, 051114 (2007). 10.1103/PhysRevE.76.051114
13. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford University Press, Oxford, 1959).
14. N. S. Goel and N. Richter-Dyn, Stochastic Models in Biology (Academic Press, New York, 1974).
15. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, New York, 2001).
16. B. Ya. Balagurov and V. G. Vaks, Sov. Phys. JETP 38, 968 (1974).
17. M. D. Donsker and S. R. S. Varadhan, Commun. Pure Appl. Math. 28, 525 (1975) 10.1002/cpa.3160280406
18. M. D. Donsker and S. R. S. Varadhan, Commun. Pure Appl. Math. 32, 721 (1979). 10.1002/cpa.3160320602
19. M. Bramson and J. L. Lebowitz, Phys. Rev. Lett. 61, 2397 (1988) 10.1103/PhysRevLett.61.2397
20. M. Bramson and J. L. Lebowitz, J. Stat. Phys. 62, 297 (1991). 10.1007/BF01020872
21. A. J. Bray and R. A. Blythe, Phys. Rev. Lett. 89, 150601 (2002). 10.1103/PhysRevLett.89.150601
22. R. A. Blythe and A. J. Bray, Phys. Rev. E 67, 041101 (2003). 10.1103/PhysRevE.67.041101
23. J. J. Ruiz-Lorenzo, S. B. Yuste, and K. Lindenberg, J. Phys.: Condens. Matter 19, 065120 (2007). 10.1088/0953-8984/19/6/065120
24. S. B. Yuste, G. Oshanin, K. Lindenberg, O. Bénichou, and J. Klafter, Phys. Rev. E 78, 021105 (2008). 10.1103/PhysRevE.78.021105
25. A. Nagar and P. Pradhan, Physica A 320, 141 (2003). 10.1016/S0378- 4371(02)01651-5
26. R. Borrego, E. Abad, and S. B. Yuste, Phys. Rev. E 80, 061121 (2009). 10.1103/PhysRevE.80.061121
27. B. H. Hughes, Random Walks and Random Environments (Random Walks, Clarendon Press, Oxford, 1995), Vol. 1.
28. G. Mittag-Leffler, Acta Math. 29, 101 (1905) 10.1007/BF02403200
29. Tables of Integral Transform, edited by A. Erdelyi (McGraw Hill, New York, 1954), Vol. I
30. F. Mainardi and R. Gorenflo, J. Comput. Appl. Math. 118, 283 (2000). 10.1016/S0377-0427(00)00294-6
31. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. 82, 3563 (1999). 10.1103/PhysRevLett.82.3563
32. G. H. Hardy, Divergent Series (Oxford University Press, Oxford, 1949).
33. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory 2nd. ed (Springer, New York, 1999)
34. F. M. Fernández, Introduction to Perturbation Theory in Quantum Mechanics (CRC Press, Boca Raton, 2001)
35. G. A. Artega, F. M. Fernández, A. M. Mesón, and E. A. Castro, Physica A 128, 253 (1984) 10.1016/0378-4371(84)90090-6
36. I. I. Fedchenia, J. Phys. A 25, 6733 (1992) 10.1088/0305-4470/25/24/024
37. R. R. Parwani, Int. J. Mod. Phys. A 18, 293 (2003) 10.1142/ S0217751X03013764
38. G. A. Alvarez, C. J. Howls, and H. J. Silverstone, J. Phys. A 35, 4017 (2002). 10.1088/0305-4470/35/18/303
39. H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)
40. V. M. Mostepanenko and N. N. Trunov, Sov. Phys. Usp. 31, 965 (1988) 10.1070/PU1988v031n11ABEH005641
41. E. Elizalde and A. Romeo, Am. J. Phys. 59, 711 (1991) 10.1119/1.16749
42. A. Actor, I. Bender, and J. Reingruber, Fortschr. Phys. 48, 303 (2000). 10.1002/(SICI)1521-3978(200004)48:4<303::AID-PROP303>3.0.CO;2-J
43. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge, 1966).
44. R. Metzler and J. Klafter, Physica A 278, 107 (2000). 10.1016/S0378-4371(99)00503-8
45. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
46. Y. Z. Povstenko, J. Mol. Liq. 137, 46 (2008). 10.1016/j.molliq.2007.03. 006