Non-Markovian Fokker-Planck equation: Solutions and first passage time distribution

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

Volumn 73, Issue 3, 2006, Pages

  Assis, P C ^a   De Souza, R P ^b   Da Silva, P C ^a   Da Silva, L R ^a   Lucena, L S ^a   Lenzi, E K ^b  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

^b STATE UNIVERSITY OF MARINGÁ   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

FOKKER-PLANCK EQUATION; PASSAGE TIME DISTRIBUTION;

DIFFUSION; NUMERICAL ANALYSIS;

MARKOV PROCESSES;

EID: 33644695068     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.032101     Document Type: Article

References (48)

1. I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.041101 66, 041101 (2002).
2. D. Campos, V. Méndez, and J. Fort, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.031115 69, 031115 (2004).
3. B. OShaughnessy and I. Procaccia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.455 54, 455 (1985).
4. H. E. Roman, Fractals FRACEG 0218-348X 12, 149 (2004);
5. R. Metzler, W. G. Glöckle, and T. F. Nonnenmacher, Physica A PHYADX 0378-4371 10.1016/0378-4371(94)90064-7 211, 13 (1994).
6. E. K. Lenzi, R. S. Mendes, J. S. Andrade, L. R. da Silva, and L. S. Lucena, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.052101 71, 052101 (2005).
7. Kwok Sau Fa and E. K. Lenzi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.012101 71, 012101 (2005).
8. Kwok Sau Fa and E. K. Lenzi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.061105 67, 061105 (2003).
9. A. A. Vedenov, Rev. Plasma Phys. RPLPAK 0080-2050 3, 229 (1967).
10. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.2717 61, 2717 (2000).
11. H. Fujisaka, S. Grossmann, and S. Thomae, Z. Naturforsch. Teil A ZTAKDZ 0340-4811 40, 867 (1985).
12. D. Ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, New York, 2000);
13. S. Havlin and D. Ben-Avraham, Adv. Phys. ADPHAH 0001-8732 10.1080/00018738700101072 36, 695 (1987).
14. J. Crank, The Mathematics of Diffusion (Oxford University Press, London, 1956).
15. S. B. Yuste and K. Lindenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.118301 87, 118301 (2001);
16. S. B. Yuste and K. Lindenberg, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(02)00546-3 284, 169 (2002).
17. J. Yu and S. H. Dong, Phys. Lett. A PYLAAG 0375-9601 325, 194 (2004);
18. C. Chen and Z. D. Chen, Phys. Lett. A PYLAAG 0375-9601 331, 312 (2004).
19. R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000).
20. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
21. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators (Springer, New York, 2002).
22. G. M. Zaslavsky, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00331- 9 371, 461 (2002).
23. D. Kusnezov, A. Bulgac, and G. D. Dang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1136 82, 1136 (1999).
24. J. Klafter, M. F. Shlesinger, and G. Zumofen, Phys. Today PHTOAD 0031-9228 49 (2), 33 (1996).
25. A. V. Chechkin, R. Gorenflo, and I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046129 66, 046129 (2002).
26. P. C. Jagher, Physica A PHYADX 0378-4371 10.1016/0378-4371(80)90200-9 101, 629 (1980);
27. R. C. Bouret, Can. J. Phys. CJPHAD 0008-4204 38, 665 (1960).
28. G. Rangarajan and M. Ding, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00518-1 273, 322 (2000);
29. G. Rangarajan, and M. Ding, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.120 62, 120 (2000).
30. H. C. Tuckwell, Introduction to Theoretical Neurobiology (Cambridge University Press, Cambridge, England, 1988), Vol. 2.
31. B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.2626 60, 2626 (1988).
32. Y. K. Lin and G. Q. Cai, Probabilistic Structural Dynamics (McGraw-Hill, New York, 1995).
33. M. O. Vlad, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/0960-0779(94)90143-0 4, 191 (1994).
34. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, Tokyo, 1953).
35. V. Latora, A. Rapisarda, and S. Ruffo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2104 83, 2104 (1999).
36. V. Latora, A. Rapisarda, and C. Tsallis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056134 64, 056134 (2001).
37. X. L. Wu and A. Libchaber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3017 84, 3017 (2000);
38. G. Gregoire, H. Chate, and Y. Tu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.556 86, 556 (2001);
39. X. L. Wu and A. Libchaber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.557 86, 557 (2001).
40. C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, Springer Series in Synergetics (Springer, New York, 1996).
41. Z. S. Khan and S. W. Morris, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.048002 94, 048002 (2005).
42. K. Chukbar and V. Zaburdaev, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.061105 71, 061105 (2005).
43. T. Kosztolowicz, K. Dworecki, and St. Mrowczynski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.170602 94, 170602 (2005).
44. R. C. Lua and A. Y. Grosberg, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.061918 72, 061918 (2005).
45. A. M. Mathai and R. K. Saxena, The H-fucntion with Application in Statistics and Other Disciplines (Wiley Eastern, New Delhi, 1978).
46. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1980).
47. I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.056111 63, 056111 (2001);
48. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.021107 64, 021107 (2001).