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Fokker-Planck equation in a wedge domain: Anomalous diffusion and survival probability

E. K. Lenzi1, L. R. Evangelista1, M. K. Lenzi2, and L. R. da Silva3

  • 1Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, 87020-900 Maringá, PR, Brazil
  • 2Departamento de Engenharia Química, Universidade Federal do Paraná, Setor de Tecnologia–Jardim das Américas, Caixa Postal 19011, 81531-990 Curitiba, PR, Brazil
  • 3Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN, Brazil

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Phys. Rev. E 80, 021131 – Published 28 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021131

Abstract

We obtain exact solutions and the survival probability for a Fokker-Planck equation subjected to the two-dimensional wedge domain. We consider a spatial dependence in the diffusion coefficient and the presence of external forces. The results show an anomalous spreading of the solution and, consequently, a nonusual behavior of the survival probability which can be connected to anomalous diffusion.

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References (51)

  1. A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 65, 2201 (1990).
  2. J. P. Bouchaud, A. Ott, D. Langevin, and W. Urbach, J. Phys. II 1, 1465 (1991).
  3. C.-K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, Phys. Rev. Lett. 70, 1343 (1993).
  4. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
  5. F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
  6. G. M. Zaslavsky, D. Stevens, and H. Weitzner, Phys. Rev. E 48, 1683 (1993).
  7. G. M. Zaslavsky, Physica D 76, 110 (1994).
  8. G. M. Zaslavsky, Chaos 4, 25 (1994).
  9. J. Klafter and G. Zumofen, Phys. Rev. E 49, 4873 (1994).
  10. H. Spohn, J. Phys. I 3, 69 (1993).
  11. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
  12. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004).
  13. R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000).
  14. L. S. Lucena, L. R. da Silva, L. R. Evangelista, M. K. Lenzi, R. Rossato, and E. K. Lenzi, Chem. Phys. 344, 90 (2008).
  15. E. K. Lenzi, M. K. Lenzi, R. Rossato, L. R. Evangelista, and L. R. Silva, Phys. Lett. A 372, 6121 (2008).
  16. R. Rossato, M. K. Lenzi, L. R. Evangelista, and E. K. Lenzi, Phys. Rev. E 76, 032102 (2007).
  17. L. C. Malacarne, R. S. Mendes, E. K. Lenzi, and M. K. Lenzi, Phys. Rev. E 74, 042101 (2006).
  18. W. R. Schneider and W. Wyss, J. Math. Phys. 30, 134 (1989).
  19. E. K. Lenzi, R. S. Mendes, K. S. Fa, L. C. Malacarne, and L. R. Silva, J. Math. Phys. 44, 2179 (2003).
  20. E. K. Lenzi, R. S. Mendes, J. S. Andrade, L. R. da Silva, and L. S. Lucena, Phys. Rev. E 71, 052101 (2005).
  21. P. C. Assis, R. P. de Souza, P. C. da Silva, L. R. da Silva, L. S. Lucena, and E. K. Lenzi, Phys. Rev. E 73, 032101 (2006).
  22. T. A. M. Langlands, Physica A 367, 136 (2006).
  23. R. Metzler and T. F. Nonnenmacher, Chem. Phys. 284, 67 (2002).
  24. A. R. Plastino and A. Plastino, Physica A 222, 347 (1995); C. Giordano, A. R. Plastino, M. Casas, and A. Plastino, Eur. Phys. J. B 22, 361 (2001).
  25. C. Tsallis and D. J. Bukman, Phys. Rev. E 54, R2197 (1996).
  26. E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, Phys. Rev. Lett. 96, 030601 (2006).
  27. F. Mota-Furtado and P. F. O’Mahony, Phys. Rev. E 75, 041102 (2007).
  28. V. Bezuglyy, B. Mehlig, M. Wilkinson, K. Nakamura, and E. Arvedson, J. Math. Phys. 47, 073301 (2006).
  29. F. Mota-Furtado and P. F. O’Mahony, Phys. Rev. A 74, 044102 (2006).
  30. J. Bisquert, Phys. Rev. E 72, 011109 (2005).
  31. J. L. A. Dubbeldam, A. Milchev, V. G. Rostiashvili, and T. A. Vilgis, Phys. Rev. E 76, 010801(R) (2007).
  32. R. Metzler, E. Barkai, and J. Klafter, Physica A 266, 343 (1999).
  33. R. Metzler, G. Glöckle, and T. F. Nonnenmacher, Physica A 211, 13 (1994).
  34. B. O’Shaughnessy and I. Procaccia, Phys. Rev. Lett. 54, 455 (1985).
  35. P. Demontis and G. B. Suffritti, Phys. Rev. E 74, 051112 (2006).
  36. U. Achatz, J. Steinacker, and R. Schlickeiser, Astron. Astrophys. 250, 266 (1991).
  37. O. Stawicki, J. Geophys. Res. 109, A04105 (2004).
  38. G. Boffetta and I. M. Sokolov, Phys. Rev. Lett. 88, 094501 (2002).
  39. S. Chaudhury and B. J. Cherayila, J. Chem. Phys. 127, 145103 (2007).
  40. M. O. Vlad, Chaos, Solitons Fractals 4, 191 (1994).
  41. H. Risken, The Fokker-Planck Equation (Springer, New York, 1984).
  42. C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics, New York, 1996).
  43. Diandrew Lexter L. Dy and J. P. Esguerra, Phys. Rev. E 78, 062101 (2008).
  44. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
  45. H. K. Moffatt and B. R. Duffy, J. Fluid Mech. 96, 299 (1980).
  46. D. A. Kessler, Z. Olami, J. Oz, I. Procaccia, E. Somfai, and L. M. Sander, Phys. Rev. E 57, 6913 (1998).
  47. S. Redner, Phys. Rev. E 56, 4967 (1997).
  48. A. A. Vedenov, Rev. Plasma Phys. 3, 229 (1967).
  49. M. P. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  50. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
  51. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, San Diego, 2007).

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Phys. Rev. E 80, 021131– Published 28 August, 2009
  • Received 12 April 2009

© 2009 American Physical Society

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