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Inert and Reacting Transport

  • Conference paper
Chaotic Dynamics and Transport in Classical and Quantum Systems

Part of the book series: NATO Science Series ((NAII,volume 182))

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Abstract

Some aspects of passive transport in fluid flows are reviewed. Two classes of problems are considered: inert substances advected by fluid flows, and substances that chemically (or biologically) react while are advected. Concerning the former issue, we discuss it in the Lagrangian framework. In particular, we address the problem of anomalous diffusion in the asymptotic single particle motion, and we introduce a scale dependent description of the particles pair separation evolution. The Lagrangian description is very useful to characterize the non asymptotic properties of transport that often are interesting ones. For the problem of reacting transport we study the dependence of the front speed on the flow characteristics, considering the case of reaction that are slow or fast with respect to the typical time scales of the advection. Moreover, we comment about the role of Lagrangian chaos on the propagation properties.

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References

  1. H.K. Moffatt, Rep. Prog. Phys., 46, 621 (1983).

    Article  Google Scholar 

  2. J.P. Bouchaud and A. Georges, Phys. Rep., 195, 127 (1990).

    Article  MathSciNet  Google Scholar 

  3. G. Falkovich, K. Gawedzki, and M. Vergassola, Rev. Mod. Phys. 73, 913 (2001).

    Article  Google Scholar 

  4. A. Crisanti, M. Falcioni, G. Paladin and A. Vulpiani, La Rivista del Nuovo Cimento, 14, n.12, 1 (1991).

    Google Scholar 

  5. L. Biferale, A. Crisanti, M. Vergassola and A. Vulpiani, Phys. Fluids, 7, 2725 (1995).

    Article  Google Scholar 

  6. A. J. Majda, and P. R. Kramer, Phys. Rep. 314, 237 (1999).

    Article  Google Scholar 

  7. V. Artale, G. Boetta, A. Celani M. Cencini and A. Vulpiani, Phys. Fluids. 9, 3162 (1997).

    Article  Google Scholar 

  8. J. Xin, SIAM Review 42, 161 (2000).

    Article  Google Scholar 

  9. N. Peters, Turbulent combustion (Cambridge University Press, 2000).

    Google Scholar 

  10. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, Moscow Univ. Bull. Math. 1, 1 (1937).

    Google Scholar 

  11. R. A. Fisher, Ann. Eugenics 7, 355 (1937).

    Google Scholar 

  12. E. R. Abraham, Nature 391, 577 (1998).

    Article  Google Scholar 

  13. J. Ross, S. C. Müller, and C. Vidal, Science 240, 460 (1988).

    Google Scholar 

  14. M. Abel, A. Celani, D. Vergni and A. Vulpiani, Phys. Rev. E 64, 046307 (2001).

    Article  Google Scholar 

  15. P. Constantin, A. Kiselev, A. Oberman and L. Ryzhik, Arch. Rational Mechanics 154, 53 (2000).

    Article  Google Scholar 

  16. B. Audoly, H. Beresytcki and Y. Pomeau, C. R. Acad. Sci. 328, Série II b, 255 (2000).

    Google Scholar 

  17. N. Vladimirova, P. Constantin, A. Kiselev, O. Ruchayskiy, L. Ryzhik, Comb. Theory Model. 7, 487 (2003).

    Article  Google Scholar 

  18. A. R. Kerstein, W.T. Ashurst, F. A. Williams, Phys. Rev. A 37, 2728 (1988).

    Article  PubMed  Google Scholar 

  19. U. Frisch, A. Mazzino, and M. Vergassola, Phys. Rev. Lett., 80, 5532 (1998).

    Article  Google Scholar 

  20. G.I. Taylor, Proc. Lond. Math. Soc. Ser. 2, 20, 196 (1921).

    Google Scholar 

  21. E. Montroll and M. Schlesinger, in Studies in Statistical Mechanics, edited by E.W. Montroll and J.L. lebowitz vol. 11, p.1, North-Holland, Amsterdam, 1984.

    Google Scholar 

  22. M.F. Schlesinger, B. West and J. Klafter, Phys. Rev. Lett., 58, 1100 (1987).

    Article  PubMed  Google Scholar 

  23. M. Avellaneda and A. Majda, Commun. Math. Phys., 138, 339 (1991).

    Google Scholar 

  24. M. Avellaneda and M. Vergassola, Phys. Rev. E, 52, 3249 (1995).

    Article  Google Scholar 

  25. G. Matheron and G. De Marsily, Water Resouces Res., 16, 901 (1980).

    Google Scholar 

  26. G.I. Taylor, Proc. R. Soc. A, 219, 186 (1953); Proc. R. Soc. A, 225, 473 (1954).

    Google Scholar 

  27. P. Castiglione, A. Mazzino, P. Muratore-Ginanneschi, A. Vulpiani, Physica D, 134, 75 (1999).

    Google Scholar 

  28. M.E. Fisher, J. Chem. Phys. 44, 616 (1966).

    Article  Google Scholar 

  29. J.-P. Bouchaud, A. Georges, J. Koplik, A. Provat and S. Redner, Phys. Rev. Lett., 64, 2503 (1990).

    Article  PubMed  Google Scholar 

  30. R. Mancinelli, D. Vergni and A. Vulpiani, Eur. Phys. Lett. 60, 532 (2002); R. Mancinelli, D. Vergni and A. Vulpiani, Physica D 85, 175 (2003).

    Google Scholar 

  31. G.M. Zaslavsky, D. Stevens, and H. Weitzener, Phys. Rev. E, 48, 1683 (1993).

    Article  Google Scholar 

  32. T.H. Solomon and J.P. Gollub, Phys. Rev. A, 38, 6280 (1988).

    Article  PubMed  Google Scholar 

  33. A.J. Lichtenberg and M.A. Lieberman Physica D 33, 211 (1988).

    Google Scholar 

  34. Y.H. Ichikawa, T. Kamimura and T. Hatori Physica D, 29, 247 (1987).

    Google Scholar 

  35. P. Leboeuf, Physica D, 116, 8 (1998).

    Google Scholar 

  36. W.J. Cocke, Phys. Fluids 12, 2488 (1969).

    Article  Google Scholar 

  37. U. Frisch, Turbulence, (Cambridge University Press, GB, 1995).

    Google Scholar 

  38. G. Boffetta, M. Cencini, M. Falcioni and A. Vulpiani, Phys. Rep. 356, 367 (2002).

    Article  Google Scholar 

  39. G. Boetta, A. Celani, M. Cencini, G. Lacorata and A. Vulpiani Chaos 10, 50 (2000).

    Article  PubMed  Google Scholar 

  40. G. Lacorata, E. Aurell and A. Vulpiani, Ann. Geophys. 19, 121 (2001).

    Google Scholar 

  41. M.-C. Jullien, Phys. Fluids 15, 2228 (2003).

    Article  Google Scholar 

  42. G. Boffetta, M. Cencini, S. Espa and G. Querzoli, Europhys. Lett. 48, 629 (1999); Phys. Fluids 12, 3160 (2000).

    Article  Google Scholar 

  43. G. Querzoli, Atmos. Env. 16, 2821 (1996).

    Article  Google Scholar 

  44. L. F. Richardson, Proc. Roy. Soc. A110, 709 (1926).

    Google Scholar 

  45. G. Boffetta, A. Celani, A. Crisanti and A. Vulpiani, Europhy. Lett., 46, 177 (1999).

    Article  Google Scholar 

  46. G. Boffetta and A. Celani, Physica A 280, 1 (2000).

    Google Scholar 

  47. G. Boeffetta and I. M. Sokolov, Phys. Rev. Lett. 88, 094501 (2002).

    Article  PubMed  Google Scholar 

  48. M. Freidlin, Functional integration and partial differential equations (Princeton University Press, Princeton NJ, 1985).

    Google Scholar 

  49. P. F. Embid, A. J. Majda and P. E. Souganidis, Phys. Fluids 7(8), 2052 (1995).

    Article  Google Scholar 

  50. M. Cencini, A. Torcini, D. Vergni, and A. Vulpiani, Phys. Fluids 15, 679 (2003).

    Article  Google Scholar 

  51. W.T. Ashurst and G. I. Shivanshinsky, Comb. Sci. Tech. 80, 159 (1991).

    Google Scholar 

  52. P. D. Ronney, in Modeling in Combustion Science, pp. 3–22, Eds. J. Buckmaster and T. Takeno (Springer-Verlag Lecture Notes in Physics, 1994).

    Google Scholar 

  53. B. Khouider, A. Bourlioux and A.J. Majda, Comb. Th. Model. 5 295 (2001).

    Article  Google Scholar 

  54. V. Yakhot, Comb. Sci. Tech. 60, 191 (1988).

    Google Scholar 

  55. R. C. Aldredge, in Modeling in Combustion Science, pp. 23–35, Eds., J. Buckmaster and T. Takeno (Springer-Verlag Lecture Notes in Physics, 1994).

    Google Scholar 

  56. R. C. Aldredge, Comb. and Flame 106, 29 (1996).

    Article  Google Scholar 

  57. A. Oberman, PhD Thesis Univ. of Chicago 2001.

    Google Scholar 

  58. A.K. Pattanayak, Physica D 148, 1 (2001).

    Google Scholar 

  59. A. Okubo and S.A. Levin, Diffusion and ecological problems, (Springer, New York, 2001).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma ”la Sapienza” and Center for Statistical Mechanics and Complexity INFM UdR Roma1, Piazzale Aldo Moro 5, I-00185, Roma, Italy

    M. Cencini & A. Vulpiani

  2. Istituto Applicazioni del Calcolo, CNR, Viale del Policlinico 137, I-00161, Roma, Italy

    D. Vergni

Authors
  1. M. Cencini
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  2. D. Vergni
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  3. A. Vulpiani
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Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Paris, France

    P. Collet

  2. Université Paris 7-Denis Diderot, France

    M. Courbage  & S. Métens  & 

  3. Space Research Institute, Moscow, Russia

    A. Neishtadt

  4. New-York University, New York, NY, USA

    G. Zaslavsky

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© 2005 Kluwer Academic Publishers

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Cencini, M., Vergni, D., Vulpiani, A. (2005). Inert and Reacting Transport. In: Collet, P., Courbage, M., Métens, S., Neishtadt, A., Zaslavsky, G. (eds) Chaotic Dynamics and Transport in Classical and Quantum Systems. NATO Science Series, vol 182. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2947-0_17

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