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Population dynamics in compressible flows

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Abstract

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to another.

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References

  1. W. van Saarloos, Phys. Rep. 386, 29 (2003)

    Article  ADS  MATH  Google Scholar 

  2. O. Hallatschek, K. Korolev, Phys. Rev. Lett. 103, (2009) 108103, and references therein

    Article  ADS  Google Scholar 

  3. R. Fisher, Ann. Eugenics 7, 335 (1937)

    Google Scholar 

  4. A. Kolmogorov, I. Petrovsky, N. Psicounoff, Moscow, Univ. Bull. Math. 1, 1 (1937)

    Google Scholar 

  5. M. Kimura, G.H. Weiss, Genetics 49, 561 (1964)

    Google Scholar 

  6. J.F. Crow, M. Kimura, An Introduction to Population Genetics (Blackburn Press, Caldwell, NJ, 2009)

  7. For a recent review, K. Korolev, et al., Rev. Mod. Phys. 820, 1691 (2010)

    Article  ADS  Google Scholar 

  8. B.A. Whitton, M. Potts, The Ecology of Cyanobacteria: Their Diversity in Time and Space (Kluwer, Dordrecht, The Netherlands)

  9. F. D’Ovidio, et al., Proc. Natl. Acad. Sci. 107, 18366 (2010) ds (2000)

    Article  ADS  Google Scholar 

  10. W.J. McKiver, Z. Neufeld, Phys. Rev. E 79, 061902 (2009)

    Article  ADS  Google Scholar 

  11. F. Peters, C. Marraese, Marine Ecology Progr. Series 205, 291 (2000)

    Article  Google Scholar 

  12. F. Toschi, E. Bodenschatz, Annual Rev. Fluid. Mech. 41, 375 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  13. J. Bec, Phys. Fluids 15, L81 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  14. W.M. Durham, E. Ciment, R. Stocker, Phys. Rev. Lett. 106, 238102 (2011)

    Article  ADS  Google Scholar 

  15. C. Torney, Z. Neufeld, Phys. Rev. Lett. 99, 078101 (2007)

    Article  ADS  Google Scholar 

  16. P. Klein, G. Lapeyre, Annual Rev. Marine Sci. 1, 357 (2009)

    ADS  Google Scholar 

  17. K. Mizobota, Saitoh S.I., Shiomoto A., Miyamura T., Shiga N., et al., Prog. Oceanogr. 55, 65 (2002)

    Article  ADS  Google Scholar 

  18. A.P. Martin, Progr. Ocean. 57, 125 (2003)

    Article  Google Scholar 

  19. I.M. Held, R.T. Pierrehumber, S.T. Garner, K.L. Swanson, J. Fluid. Mech. 282, 1 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. X. Capet, P. Klein, B.L. Hua, G. Lapeyre, J. C. McWilliams, J. Fluid. Mech. 604, 165 (2008)

    Article  ADS  MATH  Google Scholar 

  21. P. Klein, B.L. Hua, G. Lapeyre, X. Capet, S. Le Gentil, H. Sasaki, J. Phys. Oceanogr. 38 1748 (2008)

    Article  ADS  Google Scholar 

  22. L. Thomas, A. Tandon, A. Mahadevan, J. Geophys. Res. 177, 17 (2008)

    Google Scholar 

  23. R. Benzi, D.R., Nelson, Physica D 238, 2003 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. P. Perlekar, R. Benzi, D.R. Nelson, Phys. Rev. Lett. 105, 144501 (2010)

    Article  ADS  Google Scholar 

  25. S. Pigolotti, R. Benzi, M.H. Jensen, D.R. Nelson, Phys. Rev. Lett. (submitted)

  26. A. Kolmogorov, N. Petrovsky, N. Piscounov, Moscow Univ. Math. Bull. 1, 1 (1937)

    Google Scholar 

  27. S. Berti, D. Vergni, A. Vulpiani, Europhys. Lett. 83, 54003 (2008)

    Article  ADS  Google Scholar 

  28. L. Biferale, Annu. Rev. Fluid Mech. 35, 441 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  29. U. Frisch, Turbulence the legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1996)

  30. T. Tel, et al., Phys. Reports 413, 91 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  31. A.R. Robinson, Proc. R. Soc. Lond. A453, 2295 (1997)

    ADS  Google Scholar 

  32. A.R. Robinson, Proc. R. Soc. Lond. A455, 1813 (1999)

    ADS  Google Scholar 

  33. D.R. Nelson, N.M. Shnerb., Phys. Rev. E. 58, 1383 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  34. K.A. Dahmen, D.R. Nelson, N.M. Shnerb., J. Math. Biol. 41, 1 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  35. N.M. Shnerb, Phys. Rev. E 63, 011906 (2001), and references therein

    Article  ADS  Google Scholar 

  36. T. Neicu, A. Pradhan, D.A. Larochelle, A. Kudrolli. Phys. Rev. E. 62 1059 (2000)

    Article  ADS  Google Scholar 

  37. O. Hallatschek, D.R. Nelson, Theor. Popul. Biology 73, 158 (2007)

    Article  Google Scholar 

  38. J.R. Cressman, et al., Europhys. Lett. 66, 219 (2004)

    Article  ADS  Google Scholar 

  39. G. Boffetta, et al., Phys. Rev. Lett. 93, 134501 (2004)

    Article  ADS  Google Scholar 

  40. J. ichi Wakita, et al., J. Phys. Soc. Jpn. 63, 1205 (1994)

    Article  ADS  Google Scholar 

  41. R. Benzi, D. Nelson, Physica D 238, 2003 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. G. Boffetta, J. Davoudi, B. Eckhardt, J. Schumacher, Phys. Rev. Lett. 93, 134501 (2004)

    Article  ADS  Google Scholar 

  43. J. Bec, Phys. Fluids 15, L81 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  44. J. Bec, J. Fluid Mech. 528, 255 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. G. Falkovich, K. Gawedzki, M. Vergassola, Rev. Mod. Phys. 73, 914 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  46. O. Hallatschek, D. Nelson, Proc. Natl. Acad. Sci. 104, 19926 (2007)

    Article  ADS  Google Scholar 

  47. W. McKiver, Z. Neufeld, Phys. Rev. E 79, 061902 (2009)

    Article  ADS  Google Scholar 

  48. A. Martin, Prog. Oceanography 57, 125 (2003)

    Article  ADS  Google Scholar 

  49. A. Kurganov, E. Tadmor, J. Comp. Phys. 160, 241 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. J. Mannik, et al., Proc. Natl. Acad. Sci. 35, 14861 (2009)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Dip. di Fisica and INFN, Università “Tor Vergata”, via della Ricerca Scientifica 1, 00133, Roma, Italy

    R. Benzi

  2. The Niels Bohr Institut, Blegdamsvej 17, 2100, Copenhagen, Denmark

    M. H. Jensen

  3. Lyman Laboratory of Physics, Harvard University, Cambridge, MA, 02138, USA

    D. R. Nelson

  4. Department of Physics, Department of Mathematics and Computer Science, and J.M. Burgerscentrum, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    P. Perlekar & F. Toschi

  5. Dept. de Fisica i Eng. Nuclear, Universitat Politecnica de Catalunya Edif. GAIA, Rambla Sant Nebridi s/n, 08222, Terrassa, Barcelona, Spain

    S. Pigolotti

  6. International Collaboration for Turbulence Research, Eindhoven, The Netherlands

    P. Perlekar

Authors
  1. R. Benzi
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  2. M. H. Jensen
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  3. D. R. Nelson
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  4. P. Perlekar
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  5. S. Pigolotti
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  6. F. Toschi
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Benzi, R., Jensen, M.H., Nelson, D.R. et al. Population dynamics in compressible flows. Eur. Phys. J. Spec. Top. 204, 57–73 (2012). https://doi.org/10.1140/epjst/e2012-01552-0

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  • DOI: https://doi.org/10.1140/epjst/e2012-01552-0

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