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Lattice Boltzmann across scales: from turbulence to DNA translocation

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Abstract

The capability of the lattice Boltzmann (LB) method to describe complex flow behaviour across a wide range of scales of motion is discussed. This capability is illustrated by means of three examples, straddling across over ten decades of fluid motion, from macroscopic turbulence, to microfluidics, all the way down to nanoscopic flows of biological interest. It is pointed out that each of these applications requires extensions of the original LB scheme, beyond the realm of Navier-Stokes hydrodynamics for which the method was originally designed. The main qualitative ideas behind such extensions are discussed and commented on, with special emphasis on their direct ties with modern non-equilibrium statistical mechanics.

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References

  1. L. Boltzmann, Lectures on Gas Theory (English translation by S. Brush) (Univ. of California Press, 1964); S. Chapman, T.G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, 1952); C. Cercignani, Theory and Applications of the Boltzmann Equation (Scottish Academic Press, 1975)

  2. J.R. Dorfman, E.G.D. Cohen, J. Math. Phys. 2, 282 (1967)

    Article  ADS  Google Scholar 

  3. R. Benzi, S. Succi, M. Vergassola, Phys. Rep. 222, 145 (1992); D. Wolf-Gladrow, Lattice Gas Cellular Automata and Lattice Boltzmann Model (Springer Verlag, 2000); S. Succi, The Lattice Boltzmann Equation (Oxford Univ. Press, Oxford, 2001); S. Chen, G. Doolen, Ann. Rev. Fluid Mech. 30, 329 (1998)

    Article  ADS  Google Scholar 

  4. S. Succi, R. Benzi, Physica D 69, 327 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. U. Frisch, B. Hasslacher, Y. Pomeau, Phys. Rev. Lett. 56, (1986), 1505

    Article  ADS  Google Scholar 

  6. F. Higuera, S. Succi, R. Benzi, Europhys. Lett. 9, 345 (1989)

    Article  ADS  Google Scholar 

  7. Y. Qian, D. D’Humieres, P. Lallemand, Europhys. Lett. 17, 479 (1992)

    Article  MATH  ADS  Google Scholar 

  8. P. Bhatnagar, M. Krook, E. Gross, Phys. Rev. 94, 511 (1954)

    Article  MATH  ADS  Google Scholar 

  9. I. Karlin, A. Ferrante, H.C. Oettinger, Europhys. Lett. 47, 182 (1999)

    Article  ADS  Google Scholar 

  10. X. He, X. Shan, Phys. Rev. Lett. 80, 65 (1998)

    Article  ADS  Google Scholar 

  11. L.S. Luo, Phys. Rev. Lett. 92, 139401 (2004)

    Article  ADS  Google Scholar 

  12. M. Sbragaglia, S. Succi, Europhys. Lett. 73, 370 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  13. S. Ansumali, I.V. Karlin, Phys. Rev. E 66, 026311 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  14. X. Shan, J. Fluid Mech. 550, 413 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, V. Yakhot, Science 301, 633 (2003)

    Article  ADS  Google Scholar 

  16. G. Parisi, Statistical Field Theory (Addison Wesley, 1986)

  17. N. Bogolubov, J. Phys. (USSR) 10, 256 (1946)

    Google Scholar 

  18. H. Chen, S. Orszag, I. Staroselsky, S. Succi, J. Fluid Mech. 519, 301 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  19. V. Yakhot, J. Fluid Mech. (2007, submitted to)

  20. see http://www.exa.com

  21. S. Ansumali, I.V. Karlin, Phys. Rev. Lett. 97, 010201 (2006)

    Article  MathSciNet  Google Scholar 

  22. G.Mc Namara, G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988)

    Article  ADS  Google Scholar 

  23. H. Chen, X. Shan, Phys. Rev. E 47, 1815 (1993)

    Article  ADS  Google Scholar 

  24. M. Swift et al, Phys. Rev. Lett. 75, 830 (1996)

    Article  ADS  Google Scholar 

  25. S. Succi, Phys. Rev. Lett. 89, 064502 (2002)

    Article  ADS  Google Scholar 

  26. M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, F. Toschi, Phys. Rev. Lett. 97, 204503 (2006)

    Article  ADS  Google Scholar 

  27. C. Cotin-Bizonne, J.L. Barrat, L. Bocquet et al., Nature Materials, 2, 237 (2003)

    Article  ADS  Google Scholar 

  28. A. Ladd, J. Fluid Mech. 271, 285 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. L. Landau, E. Lifschitz, Fluid Mechanics (Pergamon, London, 1959)

    Google Scholar 

  30. P. Ahlrichs, B. Duenweg, Int. J. Mod. Phys C 9 1429 (1998)

    Article  ADS  Google Scholar 

  31. J. Horbach, S. Succi, Phys. Rev. Lett. 96 224503 (2006)

    Article  ADS  Google Scholar 

  32. M. Fyta, S. Melchionna, E. Kaxiras, S. Succi, Multiscale Modeling and Simulation 5 1156 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  33. A.J. Storm, C. Storm, J.H. Chen, Nanoletters 7 137 (2005)

    Google Scholar 

  34. S. Ansumali, I. Karlin, Phys. Rev. Lett. 98 124502 (2007)

    Article  ADS  Google Scholar 

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  1. Istituto per le Applicazioni del Calcolo, CNR, Viale del Policlinico 137, 00161, Roma, Italy

    S. Succi

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  1. S. Succi
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Succi, S. Lattice Boltzmann across scales: from turbulence to DNA translocation. Eur. Phys. J. B 64, 471–479 (2008). https://doi.org/10.1140/epjb/e2008-00067-3

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