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From simple lattice models to systems of interacting particles: the role of stochastic regularity in transport models

  • Antonio Brasiello
  • Davide Cocco
  • Fabio Garofalo
  • Massimiliano GionaEmail author
Regular Article
  • 14 Downloads
Part of the following topical collections:
  1. Microscopic Dynamics, Chaos and Transport in Nonequilibrium Processes

Abstract

The concept of stochastic regularity in lattice models corresponds to the physical constraint that the lattice parameters defining particle stochastic motion (specifically, the lattice spacing and the hopping time) attain finite values. This assumption, that is physically well posed, as it corresponds to the existence of bounded mean free path and root mean square velocity, modifies the formulation of the classical hydrodynamic limit for lattice models of particle dynamics, transforming the resulting balance equations for the probability density function from parabolic to hyperbolic. Starting from simple, but non trivial, lattice models of non interacting particles, the article analyzes the role of stochastic regularity in the formulation of the hydrodynamic equations. Specifically, the case of multiphase lattice models is considered both in regular and disordered structures, and the way of including interaction potential within the hyperbolic transport formalism analyzed.

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References

  1. 1.
    P.L. Krapivsky, S. Redner, E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, Cambridge, 2010) Google Scholar
  2. 2.
    G.H. Weiss, Aspects and Applications of the Random Walk (North-, Amsterdam, 1994) Google Scholar
  3. 3.
    M. Colangeli, A. De Masi, E. Presutti, Phys. Lett. A 380, 1710 (2016) ADSCrossRefGoogle Scholar
  4. 4.
    R. Krishna, Chem. Soc. Rev. 44, 2812 (2015) CrossRefGoogle Scholar
  5. 5.
    M. Colangeli, A. De Masi, E. Presutti, J. Phys. A 50, 435002 (2017) CrossRefGoogle Scholar
  6. 6.
    R. Taylor, R. Krishna, Multicomponent Mass Transfer (J. Wiley and Sons, New York, 1993) Google Scholar
  7. 7.
    L.S. Darken, Trans. AIME 180, 430 (1949) Google Scholar
  8. 8.
    M. Giona, Phys. Scr. 93, 095201 (2018) ADSCrossRefGoogle Scholar
  9. 9.
    K. Falconer, Fractal geometry: mathematical foundations and applications (J. Wiley and Sons, New York, 2004) Google Scholar
  10. 10.
    M. Giona, A. Brasiello, S. Crescitelli, J. Phys. A 50, 335002 (2017) MathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Giona, A. Brasiello, S. Crescitelli, J. Phys. A 50, 335003 (2017) MathSciNetCrossRefGoogle Scholar
  12. 12.
    M. Giona, A. Brasiello, S. Crescitelli, J. Phys. A 50, 335004 (2017) MathSciNetCrossRefGoogle Scholar
  13. 13.
    M. Giona, A. Brasiello, S. Crescitelli, Europhys. Lett. 112, 30001 (2015) ADSCrossRefGoogle Scholar
  14. 14.
    A. Brasiello, S. Crescitelli, M. Giona, Physica A 449, 176 (2016) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits (Springer Verlag, Berlin, 1991) Google Scholar
  16. 16.
    C. Kipnis, C. Landim, Scaling Limits of Interacting Particle Systems (Springer Verlag, Berlin, 1999) Google Scholar
  17. 17.
    I. Müller, T. Ruggeri, Extended Thermodynamics (Springer Verlag, Berlin, 1993) Google Scholar
  18. 18.
    E. Wong, M. Zakai, Int. J. Eng. Sci. 3, 213 (1965) CrossRefGoogle Scholar
  19. 19.
    E. Wong, M. Zakai, Ann. Math. Stat. 36, 1560 (1965) CrossRefGoogle Scholar
  20. 20.
    R. Huang, I. Chavez, K.M. Taute, B. Lukic, S. Jeney, M. Raizen, E.-L. Florin, Nat. Phys. 7, 576 (2011) CrossRefGoogle Scholar
  21. 21.
    M. Giona, D. Cocco, https://doi.org/arXiv:1806.03159 (2018)
  22. 22.
    M. Giona, D. Cocco, https://doi.org/arXiv:1806.04013 (2018)
  23. 23.
    N. Korabel, E. Barkai, Phys. Rev. E 83, 051113 (2011) ADSCrossRefGoogle Scholar
  24. 24.
    N. Korabel, E. Barkai, Phys. Rev. Lett. 104, 170603 (2010) ADSCrossRefGoogle Scholar
  25. 25.
    M. Marseguerra, A. Zoia, Ann. Nucl. Energy 33, 1396 (2006) CrossRefGoogle Scholar
  26. 26.
    T. Kosztolowicz, J. Membr. Sci. 320, 492 (2008) CrossRefGoogle Scholar
  27. 27.
    M. Giona, A. Brasiello, S. Crescitelli, Physica A 450, 148 (2016) ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    E.N.M. Cirillo, M. Colangeli, Phys. Rev. E 96, 052137 (2017) ADSCrossRefGoogle Scholar
  29. 29.
    G. Eyink, J.L. Lebowitz, H. Spohn, Commun. Math. Phys. 132, 253 (1990) ADSCrossRefGoogle Scholar
  30. 30.

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Antonio Brasiello
    • 1
  • Davide Cocco
    • 2
  • Fabio Garofalo
    • 3
  • Massimiliano Giona
    • 2
    Email author
  1. 1.Dipartimento di Ingegneria Industriale, Università degli Studi di SalernoFisciano (SA)Italy
  2. 2.Dipartimento di Ingegneria Chimica DICMA Facoltà di Ingegneria, La Sapienza Università di RomaRomaItaly
  3. 3.Department of Biomedical EngineeringLund UniversityLundSweden

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