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

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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. P.L. Krapivsky, S. Redner, E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, Cambridge, 2010)

  2. G.H. Weiss, Aspects and Applications of the Random Walk (North-, Amsterdam, 1994)

  3. M. Colangeli, A. De Masi, E. Presutti, Phys. Lett. A 380, 1710 (2016)

    Article  ADS  Google Scholar 

  4. R. Krishna, Chem. Soc. Rev. 44, 2812 (2015)

    Article  Google Scholar 

  5. M. Colangeli, A. De Masi, E. Presutti, J. Phys. A 50, 435002 (2017)

    Article  Google Scholar 

  6. R. Taylor, R. Krishna, Multicomponent Mass Transfer (J. Wiley and Sons, New York, 1993)

  7. L.S. Darken, Trans. AIME 180, 430 (1949)

    Google Scholar 

  8. M. Giona, Phys. Scr. 93, 095201 (2018)

    Article  ADS  Google Scholar 

  9. K. Falconer, Fractal geometry: mathematical foundations and applications (J. Wiley and Sons, New York, 2004)

  10. M. Giona, A. Brasiello, S. Crescitelli, J. Phys. A 50, 335002 (2017)

    Article  MathSciNet  Google Scholar 

  11. M. Giona, A. Brasiello, S. Crescitelli, J. Phys. A 50, 335003 (2017)

    Article  MathSciNet  Google Scholar 

  12. M. Giona, A. Brasiello, S. Crescitelli, J. Phys. A 50, 335004 (2017)

    Article  MathSciNet  Google Scholar 

  13. M. Giona, A. Brasiello, S. Crescitelli, Europhys. Lett. 112, 30001 (2015)

    Article  ADS  Google Scholar 

  14. A. Brasiello, S. Crescitelli, M. Giona, Physica A 449, 176 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  15. A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits (Springer Verlag, Berlin, 1991)

  16. C. Kipnis, C. Landim, Scaling Limits of Interacting Particle Systems (Springer Verlag, Berlin, 1999)

  17. I. Müller, T. Ruggeri, Extended Thermodynamics (Springer Verlag, Berlin, 1993)

  18. E. Wong, M. Zakai, Int. J. Eng. Sci. 3, 213 (1965)

    Article  Google Scholar 

  19. E. Wong, M. Zakai, Ann. Math. Stat. 36, 1560 (1965)

    Article  Google Scholar 

  20. R. Huang, I. Chavez, K.M. Taute, B. Lukic, S. Jeney, M. Raizen, E.-L. Florin, Nat. Phys. 7, 576 (2011)

    Article  Google Scholar 

  21. M. Giona, D. Cocco, https://doi.org/arXiv:1806.03159 (2018)

  22. M. Giona, D. Cocco, https://doi.org/arXiv:1806.04013 (2018)

  23. N. Korabel, E. Barkai, Phys. Rev. E 83, 051113 (2011)

    Article  ADS  Google Scholar 

  24. N. Korabel, E. Barkai, Phys. Rev. Lett. 104, 170603 (2010)

    Article  ADS  Google Scholar 

  25. M. Marseguerra, A. Zoia, Ann. Nucl. Energy 33, 1396 (2006)

    Article  Google Scholar 

  26. T. Kosztolowicz, J. Membr. Sci. 320, 492 (2008)

    Article  Google Scholar 

  27. M. Giona, A. Brasiello, S. Crescitelli, Physica A 450, 148 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  28. E.N.M. Cirillo, M. Colangeli, Phys. Rev. E 96, 052137 (2017)

    Article  ADS  Google Scholar 

  29. G. Eyink, J.L. Lebowitz, H. Spohn, Commun. Math. Phys. 132, 253 (1990)

    Article  ADS  Google Scholar 

  30. M. Giona, https://doi.org/arXiv:1806.03266 (2018)

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Correspondence to Massimiliano Giona.

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Brasiello, A., Cocco, D., Garofalo, F. et al. From simple lattice models to systems of interacting particles: the role of stochastic regularity in transport models. Eur. Phys. J. Spec. Top. 228, 93–109 (2019). https://doi.org/10.1140/epjst/e2019-800111-4

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  • DOI: https://doi.org/10.1140/epjst/e2019-800111-4

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