A Langevin Description for Driven Granular Gases

P. Maynar; M. I. García de Soria

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 4, page 87-117
  • ISSN: 0973-5348

Abstract

top
The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also studied.

How to cite

top

Maynar, P., and García de Soria, M. I.. "A Langevin Description for Driven Granular Gases." Mathematical Modelling of Natural Phenomena 6.4 (2011): 87-117. <http://eudml.org/doc/222351>.

@article{Maynar2011,
abstract = {The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also studied. },
author = {Maynar, P., García de Soria, M. I.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {kinetic theory; Boltzmann equation; granular gases; hydrodynamics},
language = {eng},
month = {7},
number = {4},
pages = {87-117},
publisher = {EDP Sciences},
title = {A Langevin Description for Driven Granular Gases},
url = {http://eudml.org/doc/222351},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Maynar, P.
AU - García de Soria, M. I.
TI - A Langevin Description for Driven Granular Gases
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/7//
PB - EDP Sciences
VL - 6
IS - 4
SP - 87
EP - 117
AB - The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also studied.
LA - eng
KW - kinetic theory; Boltzmann equation; granular gases; hydrodynamics
UR - http://eudml.org/doc/222351
ER -

References

top
  1. A. Baskaran, J. W. Dufty, J. J. Brey. Transport coefficients for the hard-sphere granular fluid. Phys. Rev. E, 77 (2008), No. 3, 031311.  
  2. M. Bixon, R. Zwanzig. Boltzmann-Langevin Equation and Hydrodynamic Fluctuations. Phys. Rev., 187 (1969), No. 1, 267–272.  
  3. J. J. Brey, J. W. Dufty, M. J. Ruiz-Montero, in Granular Gas Dynamics, edited by T. Pöschel and N. Brilliantov. Springer, Berlin, 2003.  
  4. J. J. Brey, M. I. García de Soria, P. Maynar. Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases. Phys. Rev. E, 82 (2010), No. 2, 021303.  
  5. J. J. Brey, M. I. García de Soria, P. Maynar. Breakdown of the fluctuation-dissipation relations in granular gases. EPL, 84 (2008), No. 2, 24002.  
  6. J. J. Brey, P. Maynar, M. I. García de Soria. Fluctuating hydrodynamics for dilute granular gases. Phys. Rev. E, 79 (2009), No. 5, 051305.  
  7. J. J. Brey, M. I. García de Soria, P. Maynar, M. J. Ruiz-Montero. Energy fluctuations in the homogeneous cooling state of granular gases. Phys. Rev. E, 70 (2004), No. 1, 011302.  
  8. J. J. Brey, M. J. Ruiz-Montero, F. Moreno. Boundary conditions and normal state for a vibrated granular fluid. Phys. Rev. E, 62 (2000), No. 4, 5339–5346.  
  9. R. Cafiero, S. Luding, H. J. Herrmann. Two-Dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving. Phys. Rev. Lett., 84 (2000), No. 26, 6014–6017.  
  10. M. H. Ernst, E. Trizac, A. Barrat. The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres. J. Stat. Phys., 124 (2006), No. 2–4, 549–586.  Zbl1134.82034
  11. M. H. Ernst, E. Trizac, A. Barrat. The rich behavior of the Boltzmann equation for dissipative gases. Europhys. Lett., 76 (2006), No. 1, 56–62.  
  12. A. Fiege, T. Aspelmeier, A. Zippelius. Long-Time Tails and Cage Effect in Driven Granular Fluids. Phys. Rev. Lett., 102 (2009), No. 9, 098001.  
  13. M. I. García de Soria, P. Maynar, G. Schehr, A. Barrat, E. Trizac. Dynamics of annihilation. II. Fluctuations of global quantities. Phys. Rev. E, 77 (2008), No. 5, 051128.  
  14. M. I. García de Soria, P. Maynar, E. Trizac. Energy fluctuations in a randomly driven granular fluid. Mol. Phys., 107 (2009), No. 4–6, 383–392.  
  15. V. Garzó, J. M. Montanero. Transport coefficients of a heated granular gas. Physica A, 313 (2002), No. 3–4, 336–356.  Zbl0998.82026
  16. I. Goldhirsch, G. Zanetti. Clustering instability in dissipative gases. Phys. Rev. Lett., 70 (1993), No. 11, 1619–1622.  
  17. A. Goldshtein, M. Shapiro. Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid. Mech., 282 (1995), 75–114.  Zbl0881.76010
  18. P. K. Haff. Grain flow as a fluid-mechanical phenomenon. J. Fluid. Mech., 134 (1983), 401–430.  Zbl0537.76005
  19. C. C. Maaß, N. Isert, G. Maret, C. M. Aegerter. Experimental Investigation of the Freely Cooling Granular Gas. Phys. Rev. Lett., 100 (2008), No. 24, 248001.  
  20. P. Maynar, M. I. García de Soria, E. Trizac. Fluctuating hydrodynamics for driven granular gases. EPJ ST, 179 (2009), 123–139.  
  21. S. McNamara, W. R. Young. Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E, 53 (1996), No. 5, 5089–5100.  
  22. J. M. Montanero, A. Santos. Computer simulation of uniformly heated granular fluids. Granular Matter, 2 (2000), No. 2, 53–64.  
  23. S. J. Moon, M. D. Shattuck, J. B. Swift. Velocity distributions and correlations in homogeneously heated granular media. Phys. Rev E, 64 (2001), No. 3, 031303.  
  24. I. Pagonabarraga, E. Trizac, T. P. C. van Noije, M. H. Ernst. Randomly driven granular fluids: Collisional statistics and short scale structure. Phys. Rev. E, 65 (2001), No. 1, 011303.  
  25. B. Painter, M. Dutt, R. Behringer. Energy dissipation and clustering for a cooling granular material on a substrate. Physica D, 175 (2003), No. 1–2, 43–68.  Zbl1011.82510
  26. A. Prevost, D. A. Egolf, J. S. Urbach. Forcing and Velocity Correlations in a Vibrated Granular Monolayer. Phys. Rev. Lett., 89 (2002), No. 8, 084301.  
  27. A. Puglisi, V. Loreto, U. M. B. Marconi, A. Vulpiani. Kinetic approach to granular gases. Phys. Rev E, 59 (1999), No. 5, 5582–5595.  
  28. P. Résibois, M. de Leener. Classical Kinetic Theory of Fluids. Wiley, New York, 1977.  Zbl0152.46503
  29. N. G. van Kampen. Stochastic Proccesses in Physics and Chemistry. North-Holland, Amsterdam, 1992.  
  30. T. P. C. van Noije, M. H. Ernst. Velocity distributions in homogeneous granular fluids: the free and the heated case. Granular Matter, 1 (1998), No. 2, 57–64.  
  31. T. P. C. van Noije, M. H. Ernst, E. Trizac, I. Pagonabarraga. Randomly driven granular fluids: Large-scale structure. Phys. Rev. E, 59 (1999), No. 4, 4326–4341.  
  32. P. Visco, A. Puglisi, A. Barrat, F. van Wijland, E. Trizac. Energy fluctuations in vibrated and driven granular gases. Eur. Phys. J. B, 51 (2006), No. 3, 377–387.  Zbl1107.82369
  33. D. R. M. Williams, F. C. MacKintosh. Driven granular media in one dimension: Correlations and equation of state. Phys. Rev. E, 54 (1996), No. 1, R9–R12.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.