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Journal of Statistical Physics

, Volume 105, Issue 5–6, pp 745–769 | Cite as

Inhomogeneous Ballistic Aggregation

  • L. Frachebourg
  • V. Jacquemet
  • Ph. A. Martin
Article

Abstract

The one-dimensional ballistic aggregation process is considered when the initial mass density or the initial particle velocities vanish outside of a finite or semi-infinite interval. In all cases, we compute the mass distributions in closed analytical form and study their long time asymptotics. The relevant length scales are found different (of the order tt2/3t1/2) if, at the initial time, particles occupy a finite (or semi-infinite) interval and if a finite (or infinite) number of them are set into motion.

statistical mechanics non equilibrium adhesive dynamics density profile 

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REFERENCES

  1. 1.
    G. F. Carnevale, Y. Pomeau, and W. R. Young, Phys. Rev. Lett. 64:2913 (1990).Google Scholar
  2. 2.
    J. M. Burgers, The Nonlinear Diffusion Equation(Reidel, Dordrecht, 1974).Google Scholar
  3. 3.
    S. Kida, J. Fluid Mech. 93:337 (1979).Google Scholar
  4. 4.
    W. A. Woyczyński, Burgers-KPZ Turbulence, Lecture Notes in Mathematics, Vol. 1700 (Springer, Berlin, 1998).Google Scholar
  5. 5.
    S. Gurbatov, A. Malakhov, and A. Saichev, Nonlinear Random Waves and Turbulence in Non Dispersive Media: Waves, Rays and Particles(Nonlinear Science, Manchester University Press, 1991).Google Scholar
  6. 6.
    S. N. Shandarin and Ya. B. Zeldovich, Rev. Mod. Phys. 61:185(1989).Google Scholar
  7. 7.
    M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56:889 (1986).Google Scholar
  8. 8.
    T. M. Ligett, Ann. Probab. 25:1 (1997).Google Scholar
  9. 9.
    Ph. A. Martin and J. Piasecki, J. Statist. Phys. 76:447 (1994).Google Scholar
  10. 10.
    L. Frachebourg, Ph. A. Martin, and J. Piasecki, Physica A 279:69 (2000).Google Scholar
  11. 11.
    J. Bertoin, Some properties of Burgers turbulence with white or stable noise initial data, in Lévy Processes: Theory and Applications, Barndorff-Nielsen, Mikosch, and Resnick, eds. (Birkhäuser, 2001).Google Scholar
  12. 12.
    L. Frachebourg and Ph. A. Martin, J. Fluid Mech. 417:323 (2000).Google Scholar
  13. 13.
    T. Suidan, J. Statist. Phys. 101:893 (2000).Google Scholar
  14. 14.
    I. S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic Press, 1994).Google Scholar
  15. 15.
    R. Tribe and O. Zaboronski, Comm. Math. Phys. 212:415(2000).Google Scholar
  16. 16.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions(Dover, New York, 1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • L. Frachebourg
    • 1
  • V. Jacquemet
    • 1
  • Ph. A. Martin
    • 1
  1. 1.Institut de Physique ThéoriqueÉcole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland

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