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 t, t 2/3, t 1/2) 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.
Similar content being viewed by others
REFERENCES
G. F. Carnevale, Y. Pomeau, and W. R. Young, Phys. Rev. Lett. 64:2913 (1990).
J. M. Burgers, The Nonlinear Diffusion Equation(Reidel, Dordrecht, 1974).
S. Kida, J. Fluid Mech. 93:337 (1979).
W. A. Woyczyński, Burgers-KPZ Turbulence, Lecture Notes in Mathematics, Vol. 1700 (Springer, Berlin, 1998).
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).
S. N. Shandarin and Ya. B. Zeldovich, Rev. Mod. Phys. 61:185(1989).
M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56:889 (1986).
T. M. Ligett, Ann. Probab. 25:1 (1997).
Ph. A. Martin and J. Piasecki, J. Statist. Phys. 76:447 (1994).
L. Frachebourg, Ph. A. Martin, and J. Piasecki, Physica A 279:69 (2000).
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).
L. Frachebourg and Ph. A. Martin, J. Fluid Mech. 417:323 (2000).
T. Suidan, J. Statist. Phys. 101:893 (2000).
I. S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, 5th ed. (Academic Press, 1994).
R. Tribe and O. Zaboronski, Comm. Math. Phys. 212:415(2000).
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions(Dover, New York, 1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Frachebourg, L., Jacquemet, V. & Martin, P.A. Inhomogeneous Ballistic Aggregation. Journal of Statistical Physics 105, 745–769 (2001). https://doi.org/10.1023/A:1013540925139
Issue Date:
DOI: https://doi.org/10.1023/A:1013540925139