Abstract
We study mass-transport models with multiple-chipping processes. The rates of these processes are dependent on the chip size and mass of the fragmenting site. In this context, we consider k-chip moves (where k = 1, 2, 3, ...); and combinations of 1-chip, 2-chip and 3-chip moves. The corresponding mean-field (MF) equations are solved to obtain the steady-state probability distributions, P(m) vs. m. We also undertake Monte Carlo (MC) simulations of these models. The MC results are in excellent agreement with the corresponding MF results, demonstrating that MF theory is exact for these models.
Similar content being viewed by others
References
Kinetics of Ordering and Growth at Surfaces, edited by M. Lagally, NATO Advanced Study Institute, Series B: Physics (Plenum, New York, 1990), Vol. 239
Morphological Organization of Epitaxial Growth and Removal, edited by Z. Zang, M.G. Lagally (World Scientific, Singapore, 1998)
J.A. Venables, Philos. Mag. 27, 697 (1973)
M.C. Bartelt, J.W. Evans, Phys. Rev. B 46, 12675 (1992)
G.S. Bales, D.C. Chrzan, Phys. Rev. B 50, 6057 (1994)
G.S. Bales, D.C. Chrzan, Phys. Rev. Lett. 74, 4879 (1995)
L. Kuipers, R.E. Palmer, Phys. Rev. B 53, R7646 (1996)
H. Takayasu, I. Nishikawa, H. Tasaki, Phys. Rev. A 37, 3110 (1988)
H. Takayasu, Phys. Rev. Lett. 63, 2563 (1989)
S.N. Majumdar, S. Krishnamurthy, M. Barma, Phys. Rev. Lett. 81, 3691 (1998)
M. Rusanen, I.T. Koponen, J. Asikainen, Eur. Phys. J. B 36, 567 (2003)
P. Blandin, Phys. Rev. B 47, 13687 (1993)
P. Blandin, C. Massobrio, P. Ballone, Phys. Rev. Lett. 72, 3072 (1994)
H. Röder, H. Brune, K. Kern, Phys. Rev. Lett. 73, 2143 (1994)
A. Wucher, A.D. Bekkerman, N.K. Dzhemilev, S.V. Verkhoturov, I.V. Veryovkin, Nucl. Instr. Meth. B 140, 311 (1998)
A. Wucher, N.K. Dzhemilev, I.V. Veryovkin, S.V. Verkhoturov, Nucl. Instr. Meth. B 149, 285 (1994)
P.K. Kuiri, B. Joseph, H.P. Lenka, G. Sahu, J. Ghatak, D. Kanjilal, D.P. Mahapatra, Phys. Rev. Lett. 100, 245501 (2008)
E. Bonabeau, L. Dagorn, P. Freon, Proc. Natl. Acad. Sci. USA 96, 4472 (1999)
E. Bonabeau, L. Dagorn, Phys. Rev. E 51, R5220 (1995)
R.M. Ziff, J. Stat. Phys. 23, 241 (1980)
S. Kwon, S. Lee, Y. Kim, Phys. Rev. E 73, 056102 (2006)
S. Kwon, S. Lee, Y. Kim, Phys. Rev. E 78, 036113 (2008)
P.W. Davies, M.A. Quinlan, G.A. Samorjai, Surf. Sci. 121, 290 (1982)
G.P. Shrivastav, V. Banerjee, S. Puri, Phase Transitions 83, 140 (2010)
S.N. Majumdar, S. Krishnamurthy, M. Barma, J. Stat. Phys. 99, 1 (2000)
R. Rajesh, D. Das, B. Chakraborty, M. Barma, Phys. Rev. E 66, 056104 (2002)
M.R. Evans, S.N. Majumdar, R.K.P. Zia, J. Phys. A: Math. Gen. 39, 4859 (2006)
Handbook of Mathematical Functions, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1972)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shrivastav, G., Banerjee, V. & Puri, S. Mass-transport models with multiple-chipping processes. Eur. Phys. J. B 78, 217–223 (2010). https://doi.org/10.1140/epjb/e2010-10592-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2010-10592-y