Skip to main content
SpringerLink
Log in

Mass-transport models with multiple-chipping processes

  • Published:
The European Physical Journal B Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kinetics of Ordering and Growth at Surfaces, edited by M. Lagally, NATO Advanced Study Institute, Series B: Physics (Plenum, New York, 1990), Vol. 239

  2. Morphological Organization of Epitaxial Growth and Removal, edited by Z. Zang, M.G. Lagally (World Scientific, Singapore, 1998)

  3. J.A. Venables, Philos. Mag. 27, 697 (1973)

    Article  ADS  Google Scholar 

  4. M.C. Bartelt, J.W. Evans, Phys. Rev. B 46, 12675 (1992)

    Article  ADS  Google Scholar 

  5. G.S. Bales, D.C. Chrzan, Phys. Rev. B 50, 6057 (1994)

    Article  ADS  Google Scholar 

  6. G.S. Bales, D.C. Chrzan, Phys. Rev. Lett. 74, 4879 (1995)

    Article  ADS  Google Scholar 

  7. L. Kuipers, R.E. Palmer, Phys. Rev. B 53, R7646 (1996)

    Article  ADS  Google Scholar 

  8. H. Takayasu, I. Nishikawa, H. Tasaki, Phys. Rev. A 37, 3110 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  9. H. Takayasu, Phys. Rev. Lett. 63, 2563 (1989)

    Article  ADS  Google Scholar 

  10. S.N. Majumdar, S. Krishnamurthy, M. Barma, Phys. Rev. Lett. 81, 3691 (1998)

    Article  ADS  Google Scholar 

  11. M. Rusanen, I.T. Koponen, J. Asikainen, Eur. Phys. J. B 36, 567 (2003)

    Article  ADS  Google Scholar 

  12. P. Blandin, Phys. Rev. B 47, 13687 (1993)

    Article  ADS  Google Scholar 

  13. P. Blandin, C. Massobrio, P. Ballone, Phys. Rev. Lett. 72, 3072 (1994)

    Article  ADS  Google Scholar 

  14. H. Röder, H. Brune, K. Kern, Phys. Rev. Lett. 73, 2143 (1994)

    Article  ADS  Google Scholar 

  15. A. Wucher, A.D. Bekkerman, N.K. Dzhemilev, S.V. Verkhoturov, I.V. Veryovkin, Nucl. Instr. Meth. B 140, 311 (1998)

    Article  ADS  Google Scholar 

  16. A. Wucher, N.K. Dzhemilev, I.V. Veryovkin, S.V. Verkhoturov, Nucl. Instr. Meth. B 149, 285 (1994)

    Article  ADS  Google Scholar 

  17. P.K. Kuiri, B. Joseph, H.P. Lenka, G. Sahu, J. Ghatak, D. Kanjilal, D.P. Mahapatra, Phys. Rev. Lett. 100, 245501 (2008)

    Article  ADS  Google Scholar 

  18. E. Bonabeau, L. Dagorn, P. Freon, Proc. Natl. Acad. Sci. USA 96, 4472 (1999)

    Article  ADS  Google Scholar 

  19. E. Bonabeau, L. Dagorn, Phys. Rev. E 51, R5220 (1995)

    Article  ADS  Google Scholar 

  20. R.M. Ziff, J. Stat. Phys. 23, 241 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  21. S. Kwon, S. Lee, Y. Kim, Phys. Rev. E 73, 056102 (2006)

    Article  ADS  Google Scholar 

  22. S. Kwon, S. Lee, Y. Kim, Phys. Rev. E 78, 036113 (2008)

    Article  ADS  Google Scholar 

  23. P.W. Davies, M.A. Quinlan, G.A. Samorjai, Surf. Sci. 121, 290 (1982)

    Article  ADS  Google Scholar 

  24. G.P. Shrivastav, V. Banerjee, S. Puri, Phase Transitions 83, 140 (2010)

    Article  Google Scholar 

  25. S.N. Majumdar, S. Krishnamurthy, M. Barma, J. Stat. Phys. 99, 1 (2000)

    Article  MATH  Google Scholar 

  26. R. Rajesh, D. Das, B. Chakraborty, M. Barma, Phys. Rev. E 66, 056104 (2002)

    Article  ADS  Google Scholar 

  27. M.R. Evans, S.N. Majumdar, R.K.P. Zia, J. Phys. A: Math. Gen. 39, 4859 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Handbook of Mathematical Functions, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1972)

Download references

Author information

Authors and Affiliations

  1. School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India

    G. P. Shrivastav & S. Puri

  2. Department of Physics, Indian Institute of Technology, Hauz Khas, 110016, New Delhi, India

    V. Banerjee

Authors
  1. G. P. Shrivastav
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Puri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Banerjee.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2010-10592-y

Keywords

Search

Navigation