Hostname: page-component-669899f699-vbsjw Total loading time: 0 Render date: 2025-05-01T00:33:51.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Growth Equation with a Conservation Law

Published online by Cambridge University Press:  10 February 2011

Kent Bækgaard Lauritsen
Kent Bækgaard Lauritsen*
Affiliation:
Center for Polymer Studies and Dept. of Physics, Boston University, Boston, MA 02215 Address from 1 Feb 1996: Center for Turbulence and Chaos Studies, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
Get access

Abstract

We investigate an interface growth equation with a conservation law. The interaction is characterized by an integral kernel. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows for a unified investigation of growth equations. We perform a dynamic renormalization-group analysis and determine the scaling behavior and universality classes for such growth models with a conservation law.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 407: Symposium M – Disordered Materials and Interfaces-Fractals, structure and Dynamics , 1995 , 295
Copyright
Copyright © Materials Research Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1] Kardar, M., Parisi, G. and Zhang, Y.-C., Phys. Rev. Lett. 56, 889 (1986).Google Scholar
[2] Krug, J. and Spohn, H., “Kinetic Roughening of Growing Surfaces”, in Solids far from Equilibrium: Growth, Morphology and Defects, ed. Godrèche, C., Cambridge University Press, Cambridge (1991).Google Scholar
[3] Halpin-Healey, T. and Zhang, Y.-C., Phys. Rep. 254, 189 (1995).Google Scholar
[4] Barabási, A.-L. and Stanley, H. E., Fractal Concepts in Surface Growth, Cambridge University Press (1995).Google Scholar
[5] Sun, T., Guo, H. and Grant, M., Phys. Rev. A 40, 6763 (1989).Google Scholar
[6] Wolf, D. E. and Villain, J., Europhys. Lett. 13, 389 (1990); Z.-W. Lai and S. Das Sarma, Phys. Rev. Lett. 66, 2348 (1991).Google Scholar
[7] Bray, A. J., Phys. Rev. B 41, 6724 (1990); Phys. Rev. Lett. 66, 2048 (1991).Google Scholar
[8] Kardar, M., J. Appl. Phys. 61, 3601 (1987).Google Scholar
[9] Kahanda, G. L. M. K. S., Zou, X.-Q., Farrell, R. and Wong, P.-Z., Phys. Rev. Lett. 68, 3741 (1992).Google Scholar
[10] Iwamoto, A., Yoshinobu, T. and Iwasaki, H., Phys. Rev. Lett. 72, 4025 (1994).Google Scholar
[11] Ma, S.-K., Modern Theory of Critical Phenomena, Frontiers in Physics, Vol.46, Benjamin (1976).Google Scholar
[12] Medina, E., Hwa, T., Kardar, M. and Zhang, Y.-C., Phys. Rev. A 39, 3053 (1989).Google Scholar
[13] Forster, D., Nelson, D. R. and Stephen, M. J., Phys. Rev. A 16, 732 (1977).Google Scholar
[14] Lauritsen, K. B., Ph.D. thesis, Aarhus University (1994).Google Scholar
[15] Lauritsen, K. B., Phys. Rev. E 52, R1261 (1995).Google Scholar
[16] In Bray, A. J. and Marsili, M. (private communication), it has been argued that under the RG tranformation the noise can also get a white noise contribution. This implies that a will be continuous as a function of τ.Google Scholar