LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Matthews, P. C. (1997)
Languages: English
Types: Article
Subjects: Nonlinear Sciences - Pattern Formation and Solitons

Classified by OpenAIRE into

arxiv: Nonlinear Sciences::Pattern Formation and Solitons
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is found experimentally that in a rectangular region, patterns of irregular hexagons are often observed. This work analyses the geometry and dynamics of irregular hexagonal patterns. These patterns occur in two different symmetry types, either with a reflection symmetry, involving two wavenumbers, or without symmetry, involving three different wavenumbers. The relevant amplitude equations are studied to investigate the detailed bifurcation structure in each case. It is shown that hexagonal patterns can bifurcate subcritically either from the trivial solution or from a pattern of rolls. Numerical simulations of a model partial differential equation are also presented to illustrate the behaviour.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] S.M. Cox, IMA J. Appl. Mathematics (1997).
    • [2] J.D. Crawford, Phys. Rev. Lett 67(4) 441-444.
    • [3] J.D. Crawford and E. Knobloch, Ann. Rev. Fluid Mech 23 (1991) 341-387.
    • [4] J.D. Crawford, J.P. Gollub and D. Lane, Nonlinearity 6 (1993) 119-164.
    • [5] B. Dionne, M.Silber and A.C. Skeldon, Nonlinearity, in press.
    • [6] M. Golubitsky, J.W. Swift and E. Knobloch, Physica D 10 (1984) 249-276.
    • [7] P. Hall and R.E. Kelly, Physical Review E 52 (1995) 3687-3696.
    • [8] R.B. Hoyle, G.B. McFadden and S.H. Davis, Phil. Trans. A 354 (1996) 2915- 2949.
    • [9] E.L. Koschmieder and S.A. Prahl, J. Fluid Mech. 215 (1990) 571-583.
    • [10] C. Kubstrup, H. Herrero and C. Perez-Garcia, Phys. Rev. E 54 (1996) 1560- 1569.
    • [11] A. Kudrolli and J.P. Gollub, Physica D 97 (1996) 133-154.
    • [12] B.A. Malomed, A.A. Nepomnyashchy and A.E. Nuz, Physica D 70 (1994) 357- 369.
    • [13] P.C. Matthews, M.R.E. Proctor and N.O. Weiss, J. Fluid Mech. 305 (1995) 281-305.
    • [14] Pattern Formation and Instabilities in Continuous Dissipative Systems, Physica D 97 (1996).
    • [15] M.R.E. Proctor and P.C. Matthews, Physica D 97 (1996) 229-241.
    • [16] A.C. Skeldon, K.A. Cliffe and D.S. Riley, J. Comp. Phys, in press.
    • [17] J. Swift and P. Hohenberg, Phys. Rev. A15, (1977) 319-328.
    • [18] N.O. Weiss, D.P. Brownjohn, P.C. Matthews and M.R.E. Proctor, Monthly Notices of the Royal Astronomical Society 283 (1996) 1153-1164.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article