13
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Gaussian Grooves Propagating Across a Moving Curved Interface in Directional Solidification

Pages 243-253 | Published online: 24 Sep 2006

References

  • Cladis , P. E. , Gleeson , J. T. and Finn , P. L. 1990 . Non-linear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems , Edited by: Busse , F. and Kramer , L. Plenum Press .
  • Lam , Lai and Morris , Hedley C. , eds. 1990 . Non-linear Structures in Physical Systems – Pattern Formation, Chaos and Waves , Springer Verlag .
  • Cladis , P. E. 1991 . J. Stat. Phys. , 64 : 1103
  • Gleeson , J. T. , Finn , P. L. and Cladis , P. E. 1992 . Phys. Rev. , A45 : 8719
  • Jackson , K. A. and Hunt , J. D. 1965 . Acta. Metall. , 13 : 1212
  • Langer , J. S. 1980 . Rev. Mod. Phys. , 52 : 1
  • Souletie , J. , Vannimenus , J. and Store , R. , eds. 1986 . Chance and Matter , 629 New York : Elsevier .
  • 1989 . Science , 243 : 1150
  • Pelcé , Pierre , ed. 1988 . Dynamics of Curved Interfaces , New York : Academic Press, Inc. .
  • Weeks , J. D. and van Saarloos , W. 1989 . Phys. Rev. , A39 : 2772
  • Merchant , G. J. and Davis , S. H. 1989 . Phys. Rev. Lett. , 63 : 573
  • Bechhoefer , J. and Libchaber , A. 1987 . Phys. Rev. , B35 : 1393
  • Oswald , P. 1988 . J. Physique , 49 : 1083
  • 1989 . J. Physique , 50 : C3 – 127 .
  • Mullins , W. W. and Sekerka , R. F. 1963 . J. Appl. Phys. , 35 : 444
  • 1964 . 34 : 323
  • Chopra , M. A. , Glicksman , M. E. and Singh , N. B. 1988 . J. Cryst. Growth , 543 : 543 In these experiments, we did not intentionally add impurities to succinonitrile. What is called the crystal state here is a plastic crystal measure D=1. 27×1015 cm2/s for succinonitrile/acetone and D=0.88×1015 cm2/s for succinonitrile/argon
  • Cladis , P. E. , Gleeson , J. T. and Finn , P. L. 1991 . Phys. Rev. , A44 : R6173
  • Cladis , P. E. , Gleeson , J. T. and Finn , P. L. 1990 . Defects, Patterns and Instabilities , Edited by: Walgraef , D. Kluwer Academic Publishers . Our experimental set-up is described in some detail in
  • Gleeson , J. T. (unpublished). The speed, v, is constant so du is the product of v and the time for the cellular pattern to appear when v < vcb As v → vcb, du → ∞. And when v > vcb du is undefined: the planar interface is stable. This method is useful if the interface becomes unstable everywhere at the same time which it does when v ≈ 3vcb.
  • Caroli , B. , Caroli , C. and Roulet , B. 1982 . J. Phys. (Paris) , 43 : 1767
  • We use “propagate” for the groove pattern in the sense that the envelope of the groove pattern moves continuously across the interface while a single groove keeps its place on the interface
  • de Cheveigné , S. , Guthmann , C. and Lebrun , M. M. 1986 . J. Phys. (Paris) , 47 : 2095
  • Bennett , M. J. and Brown , R. A. 1989 . Phys. Rev. , B39 : 11705
  • Ramprasad , N. , Bennett , M. J. and Brown , R. A. 1988 . Phys. Rev. , B38 : 583
  • Tsiveriotis , K. and Brown , R. A. 1989 . Phys. Rev. Lett. , 63 : 2048
  • Dee , G. and Langer , J. S. 1983 . Phys. Rev. Lett. , 50 : 383
  • van Saarloos , W. 1990 . Phys. Rev. , A39 : 6367
  • Kramer , L. , Ben-Jacob , E. , Brand , H. R. and Cross , M. C. 1982 . Phys. Rev. Lett. , 49 : 1891
  • Coullet , P. , Goldstein , R. E. and Gunaratne , G. H. 1989 . Phys. Rev. Lett. , 63 : 1954
  • Goldstein , R. E. , Gunaratne , G. H. , Gil , L. and Coullet , P. Hydrodynamic and Interfacial Patterns with Broken Space-Time Symmetry [preprint]
  • Misbah , C. 1989 . J. Phys. (Paris) , 50 : 971
  • Oswald , P. , Bechhoefer , J. and Libchaber , A. 1987 . Phys. Rev. Lett. , 58 : 2318
  • Gleeson , J. T. , Finn , P. L. and Cladis , P. E. 1991 . Phys. Rev. Lett. , 66 : 236
  • Simon , A. J. , Bechhoefer , J. and Libchaber , A. 1988 . Phys. Rev. Lett. , 61 : 2574

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.