×

zbMATH — the first resource for mathematics

A numerical approach to three-dimensional dendritic solidification. (English) Zbl 0811.65126
The author considers pattern formation during the supercooling solidification of a pure material. A phase field model is used which gives rise to a rich variety of 3-dimensional patterns, including very realistic dendritic crystal forms. It is shown that the anisotropy has a crucial influence on the shape of the crystals.
Reviewer: F.Zhang (Canberra)

MSC:
65Z05 Applications to the sciences
35Q72 Other PDE from mechanics (MSC2000)
82D25 Statistical mechanics of crystals
PDF BibTeX XML Cite
Full Text: DOI EMIS
References:
[1] Barbieri A., Phys. Rev. 35 pp 1802– (1986)
[2] DOI: 10.1103/PhysRevLett.51.1930
[3] Ben Amar M., Euro. Phys. Lett. pp 307– (1986)
[4] Bilgram J. H., Phys. Rev. 37 pp 685– (1988)
[5] DOI: 10.1103/PhysRevLett.51.1111
[6] DOI: 10.1007/BF00254827 · Zbl 0608.35080
[7] Caginalp G., Phys. Rev. 39 pp 5887– (1989)
[8] Caginalp G., Quart. Appl. Math. 49 pp 147– (1991)
[9] Caroli B., Phys. Rev. 33 pp 442– (1986)
[10] DOI: 10.1002/cpa.3160420502 · Zbl 0685.35054
[11] Collins J. B., Phys. Rev. 31 pp 6119– (1985)
[12] DOI: 10.1103/PhysRevLett.58.1652
[13] DOI: 10.1007/BF00250432 · Zbl 0361.35035
[14] Fix G., Free Boundary Problems pp 580– (1983)
[15] DOI: 10.1007/BF00685127
[16] Gurtin, M. E. [Gurtin], private communication
[17] Honjo H., J. Cryst. Growth 58 pp 297– (1982)
[18] DOI: 10.1016/0001-6160(81)90115-2
[19] Kessler D. A., Phys. Rev. Lett. 57 pp 3069– (1987)
[20] Kessler D. A., Phys. Rev. 33 pp 3352– (1986)
[21] Kobayashi R., RIMS Kokyuroku 614 pp 39– (1987)
[22] Kobayashi R., Computational Optimal Geometries pp 24– (1991)
[23] Kobayashi R., Pattern Formation in Complex Dissipative Systems pp 121– (1992)
[24] Kobayashi R., Physica 63 pp 410– (1993)
[25] Langer J. S., Directions in Condensed Matter Physics pp 165– (1986)
[26] Maurer J., Euro. Phys. Lett. pp 67– (1989)
[27] McFadden G. B., Phys. Rev. 48 pp 2016– (1993)
[28] Meiron D. I., Phys. Rev. 33 pp 2704– (1986)
[29] de Mottoni P., Proc. Royal Soc. Edin. 116 pp 207– (1990) · Zbl 0725.35009
[30] PelcĂ© P., Studies in Appl. Math. 74 pp 245– (1986) · Zbl 0617.45009
[31] Penrose O., Physica 43 pp 44– (1990)
[32] DOI: 10.1103/PhysRevLett.58.1541
[33] Sawada, Y. and Inoue, T. [Sawada and Inoue], private communication
[34] Umantsev A. R., Sov. Phys. Solid State 30 pp 651– (1988)
[35] Wheeler A. A., Physica 66 pp 243– (1993)
[36] Yokoyama Y., Phys. Rev. 41 pp 2038– (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.