| Автор | Kobayashi, Ryo |
| Дата выпуска | 1994 |
| dc.description | We consider pattern formation during the supercooling solidification of a pure material, using a phase field model. The model gives rise to a rich variety of three-dimensional patterns, including very realistic dendritic crystal forms. We show how the strength of anisotropy has a crucial influence on the shape of crystals. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | A Numerical Approach to Three-Dimensional Dendritic Solidification |
| Тип | research-article |
| DOI | 10.1080/10586458.1994.10504577 |
| Electronic ISSN | 1944-950X |
| Print ISSN | 1058-6458 |
| Журнал | Experimental Mathematics |
| Том | 3 |
| Первая страница | 59 |
| Последняя страница | 81 |
| Аффилиация | Kobayashi, Ryo; Department of Applied Mathematics and Informatics, Ryukoku University |
| Выпуск | 1 |
| Библиографическая ссылка | Barbieri, A., Hong, D. C. and Langer, J. S. 1986. “Velocity selection in the symmetric model of dendritic crystal growth”. Phys. Rev., A35: 1802–1808. [Barbieri et al. 1986] |
| Библиографическая ссылка | Ben-Jacob, E., Goldenfeld, N. D., Langer, J. S. and Schön, G. 1983. “Dynamics of interfacial pattern formations”. Phys. Rev. Lett., 51: 1930–1932. [Ben-Jacob et al. 1984], and “Boundary-layer model of pattern formation in solidification”, Phys. Rev. A29 (1984) 330–340 |
| Библиографическая ссылка | Ben Amar, M. and Pomeau, Y. 1986. “Theory of dendritic growth in a weakly undercooled melt”. Euro. Phys. Lett., : 307–314. [Ben Amar and Pomeau 1986] |
| Библиографическая ссылка | Bilgram, J. H., Fireman, M. and Känzig, W. 1988. “Dendritic solidification of krypton”. Phys. Rev., B37: 685–688. [Bilgram et al. 1988] |
| Библиографическая ссылка | Brower, C., Kessler, D. A., Koplik, J. and Levine, H. 1983. “Geometrical approach to moving-interface dynamics”. Phys. Rev. Lett., 51: 1111–1114. [Brower et al. 1983] |
| Библиографическая ссылка | Caginalp, G. 1986. “An analysis of a phase field model of a free boundary”. Arch. Rat. Mech. Anal., 92: 205–245. [Caginalp 1986] |
| Библиографическая ссылка | Caginalp, G. 1989. “Stefan and Hele–Shaw type models as asymptotic limits of the phase–field equations”. Phys. Rev., A39: 5887–5896. [Caginalp 1989] |
| Библиографическая ссылка | Caginalp, G. and Nishiura, Y. 1991. “The existence of travelling waves for phase field equations and convergence to sharp interface models in the singular limit”. Quart. Appl. Math., 49: 147–162. [Caginalp and Nishiura 1991] |
| Библиографическая ссылка | Caroli, B., Caroli, C., Roulet, B. and Langer, J. S. 1986. “Solvability condition for needle crystals at large undercooling in a nonlocal models of solidification”. Phys. Rev., A33: 442–452. [Caroli et al. 1986] |
| Библиографическая ссылка | Carr, J. and Pego, R. L. 1989. “Metastable patterns in solutions of =ε <sub>xx</sub> − f(u)”. Comrn. Pure Appl. Math., 42: 523–576. [Carr and Pego 1989] |
| Библиографическая ссылка | Collins, J. B. and Levine, H. 1985. “Diffuse interface model of diffusion-limited crystal growth”. Phys. Rev., B31: 6119–6122. [Collins and Levine 1985] |
| Библиографическая ссылка | Dougherty, A., Kaplan, P. D. and Gollub, J. P. 1987. “Development of side branching in dendritic crystal growth”. Phys. Rev. Lett., 58: 1652–1655. [Dougherty et al. 1987] |
| Библиографическая ссылка | Fife, P. C. and McLeod, J. B. 1977. “The approach of solutions of nonlinear diffusion equations to travelling front solutions”. Arch. Rat. Mech. Anal., 65: 335–361. [Fife and McLeod 1977] |
| Библиографическая ссылка | Fix, G. 1983. “Phase field models for free boundary problems”.”. In Free Boundary Problems Edited by: Fasano, A. and Primicero, M. 580–589. New York: Pitman.. [Fix 1983] |
| Библиографическая ссылка | Franck, J. P. and Jung, J. 1986. “Dendritic crystal growth in pure He. J. Low Temp. Phys., 64: 165–186. [Franck and Jung 1986] |
| Библиографическая ссылка | Gurtin, M. E. [Gurtin], private communication |
| Библиографическая ссылка | Honjo, H. and Sawada, Y. 1982. “Quantitative measurements on the morphology of a NHBr dendritic crystal growth in a capillary”. J. Cryst. Growth, 58: 297–303. [Honjo and Sawada 1982] |
| Библиографическая ссылка | Huang, S.-C. and Glicksman, M. E. 1981. “Fundamentals of dendritic solidification, I: Steady-state tip growth” and “II: Development of sidebranch structure”. Acta. Metal., 29: 701–716. [Huang and Glicksman 1981], and 717–734 |
| Библиографическая ссылка | Kessler, D. A. and Levine, H. 1987. “Stability of dendritic crystals”. Phys. Rev. Lett., 57: 3069–3072. [Kessler and Levine 1987] |
| Библиографическая ссылка | Kessler, D. A., Koplik, J. and Levine, H. 1986. “Steady-state dendritic crystal growth”. Phys. Rev., A33: 3352–3357. [Kessler et al. 1986] |
| Библиографическая ссылка | Kobayashi, R. 1987. “Dynamics of interfaces in systems of reaction diffusion”. RIMS Kokyuroku, 614: 39–54. [Kobayashi 1987], (in Japanese) |
| Библиографическая ссылка | Kobayashi, R. 1991. “Modeling and simulations of crystal growth”.”. In Computational Optimal Geometries Edited by: Taylor, J. E. 24–25. Providence: Amer. Math. Soc.. [Kobayashi 1991], (includes videotape footage) |
| Библиографическая ссылка | Kobayashi, R. 1992. “Simulations of three dimensional dendrites”.”. In Pattern Formation in Complex Dissipative Systems Edited by: Kai, S. 121–128. Singapore and Philadelphia: World Scientific.. [Kobayashi 1992] |
| Библиографическая ссылка | Kobayashi, R. 1993. “Modeling and numerical simulations of dendritic crystal growth”. Physica, D63: 410–423. [Kobayashi 1993] |
| Библиографическая ссылка | Langer, J. S. 1986. “Models of pattern formation in first-order phase transitions”.”. In Directions in Condensed Matter Physics Edited by: Grinstein, G. and Mazenko, G. 165–186. Singapore and Philadelphia: World Scientific.. [Langer 1986] |
| Библиографическая ссылка | Maurer, J., Boissou, P., Perrin, B. and Tabeling, P. 1989. “Faceted dendrites in the growth of NHBr crystals”. Euro. Phys. Lett., : 67–72. [Maurer et al. 1989] |
| Библиографическая ссылка | McFadden, G. B., Wheeler, A. A., Braun, R. J., Coriell, S. R. and Sekerka, R. F. 1993. “Phase-field models for anisotropic interfaces”. Phys. Rev., E48: 2016–2024. [McFadden et al. 1993] |
| Библиографическая ссылка | Meiron, D. I. 1986. “Selection of steady states in the two-dimensional symmetric model of dendritic growth”. Phys. Rev., A33: 2704–2715. [Meiron 1986] |
| Библиографическая ссылка | de Mottoni, P. and Schatzman, M. 1990. “Development of interfaces in. Proc. Royal Soc. Edin., 116A: 207–220. [Mottoni and Schatzman 1990] |
| Библиографическая ссылка | Pelcé, P. and Pomeau, Y. 1986. “Dendrites in the small undercooling limit”. Studies in Appl. Math., 74: 245–258. [Pelcé and Pomeau 1986] |
| Библиографическая ссылка | Penrose, O. and Fife, P. C. 1990. “Thermodynamically consistent models of phasefield type for the kinetics of phase transitions”. Physica, D43: 44–62. [Penrose and Fife 1990] |
| Библиографическая ссылка | Saito, Y., Goldbeck-Wood, G. and Müller-Krumbhaar, H. 1987. “Dendritic Crystalization: Numerical study of one-sided model”. Phys. Rev. Lett., 58: 1541–1543. [Saito et al. 1987] |
| Библиографическая ссылка | Sawada, Y. and Inoue, T. [Sawada and Inoue], private communication |
| Библиографическая ссылка | Umantsev, A. R. and Roitburd, A. L. 1988. “Nonisothermal relaxation in a nonlocal medium”. Sov. Phys. Solid State, 30: 651–655. [Umantsev and Roitburd 1988] |
| Библиографическая ссылка | Wheeler, A. A., Murray, B. T. and Schaefer, R. J. 1993. “Computation of dendrites using a phase field model”. Physica, D66: 243–262. [Wheeler et al. 1993] |
| Библиографическая ссылка | Yokoyama, Y. and Kuroda, T. 1990. “Pattern formation in growth of snow crystals occurring in the surface kinetic process and the diffusion process”. Phys. Rev., A41: 2038–2049. [Yokoyama and Kuroda 1990] |
