메뉴 건너뛰기




Volumn 301, Issue 1-3, 1998, Pages 9-43

Three basic issues concerning interface dynamics in nonequilibrium pattern formation

Author keywords

02.30.Jr; 47.20.Ky; 47.54.+r; 68.35.Rh; Interface dynamics; Pattern formation; Relaxation

Indexed keywords


EID: 0002664991     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(98)00004-0     Document Type: Article
Times cited : (59)

References (74)
  • 2
    • 4143143102 scopus 로고    scopus 로고
    • U. Ebert, W. van Saarloos, C. Caroli, Phys. Rev. Lett. 77 (1996) 4178; Phys. Rev. E 55 (1997) 1530.
    • (1997) Phys. Rev. e , vol.55 , pp. 1530
  • 5
    • 36849120852 scopus 로고
    • W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 34 (1963) 323; J. Appl. Phys. 35 (1964) 444.
    • (1964) J. Appl. Phys. , vol.35 , pp. 444
  • 6
  • 7
    • 0031145233 scopus 로고    scopus 로고
    • The literature on phase-field models is vast by now. An entry into the more mathematically oriented literature can be got from
    • The literature on phase-field models is vast by now. An entry into the more mathematically oriented literature can be got from P.W. Bates, P.C. Fife, R.A. Gardner, C.K.R.T. Jones, Physica D 104 (1997) 1.
    • (1997) Physica D , vol.104 , pp. 1
    • Bates, P.W.1    Fife, P.C.2    Gardner, R.A.3    Jones, C.K.R.T.4
  • 8
    • 4243643071 scopus 로고    scopus 로고
    • An example where a phase-field model has been exploited numerically to study the dendrite problem is preprint, July
    • An example where a phase-field model has been exploited numerically to study the dendrite problem is A. Karma, W.-J. Rappel, Phys. Rev. E 53 (1996) R3017, preprint, July 1997. These papers also give an entry to the more physics oriented literature. An early use of the word "phase-field model" is found in J.S. Langer, in: G. Grinstein, G. Mazenko (Eds.), Directions in Condensed Matter Physics, World Scientific, Singapore, 1986.
    • (1996) Phys. Rev. e , vol.53
    • Karma, A.1    Rappel, W.-J.2
  • 9
    • 0003605398 scopus 로고
    • These papers also give an entry to the more physics oriented literature. An early use of the word "phase-field model" is found in in: G. Grinstein, G. Mazenko (Eds.), World Scientific, Singapore
    • An example where a phase-field model has been exploited numerically to study the dendrite problem is A. Karma, W.-J. Rappel, Phys. Rev. E 53 (1996) R3017, preprint, July 1997. These papers also give an entry to the more physics oriented literature. An early use of the word "phase-field model" is found in J.S. Langer, in: G. Grinstein, G. Mazenko (Eds.), Directions in Condensed Matter Physics, World Scientific, Singapore, 1986.
    • (1986) Directions in Condensed Matter Physics
    • Langer, J.S.1
  • 11
    • 0020779215 scopus 로고
    • A very nice elementary account of several of the essential ingredients of flame fronts and their instabilities can be found in
    • A very nice elementary account of several of the essential ingredients of flame fronts and their instabilities can be found in J.D. Buckmaster, Physica 12D (1984) 173.
    • (1984) Physica , vol.12 D , pp. 173
    • Buckmaster, J.D.1
  • 12
    • 0001883519 scopus 로고
    • See, e.g.
    • See, e.g., E. Meron, Phys. Rep. 218 (1992) 1.
    • (1992) Phys. Rep. , vol.218 , pp. 1
    • Meron, E.1
  • 17
    • 0003499994 scopus 로고
    • in: C. Godreche (Ed.), Cambridge University Press, Cambridge
    • J.S. Langer, in: C. Godreche (Ed.), Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992.
    • (1992) Solids Far from Equilibrium
    • Langer, J.S.1
  • 18
    • 0018480694 scopus 로고
    • Here, smooth interface models go back to the classic work of
    • Here, smooth interface models go back to the classic work of S.M. Allen, J.W. Cahn, Acta Metall. 27 (1979) 1085.
    • (1979) Acta Metall. , vol.27 , pp. 1085
    • Allen, S.M.1    Cahn, J.W.2
  • 27
    • 0002157780 scopus 로고
    • For an overview of adiabatic decoupling in ordinary differential equations as a result of the separation of time scales, see e.g.
    • For an overview of adiabatic decoupling in ordinary differential equations as a result of the separation of time scales, see e.g., N.G. van Kampen, Phys. Rep. 124 (1985) 69.
    • (1985) Phys. Rep. , vol.124 , pp. 69
    • Van Kampen, N.G.1
  • 29
    • 0342583796 scopus 로고
    • J.S. Langer, Rev. Mod. Phys. 52 (1980) 1; in: J. Souletie (Ed.), Chance and Matter, North-Holland, Amsterdam, 1987.
    • (1980) Rev. Mod. Phys. , vol.52 , pp. 1
    • Langer, J.S.1
  • 30
    • 0342583796 scopus 로고
    • in: (Ed.), North-Holland, Amsterdam
    • J.S. Langer, Rev. Mod. Phys. 52 (1980) 1; in: J. Souletie (Ed.), Chance and Matter, North-Holland, Amsterdam, 1987.
    • (1987) Chance and Matter
    • Souletie, J.1
  • 33
    • 0004249145 scopus 로고
    • For a review of the issues related to the microscopic nature of the crystal-melt interface, see, e.g., in: T. Riste (Ed.), Plenum, New York
    • For a review of the issues related to the microscopic nature of the crystal-melt interface, see, e.g., J.D. Weeks, in: T. Riste (Ed.), Ordering in Strongly Fluctuating Condensed Matter Systems, Plenum, New York, 1980, or P. Nozières, in: G. Godrèche (Ed.), Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992.
    • (1980) Ordering in Strongly Fluctuating Condensed Matter Systems
    • Weeks, J.D.1
  • 34
    • 0003499994 scopus 로고
    • or in: G. Godrèche (Ed.), Cambridge University Press, Cambridge
    • For a review of the issues related to the microscopic nature of the crystal-melt interface, see, e.g., J.D. Weeks, in: T. Riste (Ed.), Ordering in Strongly Fluctuating Condensed Matter Systems, Plenum, New York, 1980, or P. Nozières, in: G. Godrèche (Ed.), Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992.
    • (1992) Solids Far from Equilibrium
    • Nozières, P.1
  • 39
    • 0024000989 scopus 로고
    • D.A. Kessler, J. Koplik, H. Levine, Adv. Phys. 37 (1988) 255; P. Pelcé, Dynamics of Curved Fronts, Academic, Boston, 1988; Y. Pomeau, M. Ben Amar, in: C. Godreche (Ed.), Dendritic growth and related topics, in: Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992; E.A. Brener, V.I. Mel'nikov, Adv. Phys. 40 (1991) 53.
    • (1988) Adv. Phys. , vol.37 , pp. 255
    • Kessler, D.A.1    Koplik, J.2    Levine, H.3
  • 40
    • 0024000989 scopus 로고
    • Academic, Boston
    • D.A. Kessler, J. Koplik, H. Levine, Adv. Phys. 37 (1988) 255; P. Pelcé, Dynamics of Curved Fronts, Academic, Boston, 1988; Y. Pomeau, M. Ben Amar, in: C. Godreche (Ed.), Dendritic growth and related topics, in: Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992; E.A. Brener, V.I. Mel'nikov, Adv. Phys. 40 (1991) 53.
    • (1988) Dynamics of Curved Fronts
    • Pelcé, P.1
  • 41
    • 0024000989 scopus 로고
    • Dendritic growth and related topics
    • in: C. Godreche (Ed.), Cambridge University Press, Cambridge
    • D.A. Kessler, J. Koplik, H. Levine, Adv. Phys. 37 (1988) 255; P. Pelcé, Dynamics of Curved Fronts, Academic, Boston, 1988; Y. Pomeau, M. Ben Amar, in: C. Godreche (Ed.), Dendritic growth and related topics, in: Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992; E.A. Brener, V.I. Mel'nikov, Adv. Phys. 40 (1991) 53.
    • (1992) In: Solids Far from Equilibrium
    • Pomeau, Y.1    Ben Amar, M.2
  • 42
    • 0002566103 scopus 로고
    • D.A. Kessler, J. Koplik, H. Levine, Adv. Phys. 37 (1988) 255; P. Pelcé, Dynamics of Curved Fronts, Academic, Boston, 1988; Y. Pomeau, M. Ben Amar, in: C. Godreche (Ed.), Dendritic growth and related topics, in: Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992; E.A. Brener, V.I. Mel'nikov, Adv. Phys. 40 (1991) 53.
    • (1991) Adv. Phys. , vol.40 , pp. 53
    • Brener, E.A.1    Mel'Nikov, V.I.2
  • 43
    • 33846337334 scopus 로고
    • For this reason, kinetic relations like can easily be studied with computer simulations. For an example of this, see, e.g., The interface mobility coefficient 1/β in is nothing but the slope of in this paper.
    • For this reason, kinetic relations like can easily be studied with computer simulations. For an example of this, see, e.g., J.Q. Broughton, G.H. Gilmer, K.A. Jackson, Phys. Rev. Lett. 49 (1982) 1496. The interface mobility coefficient 1/β in is nothing but the slope of in this paper.
    • (1982) Phys. Rev. Lett. , vol.49 , pp. 1496
    • Broughton, J.Q.1    Gilmer, G.H.2    Jackson, K.A.3
  • 51
    • 0040828745 scopus 로고    scopus 로고
    • Multiple front propagation in a potential non-gradient system
    • A very enjoyable article which discusses fronts in various non-gradient systems is in: E. Tirapegui, W. Zeller (Eds.) Kluwer, Dordrecht
    • A very enjoyable article which discusses fronts in various non-gradient systems is M. San Miguel, R. Montagne, A. Amengual, E. Hernández-García, Multiple front propagation in a potential non-gradient system, in: E. Tirapegui, W. Zeller (Eds.) Instabilities in Nonequilibrium Structures V, Kluwer, Dordrecht, 1996.
    • (1996) Instabilities in Nonequilibrium Structures V
    • San Miguel, M.1    Montagne, R.2    Amengual, A.3    Hernández-García, E.4
  • 58
    • 0017172820 scopus 로고
    • The terms pulled and pushed were introduced by
    • The terms pulled and pushed were introduced by A.N. Stokes, Math. Biosci. 31 (1976) 307.
    • (1976) Math. Biosci. , vol.31 , pp. 307
    • Stokes, A.N.1
  • 59
    • 0000056645 scopus 로고
    • G.C. Paquette, Y. Oono, Phys. Rev. E 49 (1994) 2368; G.C. Paquette, L.-Y. Chen, N. Goldenfeld, Y. Oono, Phys. Rev. Lett. 72 (1994) 76.
    • (1994) Phys. Rev. e , vol.49 , pp. 2368
    • Paquette, G.C.1    Oono, Y.2
  • 64
    • 33748523374 scopus 로고
    • R.C. Ball, R.L.H. Essery, J. Phys.: Condens. Matter 2 (1990) 10303; R.A.L. Jones, L.J. Norton, E.J. Kramer, F.S. Bates, P. Wiltzius, Phys. Rev. Lett. 66 (1991) 1326.
    • (1990) J. Phys.: Condens. Matter , vol.2 , pp. 10303
    • Ball, R.C.1    Essery, R.L.H.2
  • 66
    • 0011938029 scopus 로고    scopus 로고
    • T.R. Powers, R.E. Goldstein, Phys. Rev. Lett. 78 (1997) 2555; see also L. Limat, P. Jenffer, B. Dagens, E. Touron, M. Fermigier, J.E. Wesfreid, Physica D 61 (1992) 166.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 2555
    • Powers, T.R.1    Goldstein, R.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.