-
2
-
-
4143143102
-
-
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
-
-
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
-
-
0003411551
-
-
in: C. Domb, J.L. Lebowitz (Eds.), Academic, New York
-
P. Meakin, in: C. Domb, J.L. Lebowitz (Eds.), Phase Transitions and Critical Phenomena, vol. 12, Academic, New York, 1988.
-
(1988)
Phase Transitions and Critical Phenomena
, vol.12
-
-
Meakin, P.1
-
7
-
-
0031145233
-
-
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
-
-
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
-
-
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
-
-
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
-
-
See, e.g.
-
See, e.g., E. Meron, Phys. Rep. 218 (1992) 1.
-
(1992)
Phys. Rep.
, vol.218
, pp. 1
-
-
Meron, E.1
-
14
-
-
0003742606
-
-
Wiley, New York
-
M. Kléman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Ordered Media, Wiley, New York, 1983.
-
(1983)
Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Ordered Media
-
-
Kléman, M.1
-
15
-
-
0003480237
-
-
in: C. Domb, J.L. Lebowitz (Eds.), Academic, New York
-
J.D. Gunton, M. San Miguel, P.S. Sahni, in: C. Domb, J.L. Lebowitz (Eds.), Phase Transitions and Critical Phenomena, vol. 8, Academic, New York, 1983.
-
(1983)
Phase Transitions and Critical Phenomena
, vol.8
-
-
Gunton, J.D.1
San Miguel, M.2
Sahni, P.S.3
-
17
-
-
0003499994
-
-
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
-
-
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
-
21
-
-
0000222331
-
-
See and references therein.
-
See M.A. Anisimov, P.E. Cladis, E.E. Gorodetskii, D.A. Huse, V.E. Podneks, V.G. Taratuta, W. van Saarloos, V.P. Voronov, Phys. Rev. A 41 (1990) 6749, and references therein.
-
(1990)
Phys. Rev. a
, vol.41
, pp. 6749
-
-
Anisimov, M.A.1
Cladis, P.E.2
Gorodetskii, E.E.3
Huse, D.A.4
Podneks, V.E.5
Taratuta, V.G.6
Van Saarloos, W.7
Voronov, V.P.8
-
23
-
-
0003411551
-
-
in: C. Domb, J.L. Lebowitz (Eds.), Academic, New York
-
M.P.M. den Nijs, in: C. Domb, J.L. Lebowitz (Eds.), Phase Transitions and Critical Phenomena, vol. 12, Academic, New York, 1988.
-
(1988)
Phase Transitions and Critical Phenomena
, vol.12
-
-
Den Nijs, M.P.M.1
-
27
-
-
0002157780
-
-
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
-
-
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
-
-
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
-
31
-
-
0003673241
-
-
in: G. Godrèche (Ed.), Cambridge University Press, Cambridge
-
B. Caroli, C. Caroli, B. Roulet, in: G. Godrèche (Ed.), Solids far from Equilibrium, Cambridge University Press, Cambridge, 1992.
-
(1992)
Solids Far from Equilibrium
-
-
Caroli, B.1
Caroli, C.2
Roulet, B.3
-
33
-
-
0004249145
-
-
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
-
-
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
-
38
-
-
0003574175
-
-
in: B.M. Penetrante, S.E. Schultheis (Eds.), Springer, Berlin
-
P.A. Vitello, B.M. Penetrante, J.N. Bardsley, in: B.M. Penetrante, S.E. Schultheis (Eds.), Non-Thermal Plasma Techniques for Pollution Control, Springer, Berlin, 1993.
-
(1993)
Non-Thermal Plasma Techniques for Pollution Control
-
-
Vitello, P.A.1
Penetrante, B.M.2
Bardsley, J.N.3
-
39
-
-
0024000989
-
-
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
-
-
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
-
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
-
-
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
-
-
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
-
48
-
-
0039092608
-
-
Bensimon D., Kadanoff L.P., Liang S., Shraiman B.I., Tang C. Rev. Mod. Phys. 58:1986;977.
-
(1986)
Rev. Mod. Phys.
, vol.58
, pp. 977
-
-
Bensimon, D.1
Kadanoff, L.P.2
Liang, S.3
Shraiman, B.I.4
Tang, C.5
-
49
-
-
0006075903
-
-
in: F.H. Busse, L. Kramer (Eds.), Plenum, New York
-
A. Arneodo, Y. Couder, G. Grasseau, V. Hakim, M. Rabaud, in: F.H. Busse, L. Kramer (Eds.), Nonlinear evolution of spatio-temporal structures in dissipative continuous systems, Plenum, New York, 1990.
-
(1990)
Nonlinear Evolution of Spatio-temporal Structures in Dissipative Continuous Systems
-
-
Arneodo, A.1
Couder, Y.2
Grasseau, G.3
Hakim, V.4
Rabaud, M.5
-
51
-
-
0040828745
-
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
-
52
-
-
0022025303
-
-
Ben-Jacob E., Brand H.R., Dee G., Kramer L., Langer J.S. Physica D. 14:1985;348.
-
(1985)
Physica D
, vol.14
, pp. 348
-
-
Ben-Jacob, E.1
Brand, H.R.2
Dee, G.3
Kramer, L.4
Langer, J.S.5
-
58
-
-
0017172820
-
-
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
-
-
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
-
60
-
-
0002200283
-
-
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. Lett.
, vol.72
, pp. 76
-
-
Paquette, G.C.1
Chen, L.-Y.2
Goldenfeld, N.3
Oono, Y.4
-
61
-
-
0021427253
-
-
C. Mathis, M. Provansal, L. Boyer, J. Phys. Lett. 45 (1984) L483; G.S. Triantafyllou, K. Kupfer, A. Bers, Phys. Rev. Lett. 59 (1987) 1914.
-
(1984)
J. Phys. Lett.
, vol.45
-
-
Mathis, C.1
Provansal, M.2
Boyer, L.3
-
62
-
-
0041032912
-
-
C. Mathis, M. Provansal, L. Boyer, J. Phys. Lett. 45 (1984) L483; G.S. Triantafyllou, K. Kupfer, A. Bers, Phys. Rev. Lett. 59 (1987) 1914.
-
(1987)
Phys. Rev. Lett.
, vol.59
, pp. 1914
-
-
Triantafyllou, G.S.1
Kupfer, K.2
Bers, A.3
-
64
-
-
33748523374
-
-
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
-
65
-
-
0001242874
-
-
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.
-
(1991)
Phys. Rev. Lett.
, vol.66
, pp. 1326
-
-
Jones, R.A.L.1
Norton, L.J.2
Kramer, E.J.3
Bates, F.S.4
Wiltzius, P.5
-
66
-
-
0011938029
-
-
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
-
67
-
-
0001020350
-
-
see also
-
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.
-
(1992)
Physica D
, vol.61
, pp. 166
-
-
Limat, L.1
Jenffer, P.2
Dagens, B.3
Touron, E.4
Fermigier, M.5
Wesfreid, J.E.6
-
72
-
-
0038527473
-
-
Pergamon, New York
-
L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, vol. 10, Pergamon, New York, 1981.
-
(1981)
Course of Theoretical Physics
, vol.10
-
-
Landau, L.D.1
Lifshitz, E.M.2
|