Current theoretical approaches to collective behavior of dislocations

Physics Reports

Volumn 440, Issue 4-6, 2007, Pages 113-259

  Ananthakrishna, G ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947144712     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2006.10.003     Document Type: Review

References (387)

1. Neuhäuser H. In: Nabarro F.R.N. (Ed). Dislocations in Solids vol. 6 (1983), North-Holland, Amsterdam
2. Brinck A., Engeleke C., Neuhäuser H., Molénat G., Rösner H., Langmaack E., and Nembach E. Mat. Sci. Eng. A 258 (1997) 32
3. Brinck A., Engeleke C., Kopmann W., and Neuhäuser H. Mat. Sci. Eng. A 239-240 (1997) 180
4. Kubin L.P., Fressengeas C., and Ananthakrishna G. In: Nabarro F.R.N., and Duesbury M.S. (Eds). Collective Behaviour of Dislocations, Dislocations in Solids vol. 11 (2002), North-Holland, Amsterdam 101
5. Piobert A. Mem. de l'artillerie 5 (1842) 525
6. Lüders W. Dinglers Polytech. J. 155 (1860) 18
7. Le Chatelier F. Rev. de Métal 6 (1909) 914
8. Portevin A., and Le Chatelier F. C. R. Acad. Sci. Paris 176 (1923) 507
9. Zaiser M., and Hähner P. Phys. Stat. Sol. B 199 (1997) 267
10. Taylor G.I., and Quinney H. Proc. Roy. Soc. Lond. A 143 (1934) 307
11. Quinney H., and Taylor G.I. Proc. Roy. Soc. Lond. A 163 (1937) 157
12. Titchner A.L., and Bever M.B. Progr. Metal. Phys. 7 (1958) 247
13. Frisch U., and Parisi G. In: Ghil M., Benzi R., and Parisi G. (Eds). Turbulence and Predictability of Geophysical Flows and Climate Dynamics (1985), North-Holland, New York 84
14. Zaiser M., and Seeger A. In: Nabarro F.R.N., and Duesbury M.S. (Eds). Collective Behaviour of Dislocations, Dislocations in Solids vol. 11 (2002), North-Holland, Amsterdam 1
15. Kiritani M. J. Phys. Soc. Japan 35 (1973) 95
16. Ananthakrishna G. Pramana 12 (1979) 527 (1979) 543; (1979) 581; (1979) 581
17. Mughrabi H. In: Haasen P., Gerold V., and Kostorz G. (Eds). Strength of Metals and Alloys, ICSMA 5 vol. 3 (1979), Pergamon Press, Oxford 1615
18. Brown L.M. In: Ashby M.F., et al. (Ed). Dislocation Modeling of Physical Systems (1981), Pergamon Press, Oxford 51
19. Laird C. In: Nabarro F.R.N. (Ed). Dislocations in Solids vol. 6 (1983), North-Holland, Amsterdam 55
20. Mughrabi H. In: McQueen H.J., et al. (Ed). Strength of Metals and Alloys (ICSMA-CIRMA 7) vol. 3 (1985), Pergamon Press, Oxford 1917
21. Kubin L.P. In: Mughrabi H. (Ed). Treatise in Materials Science and Technology (1993), VCH, Wienberg 137
22. Kubin L.P. In: Gonis A., Turchi P., and Kudrnovsky J. (Eds). Stability of Materials, NATO ASI Series B 355 (1996), Plenum Press, New York 99
23. Ananthakrishna G., and Sahoo D. J. Phys. D 14 (1981) 699
24. Lagneborg R., and Forsen B.H. Acta Metal. 21 (1973) 781
25. Ostrom P., and Lagneborg R. Trans. ASME 98 (1976) 114
26. Valsakumar M.C., Murthy K.P.N., and Ananthakrishna G. J. Stat. Phys. 30 (1983) 637
27. Berg P., Pomeau Y., and Vidal C. Order in Chaos (1984), Wiley, New York
28. Abarbanel H.D.I. Analysis of the Observed Data (1996), Springer, New York
29. Kumar N. Deterministic Chaos. Complex Chance Out of Simple Necessity (1996), Universities Press, (India) Limited
30. Schreiber T., and Kantz H. Nonlinear Time Series Analysis (1997), Cambridge University Press, Cambridge
31. Mughrabi H., and Ungar T. In: Nabarro F.R.N., and Duesbury M.S. (Eds). Collective Behaviour of Dislocations, Dislocations in Solids vol. 11 (2002), North-Holland, Amsterdam 344
32. Malygin G.A. Physics-Uspekhi 42 (1999) 887
33. Malygin G.A. Phys. Solid State 38 (1996) 1329
34. Basinski Z.S., and Basinski S.J. Progr. Mater. Sci. 36 (1992) 89
35. Winter A.T. Philos. Mag. A 37 457 (1978)
36. Zaiser M., Bay K., and Hähner P. Acta Mater. 47 (1999) 2463
37. H. Mughrabi, F. Ackerman, K. Herz, in: J. Fang (Ed.), Fatigue Mechanisms, Proceedings of the ASTM-NBS-NSF Symposium, ASTM-STP, vol. 675, 1979, p. 69.
38. Raj S.V., and Pharr G.M. Mater. Sci. Eng. 81 (1986) 217
39. Savart F. Recherches sue les vibrations longitudinales. Annales de Chimie et de Physique (second series) 65 (1837) 337-402
40. Lebyodkin M., Dunin-Barkovskii L., Bréchet Y., Estrin Y., and Kubin L.P. Acta Mater. 48 (2000) 2529
41. Cottrell A.H., and Bilby B.A. Proc. R. Soc. London, Ser. A 62 (1949) 49
42. Cottrell A.H. Philos. Mag. 44 (1953) 829
43. Cottrell A.H. Dislocations and Plastic Flow in Crystals (1953), University Press, Oxford
44. Penning P. Acta Metall. 20 (1972) 1179
45. McCormic P.G. Acta Metall. 19 (1971) 463
46. McCormic P.G. Acta Metall. 20 (1972) 352
47. McCormic P.G. Acta Metall. 21 (1973) 873
48. Van den Beukel A. Phys. Stat. Sol. A 30 (1975) 197
49. Mullford R.A., and Kocks U.F. Acta Metall. 277 (1979) 1125
50. Kubin L.P., and Estrin Y. Acta Metall. 33 (1985) 397
51. Kalk A., and Schwink Ch. Phys. Stat. Sol. B 172 (1992) 133
52. Kalk A., and Schwink Ch. Philos. Mag. A 72 (1995) 315
53. Springer F., Nortmann A., and Schwink Ch. Phys. Stat. Sol. A 170 (1998) 63
54. Chihab K., Estrin Y., Kubin L.P., and Vergnol J. Scripta. Metall. 21 (1987) 203
55. Hähner P., Ziegenbein A., Rizzi E., and Neuhäusser H. Phys. Rev. B 65 (2002) 134109
56. Basinski Z.S. Proc. Roy. Soc. A 240 (1957) 299
57. Estrin Y., and Kubin L.P. Scripta Metall. 14 (1980) 1359
58. Estrin Y., and Tangri K. Scripta Metall. 15 (1981) 1323
59. Ogata T., Ishikawa K., Umegzawa O., and Yuri T. Adv. Crygen. Eng. 34 (1988) 209
60. Groger V., and Zehetbauer M. Mat. Sci. Eng. A 164 (1993) 240
61. Hong S.I., and Laird C. Mat. Sci. Eng. A 124 (1990) 183
62. Neumann R., and Neumann P. Scripta Metall. 4 (1970) 645
63. Gilman J.J. Micromechanics of Flow in Solids (1969), McGraw-Hill, New York
64. Mughrabi H. In: Brulin O., and Hsieh R.K.T. (Eds). Proceedings of the Fourth International Conference on Continuum Models of Discrete Systems (1981), North-Holland, Amsterdam 241
65. Kocks U.F. J. Eng. Mat. Technol. 98 (1976) 76
66. Estrin Y., and Kubin L.P. Acta Metall. 34 (1986) 2455
67. Estrin Y. Dislocation-Density-Related Constitutive Modelling (1996), Academic Press, New York 69
68. Sahoo D., and Ananthakrishna G. J. Phys. D 15 (1982) 1439
69. El-Azab A. Phys. Rev. B 61 (2000) 11956
70. Holt D.L. J. Appl. Phys. 41 (1970) 3197
71. D. Walgraef, E.C. Aifantis, Int. J. Eng. Sci. 23 (1985) 1351, 1359, 1365.
72. Walgraef D., and Aifantis E.C. J. Appl. Phys. 58 (1985) 688
73. Schiller C., and Walgraef D. Acta Metall. 36 (1988) 563
74. Hutchinson J.W., and Neale K.W. J. Mech. Phys. Solids 31 (1983) 405
75. Bridgman P.W. Studies in Large Plastic Flow and Fracture (1964), Harvard University Press
76. Hähner P. Appl. Phys. A 58 (1994) 41
77. Fressengeas C., and Molinari A. Acta Metall. 33 (1985) 387
78. Estrin Y., Ling C.P., and McCormick P.G. Acta Metall. 39 (1991) 2943
79. Hampel A., Krammler T., and Neuhäuser H. Phys. Stat. Sol. (a) 135 (1993) 405
80. Malygin G.A. Phys. Solid State 37 (1995) 1
81. Y. Bréchet, Doctorate Thesis, University of Grenoble, 1987.
82. Bréchet Y., and Louchet F. Solid State Phenomena 3-4 (1988) 347
83. Estrin Y. Solid State Phenomena 3-4 (1988) 417
84. Bharathi M.S., and Ananthakrishna G. Europhys. Lett. 60 (2002) 234
85. Estrin Y., and Kubin L.P. J. Mech. Behav. Mats. 2 (1989) 255
86. Mülhaus H.B., and Aifantis E. Int. J. Solids Struct. 28 (1991) 845
87. Cosserat E., and Cosserat F. Théorie des Corps Déformables (1909), Hermann, Paris
88. Toupin R.A. Arch. Rat. Mech. 11 (1962) 385
89. Mindlin R.D., and Tiersten H.F. Arch. Rat. Mech. 11 (1962) 415
90. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Acta Metall. Mater. 42 (1994) 475
91. Smyshlyaev V.P., and Fleck N.A. J. Mech. Phys. Solids 44 (1996) 465
92. Dai H., and Parks D.M. In: Khan A.S. (Ed). Proceedings of Plasticity '97 (1997), Neat Press, Fulton MD 17
93. Barbe F., Forest S., and Cailletaud G. Int. J. Plasticity 17 (2001) 537
94. Mügge O. Nachr. Königl. Ges. Wiss. Göttingen. Math. Phys. K1 (1899) 56
95. Neuhäuser H. In: Kubin L.P., and Martin G. (Eds). Nonlinear Phenomenon in Materials Science, vol. 3 & 4 of Solid State Pheneomenon (1988), Trans. Tech. Publications, Switzerland 407
96. Kleiser T., and Boček M. Z. Metalkde 77 (1986) 587
97. Welzel G., Plessing J., and Neuhäuser H. Phys. Stat. Sol. (a) 166 (1998) 791
98. Konstantinidis A.K., and Aifantis E.C. Trans. ASME 124 (2002) 358
99. Bouchaud E. J. Phys.: Condens. Matter. 9 (1997) 4319
100. Krim J., Solina D.H., and Chiarello R. Phys. Rev. Lett. 66 (1991) 181
101. Chevrier J., Le Thanh V., and Payne A. Euro Phys. Lett. 16 (1991) 734
102. Herrasti P., Ocon P., Vazquez L., Salvarezza R.C., Vara J.M., and Arvia A.J. Phys. Rev. A 45 (1992) 7440
103. Zaiser M., Grasset F.M., Koutsos V., and Aifantis E.C. Phys. Rev. Lett. 93 (2004) 195507
104. Hansen A. In: Chakraborti B. (Ed). Lecture Notes in Physics (2006), Springer, Berlin
105. Mandelbrot B.B. Phys. Scr. 32 (1985) 257
106. Mandelbrot B.B. In: Pietrenero L., and Tossatti E. (Eds). Physics of Fractals (1986), North-Holland, Amsterdam
107. Feder J. Fractals (1988), Plenum Press, New York
108. Abercombe R.E. J. Geophys. Res. 100 (1995) 24015
109. Lockner D.A., Byerlee J.D., Kuksenko V., Ponimarev A., and Sidorin A. Nature (London) 350 (1991) 38
110. Vives E., Ortin J., Mañosa L., Ràfols I., Pérez-Magrané R., and Planes A. Phys. Rev. Lett. 72 (1994) 1694
111. Vives E., Ràfols I., Mañosa L., Ortin J., and Planes A. Phys. Rev. B 52 (1995) 12644
112. Miguel M.C., Vespignani A., Zapperi S., Weiss J., and Grasso J.R. Nature 410 (2001) 667
113. Diodati P., Marchesoni F., and Piazza S. Phys. Rev. Lett. 67 (1991) 2239
114. Petri A., Paparo G., Vespignani A., Alippi A., and Constantini M. Phys. Rev. Lett. 73 (1994) 3423
115. Rumi De, Dynamics of stick-slip: peeling of an adhesive tape and predictability in power law systems, Doctoral Thesis, Indian Institute of Science, Bangalore, India, 2006.
116. Bak P., Tang C., and Wiesenfeld K. Phys. Rev. Lett. 59 (1987) 381
117. Bak P., Tang C., and Wiesenfeld K. Phys. Rev. A 38 (1988) 364
118. Weiss J., and Marsan D. Science 299 (2003) 89
119. Lockner D.A. J. Acous. Emission 14 (1996) S88
120. Grassberger P., and Procaccia I. Physica D 9 (1983) 189
121. Essmann U. Phys. Stat. Sol. 3 (1963) 932
122. Mughrabi H. Philos. Mag. 23 (1971) 896, 931
123. Hähner P., Bay K., and Zaiser M. Phys. Rev. Lett. 81 (1998) 2470
124. Zaiser M., and Hähner P. Mat. Sci. Eng. A 270 (1999) 299
125. Sevillano G., Bouchad J., and Kubin L.P. Scripta Metall. Mater. 25 (1991) 355
126. Székely F., Groma I., and Lendvai J. Phys. Rev. B 62 (2000) 3093
127. Hughes D.A., Chrzan D.C., Liu Q., and Hansen N. Phys. Rev. Lett. 81 (1998) 4664
128. Hughes D.A. Scripta Materialia 47 (2002) 697
129. Bo Jackobsen, Poulsen H.F., Lienert U., Almer J., Shastri S.D., Sørensen H.O., Gundlach C., and Pantleon W. Science 312 (2006) 889
130. Groma I. Phys. Rev. B 56 (1997) 5807
131. Groma I., and Balough P. Acta Mater. 47 (1999) 3647
132. Groma I., and Bako B. Phys. Rev. Lett. 84 (2000) 1487
133. van Kampen N.G. Stochastic Processes in Physics and Chemistry (1981), North-Holland, Amsterdam
134. Risken H. The Fokker-Planck Equation: Methods of Solution and Applications. second ed. (1996), Springer, Berlin
135. Stratonovich R.L. Topics in the Theory of Random Noise vol. 1 (1967), Gordon & Breach, New York
136. Chaikin P.M., and Lubensky T.C. Principles of Condensed Matter Physics (1995), Cambridge University Press
137. Onuki A. Phys. Rev. E 68 (2003) 061502
138. Onuki A. J. Phys.: Condens. Matter 15 (2003) S891-S901
139. deGennes P.-G., Duran J., and Reisinger A. Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials (Partially Ordered Systems) (2000), Springer, New York
140. Balakrishnan V., Dattagupta S., and Venkatarman G. Philos. Mag. A 37 (1978) 65
141. Balakrishnan V. Pramana 11 (1978) 389
142. Balakrishnan V., and Dattagupta S. Z. Phys. B 42 (1981) 13
143. Venkataraman G. Mechanical and Thermal Behaviour of Metallic Materials vol. lXXXII (1982), corso, Soc. Italiana di Fisica, Bologna, Italy
144. Mott N.F. Philos. Mag. 44 (1953) 1151
145. Feltham P. Phys. Stat. Sol. 30 (1968) 135
146. Feltham P. J. Phys. D 6 (1973) 2048
147. Dobes F. Acta Metall. 28 (1980) 377
148. R.B. Stout, Crystal Lattice Defects, 1980.
149. Gilman J.J., and Johnston W.G. J. Appl. Phys. 31 (1960) 687
150. Ananthakrishna G. J. Phys. D 15 (1982) 77
151. Webster G.A. Philos. Mag. 14 (1966) 775
152. Peissker E., Haasen P., and Alexander H. Philos. Mag. 7 (1961) 1279
153. Reppich B., Haasen P., and Ilschner B. Acta Metall. 12 (1964) 1283
154. Ananthakrishna G., and Sahoo D. J. Phys. D 14 (1981) 2081
155. Ananthakrishna G., and Valsakumar M.C. J. Phys. D 15 (1982) L171
156. Higgens F.P., and Carpenter S.H. Acta Metall. 26 (1978) 133
157. Suzuki M. In: Pregogine I., and Rice S. (Eds). Advances in Chemical Physics vol. 46 (1981), Wiley, New York
158. Hähner P. Appl. Phys. A 62 (1996) 473
159. L.P. Kubin, B. Devincre, Deformation-induced microstructures: analysis and relation to properties, in: J.B. Bilde-Sørensen, et al. (Eds.), Proceedings of the 20th Risø International Symposium, Risø National Laboratory, Roskilde, Denmark, 1999, p. 61.
160. Bako B., and Groma I. Phys. Rev. B. 60 (1999) 122
161. Hähner P. Appl. Phys. A 63 (1996) 45
162. Hähner P. Acta Metall. 44 (1996) 2345
163. Balescu R. Equilibrium and Nonequlibrium Statistical Mechanics (1975), Wiley, New York
164. Zaiser M., Miguel M.C., and Groma I. Phys. Rev. B 64 (2001) 224102
165. Kröner E. In: Balian R., Kleman M., and Poirier J.P. (Eds). Physics of Defects (1981), North-Holland, Amsterdam 215
166. Miguel M.C., Vespignani A., Zapperi S., Weiss J., and Grasso J.R. Mat. Sci. Eng. A 309-310 (2001) 324
167. Groma I., and Bako B. Phys. Rev. B 58 (1998) 2969
168. Chandrasekhar S. Rev. Mod. Phys. 15 (1943) 8
169. Horsthemke W., and Lefever R. Noise Induced Transitions (1994), Springer, Berlin
170. Kuhlmann-Wilsdorf D. Mater. Sci. Eng. A 113 (1989) 1
171. Hansen N., and Kuhlmann-Wilsdorf D. Scripta Metal. Mater. 27 (1992) 951
172. Kratochvil J. Scripta Metall. 24 (1990) 891
173. Kratochvil J. Scripta Metall. 24 (1990) 1225
174. Essmann U., and Differt K. Scripta Metall. 22 (1988) 1337
175. Differt K., and Essmann U. Mat. Sci. Eng. A 164 (1993) 295
176. Essmann U., and Differt K. Mat. Sci. Eng. A 206 (1996) 56
177. Kratochvil J., and Orlova A. Philos. Mag. A 61 (1990) 281
178. Kuramoto Y., and Tsuzuki T. Prog. Theor. Phys. 52 (1974) 1399
179. Mashiyama H., Ito A., and Ohta T. Prog. Theor. Phys. 54 (1975) 1050
180. Richter P.H., Procaccia I., and Ross J. In: Prigogine I., and Rice S. (Eds). Advances in Chemical Physics (1982), Wiley Interscience, New York
181. Haken H. Advanced Synergetics, Instability Hierarchies of Self-Organizing Systems and Devices (1987), Springer, Berlin
182. Newell A.C., and Whitehead J.A. J. Fluid Mech. 38 (1968) 279
183. Murray J.D. Lectures on Nonlinear Differential Equation-Models in Biology (1977), Clarendon Press, Oxford (Chapter 1)
184. Rousell M.R., and Fraser S.J. J. Phys. Chem. 97 (1993) 8316
185. Davies M.J., and Skodje K.T. J. Chem. Phys. 111 (1999) 859
186. Benson S.W. Thermochemical Kinetics (1976), Wiley, New York
187. Pilling M.J., and Seatons P.W. Reaction Kinetics (1955), Oxford University Press, Oxford
188. Turanyi T., Tomlin A.S., and Pilling M.J. J. Phys. Chem. 97 (1993) 163
189. Fraser S.J. J. Chem. Phys. 88 (1988) 4732
190. Rousell M.R. J. Math. Chem. 21 (1997) 385
191. Mass U., and Pope S.B. Combus. Flame 88 (1992) 239
192. Yang B., and Pope S.B. Combus. Flame 112 (1998) 16
193. Li G., Tomlin A.S., Rabitz H., and Toth J. J. Chem. Phys. 101 (1994) 1172
194. Tomlin A.S., Li G., Rabitz H., and Toth J. J. Chem. Phys. 101 (1994) 1188 and references therein
195. Jones C.K.R.T. In: Arnold L., Jones C., Mishchaikow K., and Rangel G. (Eds). Dynamical Systems, Lecture Notes in Mathematics vol. 1609 (1995), Springer, Berlin
196. Grasman J. Asymptotic methods for relaxational oscillations and Applications. App. Math. Sci. 63 (1987)
197. J. Kerkovian, J.D. Cole, Perturbation Methods in Applied Mathematics, Lecture Notes in Mathematics, vol. 34, Springer, Berlin, New York, 1981.
198. van der Pol. Philos. Mag. 2 (1927) 978
199. J. Rinzel, A formal classification of bursting mechanisms in excitable systems, in: E. Teramoto, Y. Yamaguti (Eds.), Mathematical Topics in Population Biology, Morphogenesis and Neurosciences, Lecture Notes in Biomathematics, vol. 71, Springer, Berlin, 1987, 267.
200. Bertram R., Butte B.M.J., Kiemel T., and Sherman A. Bull. Math. Biol. 57 (1995) 413
201. Baer S.M., Erneux T., and Rinzel J. SIAM J. Appl. Math. 49 (1989) 55
202. Benoit E., Callout J.L., Diener F., and Diener M. Chasse au canard (1980), IRMA, Strasbourg
203. See also M. Diener, The Math. Intell. 6 (1984) 38.
204. Eckhaus W. Lect. Notes Maths. 905 (1983) 432
205. Baer S.M., and Erneux T. SIAM J. Appl. Math. 46 (1986) 721
206. Baer S.M., and Erneux T. SIAM J. Appl. Math. 52 (1992) 1651
207. Booth V., Carr T.W., and Erneux T. SIAM J. Appl. Math. 57 (1997) 1406
208. Eckmann J.P., Kamphorst S.O., Ruelle D., and Ciliberto S. Phys. Rev. A 34 (1986) 4971
209. Brown R., Bryant P., and Abarbanel H.D.I. Phys. Rev. A 43 (1991) 2787
210. Brown R., Bryant P., and Abarbanel H.D.I. Phys. Rev. Lett. 65 (1990) 1523
211. Whitnney H. Ann. Math. 37 (1936) 645
212. Takens F. In: Rand D.A., and Young L.S. (Eds). Dynamical Systems and Turbulence, Lecture Notes in Mathematics (1981), Springer, Berlin
213. Mané R. In: Rand D.A., and Young L.S. (Eds). Dynamical Systems and Turbulence, Lecture Notes in Mathematics (1981), Springer, Berlin
214. Ding M., Grebogi C., Ott E., Sauer T., and Yorke J.A. Phys. Rev. Lett. 70 (1993) 3872
215. Packard N.H., Crutchfield J.P., Farmer J.D., and Shaw R.S. Phys. Rev. Lett. 45 (1980) 712
216. Ruelle D. Commun. Math. Phys. 87 (1982) 287
217. Grassberger P., and Procaccia I. Phys. Rev. Lett. 50 (1983) 346
218. Hentschel H.G.E., and Procaccia I. Physica D 8 (1983) 435
219. Theiler J. Phys. Rev. A 34 (1986) 2427
220. Broomhead D., and King G. Physica D 20 (1987) 217
221. Ananthakrishna G., and Bharathi M.S. Phys. Rev. E 70 (2004) 026111
222. Noronha S.J., Ananthakrishna G., Fressengeas C., and Kubin L.P. Int. J. Bifurcation Chaos 7 (1997) 2577
223. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Physica D 16 (1985) 285
224. Sano M., and Sawada Y. Phys. Rev. Lett. 55 (1985) 1082
225. Zeng X., Eykholt R., and Pielke R.A. Phys. Rev. Lett. 66 (1991) 3229
226. Ananthakrishna G., Noronha S.J., Fressengeas C., and Kubin L.P. Phys. Rev. E 60 (1999) 5455
227. S. Noronha, Dynamical analysis of the Portevin-Le Chatelier effect: verification of theoretical prediction, Ph.D. Thesis, Indian Institute of Science, Bangalore, India, December 1998.
228. Noronha S.J., Ananthakrishna G., and Fressengeas C. In: Daniel M., Tamizhmani K.M., and Sahadevan R. (Eds). Proceedings of the International Conference on Non-Linear Dynamics: Instabilities and Chaos (2000), Narosa Publishing House, New Delhi 231
229. Theiler J., Eubank S., Longtin A., Galdrikian B., and Farmer J.D. Physica D 58 (1992) 77
230. Wilson K.G. Sci. Am. 241 (1979) 158
231. Mandelbrot B.B. Ann. Isr. Phya. Soc. 225 (1977)
232. Aref H., and Sigga E.D. J. Fluid Mech. 109 (1981) 435
233. Procaccia I. J. Stat. Phys. 36 (1984) 649
234. de Arcangelis L., Redner S., and Coniglio A. Phys. Rev. B 31 (1985) 4725
235. Witten Jr. T.A., and Sander L.M. Phys. Rev. Lett. 47 (1981) 1400
236. Halsey T.C., Jensen M.H., Kadanoff L.P., Procaccia I., and Shraiman B.I. Phys. Rev. A 33 (1986) 1141
237. Hentschel H.G.E., and Proccacia I. Physica D 8 (1983) 435
238. Chhabra A.B., and Jensen R.V. Phys. Rev. Lett. 62 (1989) 1327
239. Chhabra A.B., Maneveau C., Jensen R.V., and Sreenivasan K.R. Phys. Rev. A 40 (1989) 5284
240. Renyi A. Probability Theory (1970), North-Holland, Amsterdam
241. Bak P. How Nature Works (1996), Springer, New York
242. Jensen H.J. Self-organized Criticality (1998), Cambridge University Press, Cambridge
243. Gutenberg B., and Richter C.F. Ann. Goefis. 9 (1956) 1
244. Sreekala S., and Ananthakrishna G. Phys. Rev. Lett. 90 (2003) 135501
245. Ahluwalia R., and Ananthakrishna G. Phys. Rev. Lett. 86 (2001) 4076
246. R. De, G. Ananthakrishna, Phys. Rev. Lett. (2006) (in print).
247. Ráfols I., and Vives E. Phys. Rev. B 52 (1995) 12651
248. Kertesz J., and Kiss L.B. J. Phys. A: Math. Gen. 23 (1990) L433
249. Brindley A., and Worthington P.J. Metall. Rev. 145 (1970) 101
250. Ananthakrishna G., Fressengeas C., Grosbras M., Vergnol J., Engelke C., Plessing J., Neuhäuser H., Bouchaud E., Planes J., and Kubin L.P. Scripta Metall. Mater. 32 (1995) 1731 (The result was actually reported in an earlier paper)
251. Ananthakrishna G. Scripta Metall. Mater. 29 (1993) 1183
252. Ananthakrishna G., and Noronha S.J. In: Ananthakrishna G., Kubin L.P., and Martin G. (Eds). Non-Linear Phenomena in Materials Science vol. III (1995), Scitec, Zürich 277
253. Venkadesan S., Murthy K.P.N., and Valsakumar M.C. In: Ananthakrishna G., Kubin L.P., and Martin G. (Eds). Non-Linear Phenomena in Materials Science vol. III (1995), Scitec, Zürich 287
254. Quaouire L., and Fressengeas C. In: Ananthakrishna G., Kubin L.P., and Martin G. (Eds). Non-Linear Phenomena in Materials Science vol. III (1995), Scitec, Zürich 293
255. Bharathi M.S., Lebyodkin M., Ananthakrishna G., Fressengeas C., and Kubin L.P. Phys. Rev. Lett. 87 (2001) 165508
256. Lebyodkin M.A., Kravchenko V.Ya., and Bobrov V.S. Physica B 165-166 (1990) 267
257. Lebyodkin M.A., Kravchenko V.Ya., and Bobrov V.S. Mat. Sci. Eng. A 164 (1993) 252
258. Lebyodkin M.A., and Bobrov V.S. Solid State Phenomena 35-36 (1994) 411
259. Pascual R. Scripta Metall. 8 (1974) 1461
260. Hatano H. J. Appl. Phys. 47 (1976) 3873
261. Higgens P.F., and Carpenter S.H. Acta Metall. 26 (1978) 133
262. Heiple C.R., Carpenter S.H., and Carr M.J. Metal. Sci. 15 (1981) 587
263. Caceres C.H., and Bertorello H.R. Scripta Metall. 17 (1983) 1115
264. Caceres C.H., and Rodriguez A.M. Acta Metall. 35 (1987) 2851
265. Zeides F., and Roman I. Scripta Metall. 24 (1990) 1919
266. Chmelik F., Dosoudil J., Plessing J., Neuhäuser H., Lukac P., and Trojanova Z. Key Eng. Mats. 97-98 (1994) 263
267. Chmelik F., Trojanova Z., Prevorovsky Z., and Lukac P. J. Mat. Sci. Eng. A 164 (1993) 260
268. Ananthakrishna G., and Noronha S.J. In: Ananthakrishna G., Kubin L.P., and Martin G. (Eds). Non Linear Phenomena in Materials Science, vol. III-Instabilities and Patterning: Solid State Phenomena vols. 42-43 (1995), Scitex Publications 277
269. Quaouire L., and Fressengeas C. In: Ananthakrishna G., Kubin L.P., and Martin G. (Eds). Non Linear Phenomena in Materials Science, vol. III-Instabilities and Patterning: Solid State Phenomena vols. 42-43 (1995), Scitec Publications 293
270. Venkadesan S., Valsakumar M.C., Murthy K.P.N., and Rajasekar S. Phys. Rev. E 54 (1996) 611
271. See also S. Venkadesan, M.C. Valsakumar, K.P.N. Murthy, in: G. Ananthakrishna, L.P. Kubin, G. Martin (Eds.), Non Linear Phenomena in Materials Science, vol. III-Instabilities and Patterning: Solid State Phenomena, vols. 42-43, Scitec publications, 1995, p. 287.
272. Albano A.M., Muench J., Schwartz C., Mees A.I., and Rapp P.E. Phys. Rev. A 38 (1988) 3017
273. Ananthakrishna G., and Valsakumar M.C. Phys. Lett. A 95 (1983) 69
274. Ananthakrishna G., and De R. Dynamics of stick-slip: some universal and not so universal features. In: Chakraborthy B.K. (Ed). Lecture Notes in Physics (2006), Springer, Berlin
275. Persson B.N.J. Sliding Friction: Physical Principles and Applications. Second ed. (2000), Springer, Heidelberg
276. Carlson J.M., and Langer J.S. Phys. Rev. Lett. 62 (1989) 2632
277. Carlson J.M., and Langer J.S. Phys. Rev. A 40 (1989) 6470
278. Schmittbuhl J., Vilotte J.P., and Roux S. J. Geophys. Res. 101 B12 (1996) 27 714
279. Maugis D., and Barquins M. In: Allen K.W. (Ed). Adhesion vol. 12 (1988), Elsevier, London 205
280. De R., Maybhate A., and Ananthakrishna G. Phys. Rev. E 70 (2004) 046223
281. De R., and Ananthakrishna G. Phys. Rev. E 71 (2005) 055201R
282. Burridge P., and Knopoff L. Bull. Seismol. Soc. Am. 57 (1967) 341
283. Lebyodkin M.A., Brechet Y., Estrin Y., and Kubin L.P. Phys. Rev. Lett. 74 (1995) 4758
284. Lebyodkin M., Bréchet Y., Estrin Y., and Kubin L.P. Acta Mater. 44 (1996) 4531
285. Anderson P.W. Phys. Rev. 109 (1958) 1492
286. Schreiber M., and Grussbach G. Phys. Rev. Lett. 67 (1991) 607
287. Bharathi M.S., Lebyodkin M., Ananthakrishna G., Fressengeas C., and Kubin L.P. Acta Materialia 50 (2002) 2813
288. Stanley H.E. Introduction to Phase Transitions and Critical Phenomena (1971), Oxford University Press
289. D'Anna G., and Nori F. Phys. Rev. Lett. 85 (2000) 4096
290. Field S., Witt J., Nori F., and Ling X. Phys. Rev. Lett. 74 (1995) 1206
291. Olson C.J., Reichhardt C., and Nori F. Phys. Rev. B 56 (1997) 6175
292. Barat P., Sarkar A., Mukherjee P., and Bandyopadhyay S.K. Phys. Rev. Lett. 94 (2005) 055502
293. Scafetta N., Latora V., and Grigolini P. Phys. Rev. E 66 (2002) 036130
294. Raghavan R.S., and Ananthakrishna G. Phys. Rev. Lett. 97 (2006) 079601
295. Essmann U., and Mughrabi H. Philos. Mag. A 40 (1979) 731
296. Vegge T., Rasmussen T., Leffers T., Pedersen O.B., and Jacobsen K.W. Philos. Mag. Lett. 81 (2001) 137
297. Bonneville J., Escaig B., and Martin J.L. Acta Metall. 36 (1988) 1989
298. Tippelt B., Bretschneider J., and Hähner P. Phys. Stat. Sol. A 163 (1998) 11
299. Aslanides A., and Pontikis V. Philos. Mag. A 80 (2000) 2337
300. Essmann U. Philos. Mag. A 45 (1982) 171
301. Holzwarth U., and Essmann U. Appl. Phys. A 58 (1994) 197
302. Kratochvil J., and Saxlova M. Scripta Metall. 26 (1992) 113
303. Kratochvil J., and Saxlova M. Solid State Phenomena 23-24 (1992) 369
304. Walgraef D., and Aifantis E.C. Int. J. Eng. Sci. 24 (1986) 1789
305. Aifantis E.C. Mat. Sci. Eng. 81 (1986) 563
306. Rashkeev S.N., Glazov M.V., and Barlat F. Comput. Mat. Sci. 21 (2001) 230
307. Eckhaus W. Studies in Nonlinear Stability Theory (1965), Springer, New York
308. Sharp J.V., and Makin N.J. Philos. Mag. 10 (1964) 1011
309. Hancock J.R., and Grosskreutz J.C. Acta Metall. 17 (1969) 77
310. Tippelt B., Bretschneider J., and Holste C. Philos. Mag. Lett. 74 (1996) 161
311. Kratochvil J. Revue Phys. Appl. 23 (1988) 419
312. Franěk A., Kalus R., and Kratochvil J. Philos. Mag. A 64 (1991) 497
313. Franěk A., Kratochvil J., Saxlova M., and Sedláček R. Mater. Sci. Eng. A 137 (1991) 119
314. Kratochvil J. Solid State Phenomena 35-36 (1994) 71
315. Devincre B., and Kubin L.P. Mat. Sci. Eng. A 234-236 (1997) 8 (Proc. ICSMA 11 (Prague, 1997))
316. Vladimirov V.I., and Pegel B. Phys. Stat. Sol. B 56 (1973) K105
317. Nicolis G., and Prigogine I. Self-organization in Non-equilibrium Systems (1977), Wiley, New-York
318. Salazar J.M., Fournet R., and Banai N. Acta Metall. Mater. 43 (1995) 1127
319. Gómez-Garcia D., Devincre B., and Kubin L.P. Phys. Rev. Lett. 96 (2006) 125503
320. Sleeswyk A.W. Acta Metall. 6 (1958) 598
321. van den Beukel A. Acta Metall 30 (1980) 965
322. Louat N. Scripta Metall. 15 (1981) 1169
323. Kubin L.P., and Estrin Y. Acta Metall. Mater. 38 (1990) 697
324. Kubin L.P., and Estrin Y. J. Mech. Behav. Mater. 2 (1989-1990) 255
325. Cadel E., Fraczkiewicz A., and Blavette D. Mat. Sci. Eng. A 309-310 (2001) 32
326. Räuchle W., Vöhringer O., and Macherauch E. Mater. Sci. Eng. 12 (1973) 147
327. Lukac P., Balik J., and Chmelik F. Met. Sci. Eng. A 234 (1997) 45
328. Kalk A., Schwink Ch., and Springer F. Mat. Sci. Eng. A 164 (1993) 230
329. Kalk A., Nortmann A., and Schwink Ch. Philos. Mag. A 72 (1995) 1239
330. McCormic P.G. Acta Metall. 36 (1988) 3061
331. Hähner P. Mat. Sci. Eng. A 207 (1996) 216
332. Hähner P. Mat. Sci. Eng. A 207 (1996) 208
333. Rizzi E., and Hähner P. Int. J. Plast. 20 (2004) 121
334. Hähner P., and Rizzi E. Acta Metall. 51 (2003) 3385
335. Kok S., Bharathi M.S., Beaudoin A.J., Fressengeas C., Ananthakrishna G., Kubin L.P., and Lebyodkin M. Acta Materialia 51 (2003) 3651
336. Persson B.N.J., and Tosatti E. Physics of Sliding Friction (1996), Kluwer Academic Publishers, Dordrecht
337. D. Maugis, M. Barquins, in: K.W. Allenn (Ed.), Adhesion, vol. 12, Elsevier, London, 1988.
338. Rajesh S., and Ananthakrishna G. Phys. Rev. E 61 (2000) 3664
339. Ananthakrishna G., and John T.M. In: Bai-Lin H. (Ed). Directions in Chaos (1990), World Scientific, Singapore 133
340. Heslot F., Castaing B., and Libchaber A. Phys. Rev. A 36 (1987) 5780
341. Bohr T., Jensen M.H., Paladin G., and Vulpiani A. Dynamical Systems Approach to Turbulence (1997), Cambridge, United Kingdom
342. Bekele M., and Ananthakrishna G. Phys. Rev. E 56 (1997) 6917
343. Bekele M., and Ananthakrishna G. Int. J. Bifurc. Chaos 8 (1997) 141
344. Glazov M.V., Williams D.R., and Laird C. Appl. Phys. A 64 (1997) 373
345. Zaiser M., Glazov M., Lalli L.A., and Richmond O. Comput. Mater. Sci. 5 (1999) 35
346. Rajesh S., and Ananthakrishna G. Physica D 140 (2000) 193
347. S. Rajesh, Dynamical approach to the Portevin-Le Chatelier effect, Doctoral Thesis, Indian Institute of Science, Bangalore, India, 2000.
348. Ananthakrishna G. Solid State Phenomena 23-24 (1992) 417
349. Roux J.C., and Swinney H.L. In: Vidal C., and Pacault A. (Eds). Nonequilibrium Dynamics in Chemical Systems (1984), Springer, Berlin
350. Arneodo A., Argoul F., Elezgaray J., and Richetti P. Physica D 62 (1993) 134
351. Koper M.T.M. Physica D 80 (1995) 72
352. Epstein I.R., and Showalter K. J. Phys. Chem. 100 (1996) 13132
353. Milik A., Szmolyan P., Löffelmann H., and Gröller E. Int. J. Bifurc. Chaos 8 (1998) 505
354. Koper M.T.M., Gaspard P., and Sluyters J.H. J. Chem. Phys. 97 (1992) 8250
355. Argoul F., Huth J., Merzeau P., Arneodo A., and Swinney H.L. Physica D 62 (1993) 170
356. Chay T.R., Fan Y.S., and Lee Y.S. Int. J. Bifurc. Chaos 5 (1995) 595
357. de Tomoasi F., Hennequin D., Zambon B., and Arimondo E. J. Opt. Soc. Am. B 6 (1989) 45
358. Guckenheimer J., and Holmes P.J. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1990), Springer, Berlin
359. Shilnikov L.P. Sov. Math. Dokl. 6 (1965) 163
360. Glendinning P., and Sparrow C. J. Statist. Phys. 35 (1984) 645
361. Gavrilov N.K., and Shilnikov L.P. Math. USSR-Sb. 17 (1972) 467
362. Navrátil V., Hamerský M., and Blažková J. Czech. J. Phys. B 24 (1974) 907
363. Zagoruyko L.N., Osetskiy A.I., and Soldatov V.P. Phys. Met. Metallogr. 43 (1977) 156
364. Stejskalolvá V., Hamersky M., Lukáč P., Vostrý P., and Sprušil B. Czech. J. Phys. B 31 (1981) 195
365. Hamersky M., and Lukáč P. Czech. J. Phys. B 23 (1973) 1345
366. Valsakumar M.C., and Ananthakrishna G. J. Phys. D 16 (1983) 1055
367. Carr J. Applications of Center Manifold Theory (1981), Springer, Berlin
368. Thomson R., Koslowski M., and LeSar R. Mater. Sci. Eng. A 400-401 (2005) 199
369. Bharathi M.S., Rajesh S., and Ananthakrishna G. Scripta Mater. 48 (2003) 1355
370. Bodner S.R., and Rosen A. J. Mech. Phys. Solids 15 (1967) 63
371. Kubin L.P., and Estrin Y. J. de Physique 46 (1986) 497
372. Neelakantan K., and Venkataraman G. Acta Metall. 31 (1983) 77
373. Neelakantan K., and Venkataraman G. Bull. Mater. Sci. 14 (1991) 1279
374. Bharathi M.S., and Ananthakrishna G. Phys. Rev. E 67 (2003) 065104R
375. van Saarloos W. Phys. Rev. A 37 (1988) 211
376. Dee G., and Langer J.S. Phys. Rev. Lett. 50 (1983) 383
377. Korbel A., Zasadzinski J., and Siekluka Z. Acta Metall. 24 (1976) 921
378. Zhang S., McCormick P.G., and Estrin Y. Acta Mater. 49 (2001) 1087
379. Hähner P., and Rizzi E. Acta Metall. 51 (2003) 3385
380. Nortmann A., and Schwink Ch. Acta Metall. 45 (1997) 2043
381. Nortmann A., and Schwink Ch. Acta Metall. 45 (1997) 2051
382. Springer F., and Schwink Ch. Scr. Metall. Mater. 25 (1991) 2739
383. Springer F., and Schwink Ch. Scr. Metall. Mater. 32 (1995) 1771
384. Aifantis E.C. Mater. Sci. Eng. 81 (1986) 563
385. Kok S., Beaudoin A.J., Tortorelli D.A., and Lebyodkin M. Acta Mater. 48 (2002) 2529
386. Taylor G.I. J. Inst. Met. 62 (1938) 307
387. Valiente A. J. Appl. Mech. 68 (2001) 412