Thermodynamics of fractal signals based on wavelet analysis: Application to fully developed turbulence data and DNA sequences

Physica A: Statistical Mechanics and its Applications

Volumn 254, Issue 1-2, 1998, Pages 24-45

  Arneodo, A ^a   Audit, B ^a   Bacry, E ^b   Manneville, S ^a   Muzy, J F ^a   Roux, S G ^a  

^a CENTRE DE RECHERCHE PAUL PASCAL   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DNA SEQUENCES; FUNCTIONS; THERMODYNAMICS; TURBULENCE; WAVELET TRANSFORMS;

MULTIFRACTAL FORMALISM; WAVELET TRANSFORM MODULUS MAXIMA (WTMM) METHOD;

FRACTALS;

EID: 0032074913     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00002-8     Document Type: Article

References (172)

1. B.B. Mandelbrot, Fractals: Form, Chance and Dimension, Freeman, San Francisco, 1977; The Fractal Geometry of Nature, Freeman, San Franscisco, 1982.
2. B.B. Mandelbrot, Fractals: Form, Chance and Dimension, Freeman, San Francisco, 1977; The Fractal Geometry of Nature, Freeman, San Franscisco, 1982.
3. H.E. Stanley, N. Ostrowski (Eds.), On Growth and Form: Fractal and Non-Fractal Patterns in Physics, Martinus Nijhoff, Dordrecht, 1986; Random Fluctuations and Pattern Growth, Kluwer, Dordrecht, 1988.
4. H.E. Stanley, N. Ostrowski (Eds.), On Growth and Form: Fractal and Non-Fractal Patterns in Physics, Martinus Nijhoff, Dordrecht, 1986; Random Fluctuations and Pattern Growth, Kluwer, Dordrecht, 1988.
5. J. Feder, Fractals, Pergamon, New York, 1988.
6. T. Vicsek, Fractal Growth Phenomena, World Scientific, Singapore, 1989.
7. A. Aharony, J. Feder (Eds.), Fractals in Physics, Essays in honour of B.B. Mandelbrot, Physica D 38 (1989).
8. F. Family, T. Viscek (Eds.), Dynamics of Fractal Surfaces, World Scientific, Singapore, 1991.
9. T. Vicsek, M. Schlesinger, M. Matsushita (Eds.), Fractals in Natural Science, World Scientific, Singapore, 1994.
10. B.J. West, W. Deering, Phys. Rep. 254 (1994) 1.
11. G.G. Wilkinson, I. Kanellopoulos, J. Mégier (Eds.), Fractals in Geoscience and Remote Sensing, Image Understanding Research Series, vol. 1, ECSC-EC-EAEC, Brussels, Luxemburg, 1995.
12. P. Tabeling, O. Cardoso (Eds.), Turbulence: A Tentative Dictionary, Plenum, New York, 1995.
13. A.-L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge Univ. Press, Cambridge, 1995.
14. B.B. Mandelbrot, J.W. Van Ness, SIAM Rev. 10 (1968) 422.
15. H.O. Peitgen, D. Saupe (Eds.), The Science of Fractal Images, Springer, Berlin, 1987.
16. B.B. Mandelbrot, J. Bus. Univ. Chicago 40 (1967) 393.
17. B.B. Mandelbrot, H.M. Taylor, Oper. Res. 15 (1967) 1057.
18. W. Li, Int. J. Bifurcation Chaos 1 (1991) 583.
19. M. Goodchild, Math. Geol. 12 (1980) 85.
20. B.J. West, Fractal Physiology and Chaos in Medecine, World Scientific, Singapore, 1990.
21. F. Anselmet, Y. Gagne, E.J. Hopfinger, R.A. Antonia, J. Fluid Mech. 140 (1984) 63.
22. Y. Gagne, Thesis, University of Grenoble, 1987.
23. C.K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simons, H.E. Stanley, Nature 356 (1992) 168.
24. H.E. Stanley, S.V. Buldyrev, A.L. Goldberger, S. Havlin, S.M. Ossadnik, C.K. Peng, M. Simons, Fractals 1 (1993) 283.
25. R.F. Voss, Physica D 38 (1989) 362; in Ref. [13], p. 21.
26. B. Dubuc, J.F. Quiniou, C. Roque-Carmes, C. Tricot, S.W. Zucker, Phys. Rev. A 39 (1989) 1500.
27. G.A. Edgard, Measure, Topology and Fractal Geometry, Springer, Berlin, 1990.
28. U. Frisch, G. Parisi, in: M. Ghil, R. Benzi, G. Parisi (Eds.), Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, North-Holland, Amsterdam, 1985, p. 84.
29. A.L. Barabási, T. Vicsek, Phys. Rev. A 44 (1991) 2730.
30. J.F. Muzy, E. Bacry, A. Arneodo, Int. J. Bifurcation Chaos 4 (1994) 245.
31. A. Arneodo, E. Bacry, J.F. Muzy, Physica A 213 (1995) 232.
32. S. Jaffard, C.R. Acad. Sci. Paris 308 serie I (1989) 79; serie I (1992) 19.
33. S. Jaffard, C.R. Acad. Sci. Paris 308 serie I (1989) 79; serie I (1992) 19.
34. M. Holschneider, P. Tchamitchian, in Ref. [65], p. 102.
35. S. Mallat, W.L. Hwang, IEEE Trans. Inform. Theory 38 (1992) 617.
36. E. Bacry, J.F. Muzy, A. Arneodo, J. Stat. Phys. 70 (1993) 635.
37. R. Benzi, G. Paladin, G. Parisi, A. Vulpiani, J. Phys. A 17 (1984) 3521.
38. E.B. Vul, Ya.G. Sinai, K.M. Khanin, J. Russ. Math. Surv. 39 (1984) 1.
39. T.C. Halsey, M.H Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Phys. Rev. A 33 (1986) 1141.
40. R. Badii, Thesis, University of Zurich, 1987.
41. P. Collet, J. Lebowitz, A. Porzio, J. Stat. Phys. 47 (1987) 609.
42. M.J. Feigenbaum, J. Stat. Phys. 46 (1987) 919, 925.
43. M.H. Jensen, L.P. Kadanoff, I. Procaccia, Phys. Rev. A 36 (1987) 1409.
44. G. Paladin, A. Vulpiani, Phys. Rep. 156 (1987) 148.
45. B.B. Mandelbrot, Fractals and Multifractals: Noise, Turbulence and Galaxies, Selecta, vol. 1, Springer, New York, 1989.
46. D. Rand, Ergod Th. and Dyn. Sys. 9 (1989) 527.
47. A. Bunde, S. Havlin (Eds.), Fractals and Disordered Systems, Springer, Berlin, 1991.
48. P. Meakin, in: C. Domb, J.L. Lebowitz (Eds.), Phase Transition and Critical Phenomena, vol. 12, Academic Press, Orlando, 1988, p. 355.
49. B.B. Mandelbrot, J. Fluid. Mech. 62 (1974) 331.
50. U. Frisch, S.A. Orzag, Turbulence: Challenges for Theory and Experiments, Physics Today (1990) 24.
51. C. Meneveau, K.R. Sreenivasan, J. Fluid Mech. 224 (1991) 429.
52. Ya.G. Sinai, J. Russ. Math. Surveys 27 (1972) 21.
53. R. Bowen, Lect. Notes, in Maths 470 (1975) 1.
54. D. Ruelle, Thermodynamic Formalism, Addison-Wesley, Reading, MA, 1978.
55. T. Bohr, T. Tèl, in: B.L. Hao (Ed.), Direction in Chaos, vol. 2, World Scientific, Singapore, 1988.
56. A. Renyi, Probability Theory, North-Holland, Amsterdam, 1970.
57. P. Grassberger, Phys. Lett. A 97 (1983) 227.
58. H.G.E. Hentschel, I. Procaccia, Physica D 8 (1983) 435.
59. P. Grassberger, I. Procaccia, Physica D 13 (1984) 34.
60. P. Grassberger, R. Badii, A. Politi, J. Stat. Phys. 51 (1988) 135.
61. U. Frisch, Turbulence, Cambridge Univ. Press, Cambridge, 1995.
62. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics, vol. 2, MIT Press, Cambridge, MA, 1975.
63. J.F. Muzy, E. Bacry, A. Arneodo, Phys. Rev. E 47 (1993) 875; in Ref. [70], p. 323.
64. P. Goupillaud, A. Grossmann, J. Morlet, Geoexploration 23 (1984) 85.
65. A. Grossmann, J. Morlet, SIAM J. Math. Anal. Appl. 15 (1984) 723; in: L. Steit (Ed.), Mathematics and Physics, Lecture on Recent Results, World Scientific, Singapore, 1985, p. 135.
66. A. Grossmann, J. Morlet, SIAM J. Math. Anal. Appl. 15 (1984) 723; in: L. Steit (Ed.), Mathematics and Physics, Lecture on Recent Results, World Scientific, Singapore, 1985, p. 135.
67. J.M. Combes, A. Grossmann, P. Tchamitchian (Eds.), Wavelets, Springer, Berlin, 1989.
68. Y. Meyer, Ondelettes, Hermann, Paris, 1990.
69. P.G. Lemarié (Ed.), Les Ondelettes en 1989, Springer, Berlin, 1990.
70. Y. Meyer (Ed.), Wavelets and Applications, Springer, Berlin, 1992.
71. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
72. M.B. Ruskai, G. Beylklin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, L. Raphael (Eds.), Wavelets and Their Applications, Jones and Bartlett, Boston, 1992.
73. C.K. Chui, An Introduction to Wavelets, Academic Press, Boston, 1992.
74. Y. Meyer, S. Roques (Eds.), Progress in Wavelet Analysis and Applications, Editions Frontières, Gif sur Yvette, 1993.
75. A. Arneodo, F. Argoul, E. Bacry, J. Elezgaray, J.F. Muzy, Ondelettes, Multifractales et Turbulences: de l'ADN aux croissances cristallines, Diderot Editeur, Arts et Sciences, Paris, 1995.
76. G. Erlebacher, M.Y. Hussaini, L.M. Jameson (Eds.), Wavelets: Theory and Applications, Oxford Univ. Press, Oxford, 1996.
77. M. Holschneider, Wavelets: An Analysis Tool, Oxford Univ. Press, Oxford, 1996.
78. M. Holschneider, J. Stat. Phys. 50 (1988) 963; Thesis, University of Aix-Marseille II, 1988.
79. A. Arneodo, G. Grasseau, M. Holschneider, Phys. Rev. Lett. 61 (1988) 2281; in Ref. [63], p. 182.
80. A. Arneodo, F. Argoul, J. Elezgaray, G. Grasseau, in: G. Turchetti (Ed.), Nonlinear Dynamics, World Scientific, Singapore, 1989, p. 130.
81. F. Argoul, A. Arneodo, G. Grasseau, Y. Gagne, E.J. Hopfinger, U. Frisch, Nature 338 (1989) 52.
82. A. Arneodo, F. Argoul, G. Grasseau, in Ref. [65], p. 125.
83. F. Argoul, A. Arneodo, J. Elezgaray, G. Grasseau, R. Murenzi, Phys. Lett. A 135 (1989) 327; Phys. Rev. A 41 (1990) 5537.
84. F. Argoul, A. Arneodo, J. Elezgaray, G. Grasseau, R. Murenzi, Phys. Lett. A 135 (1989) 327; Phys. Rev. A 41 (1990) 5537.
85. A. Arneodo, F. Argoul, E. Bacry, J. Elezgaray, E. Freysz, G. Grasseau, J.F. Muzy, B. Pouligny, in Ref. [66], p. 286.
86. A. Arneodo, F. Argoul, E. Freysz, J.F. Muzy, B. Pouligny, in Ref. [68], p. 241.
87. A. Arneodo, E. Bacry, J.F. Muzy, Europhys. Lett. 25 (1994) 479.
88. A. Arneodo, in Re;f. [72], p. 349.
89. G. Grasseau, Thesis, University of Bordeaux I, 1989.
90. E. Bacry, Thesis, University of Paris VII, 1992.
91. J.F. Muzy, Thesis, University of Nice, 1993.
92. D. Sornette, in: B. Dubrulle, F. Graner, D. Sornette (Eds.), Scale Invariance and Beyond, EDP Sciences & Springer, Les Vlis & Berlin, 1997, p. 235.
93. E. Bacry, A. Arneodo, U. Frisch, Y. Gagne, E.J. Hopfinger, in: M. Lesieur, O. Metais (Eds.), Turbulence and Coherent Structures, Kluwer, Dordrecht, 1991, p. 203.
94. M. Vergassola, R. Benzi, L. Biferale, D. Pissarenko, J. Phys. A 26 (1993) 6093.
95. M. Vergassola, U. Frisch, Physica D 54 (1991) 58.
96. J.D. Farmer, E. Ott, J.A. Yorke, Physica D 7 (1983) 153.
97. J.F. Muzy, E. Bacry, A. Arneodo, Phys. Rev. Lett. 67 (1991) 3515.
98. S. Jaffard, Multifractal formalism for functions: Part I and Part II, SIAM J. Math. Anal., to appear.
99. A. Arneodo et al., Europhys. Lett. 34 (1996) 411.
100. A.N. Kolmogorov, C. R. Acad. Sci. USSR 30 (1941) 301.
101. B. Castaing, Y. Gagne, E.J. Hopfinger, Physica D 46 (1990) 177.
102. P. Tabeling, G. Zocchi, F. Belin, J. Maurer, H. Willaime, Phys. Rev. E 53 (1996) 1613.
103. S.G. Roux, Thesis, University of Aix-Marseille II, 1996.
104. A. Arneodo, E. Bacry, J.F. Muzy, in: J.P. Bonnet, M.N. Glauser (Eds.), Eddy Structure Identification in Free Turbulent Shear Flows, Kluwer, Dordrecht, 1993, p. 153; in Ref. [10], p. 139.
105. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Phys. Rev. E 48 (1993) R29; Phys. Rev. E 51 (1995) 2672.
106. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Phys. Rev. E 48 (1993) R29; Phys. Rev. E 51 (1995) 2672.
107. R. Benzi, S. Ciliberto, C. Baudet, G.R. Chavarria, R. Tripiccione, Europhys. Lett. 24 (1993) 275.
108. A.N. Kolmogorov, J. Fluid Mech. 13 (1962) 82.
109. A.M. Obukhov, J. Fluid Mech. 13 (1962) 77.
110. A. Arneodo, J.F. Muzy, S.G. Roux, J. Phys. II France 7 (1997) 363.
111. A. Arneodo, S. Manneville, J.F. Muzy, S.G. Roux, Experimental evidence for anomalous scale dependent cascading process in turbulent velocity statistics, preprint, 1997.
112. Z.S. She, E. Leveque, Phys. Rev. Lett. 72 (1994) 336.
113. Z.S. She, E.C. Waymire, Phys. Rev. Lett. 74 (1995) 262.
114. B. Dubrulle, Phys. Rev. Lett. 73 (1994) 959; J. Phys. II France 6 (1996) 1825.
115. B. Dubrulle, Phys. Rev. Lett. 73 (1994) 959; J. Phys. II France 6 (1996) 1825.
116. I. Daubechies, A. Grossmann, Y. Meyer, J. Math. Phys. 27 (1986) 1271.
117. B. Castaing, Y. Gagne, M. Marchand, Physica D 68 (1993) 387.
118. A. Naert, L. Puech, B. Chabaud, J. Peinke, B. Castaing, B. Hebral, J. Phys. II France 4 (1994) 215.
119. B. Chabaud, A. Naert, J. Peinke, F. Chillà, B. Castaing, B. Hebral, Phys. Rev. Lett. 73 (1994) 3227.
120. B. Castaing, B. Dubrulle, J. Phys. II France 5 (1995) 895.
121. B. Castaing, J. Phys. II France 6 (1996) 105.
122. F. Chillà, J. Peinke, B. Castaing, J. Phys. II France 6 (1996) 455.
123. B. Castaing, in: B. Dubrulle, F. Graner, D. Sornette (Eds.), Scale Invariance and Beyond, EDP Sciences & Springer, Les Vlis & Berlin, 1997, p. 225.
124. E.A. Novikov, Phys. Fluids A 2 (1990) 814; Phys. Rev. E 50 (1995) 3303.
125. E.A. Novikov, Phys. Fluids A 2 (1990) 814; Phys. Rev. E 50 (1995) 3303.
126. B. Dubrulle, in: B. Dubrulle, F. Graner, D. Sornette (Eds.), Scale Invariance and Beyond, EDP Sciences & Springer, Les Vlis & Berlin, 1997, p. 275.
127. W. Li, Int. J. Bifurcation Chaos 2 (1993) 137.
128. M.Ya. Azbel, Phys. Rev. Lett. 75 (1995) 168.
129. H. Herzel, I. Große, Physica A 216 (1995) 518.
130. R.F. Voss, Phys. Rev. Lett. 68 (1992) 3805; Fractals 2 (1994) 1.
131. R.F. Voss, Phys. Rev. Lett. 68 (1992) 3805; Fractals 2 (1994) 1.
132. R.N. Mantegna, S.V. Buldyrev, A.L. Goldberger, S. Havlin, C.K. Peng, M. Simons, H.E. Stanley, Phys. Rev. E 52 (1995) 2939.
133. S. Havlin, S.V. Buldyrev, A.L. Goldberger, R.N. Mantegna, C.K. Peng, M. Simons, H.E. Stanley, Fractals 3 (1995) 269.
134. S. Nee, Nature 357 (1992) 450.
135. C.A. Chazidimitriou-Dreismann, L. Larhammar, Nature 361 (1993) 212.
136. S. Karlin, V. Brendel, Science 259 (1993) 677.
137. B. Borstnick, D. Pumpernik, D. Lukman, Europhys. Lett. 23 (1993) 389.
138. S.V. Buldyrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, M.E. Matsa, C.K. Peng, M. Simons, H.E. Stanley, Phys. Rev. E 51 (1995) 5084.
139. G. Bernardi, B. Olofsson, J. Filipski, M. Zerial, J. Salinas, F. Cuny, M. Meunier-Rotival, F. Rodier, Science 228 (1985) 953.
140. G.A. Churchill, Bull. Math. Biol. 51 (1989) 79.
141. J.W. Fickett, D.C. Torney, D.R. Wolf, Genomics 13 (1992) 1056.
142. A. Arneodo, E. Bacry, P.V. Graves, J.F. Muzy, Phys. Rev. Lett. 74 (1995) 3293.
143. A. Arneodo, Y. D'Aubenton-Carafa, E. Bacry, P.V. Graves, J.F. Muzy, C. Thermes, Physica D 96 (1996) 291.
144. A. Arneodo, Y. D'Aubenton-Carafa, B. Audit, E. Bacry, J.F. Muzy, C. Thermes, Eur. Phys. J. B 1 (1998) 259.
145. P. Allegrini, M. Barbi, P. Grigolini, B.J. West, Phys. Rev. E 52 (1995) 5281.
146. G. Bernardi, Annu. Rev. Genet. 23 (1989) 637.
147. P. Sharp, G. Matassi, Current Opinion Gent. Dev. 4 (1994) 851.
148. S. Jaffard, Y. Meyer, Wavelets methods for pointwise regularity and local oscillations of functions, Mem. A.M.S., to appear.
149. A. Arneodo, E. Bacry, J.F. Muzy, Phys. Rev. Lett. 74 (1995) 4823.
150. N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrésani, IEEE Trans. Inform. Theory 38 (1992) 644.
151. A. Arneodo, E. Bacry, S. Jaffard, J.F. Muzy, J. Stat. Phys. 87 (1997) 179.
152. A. Arneodo, E. Bacry, S. Jaffard, J.F. Muzy, Singularity spectrum of multifractal functions involving oscillating singularities, J. Fourier Anal. Appl. (1997), to appear.
153. J. Arrault, Thesis, University of Bordeaux I, 1995.
154. J. Arrault, A. Arneodo, A. Davis, A. Marshak, Phys. Rev. Lett. 79 (1997) 75.
155. S. Mallat, S. Zhong, IEEE Trans. Patt. Anal. Machine Intell. 14 (1992) 710.
156. J. Canny, IEEE Trans. Pattern Anal. Machine Intell. 8 (1986) 679.
157. A. Arneodo, S. Manneville, J.F. Muzy, Phys. Rev. Lett. 80 (1998) 708.
158. A. Arneodo, J.F. Muzy, D. Sornette, Causal cascade in the stock market from the infrared to the ultraviolet, Eur. Phys. J. B 1 (1998), to appear.
159. M.J. Feigenbaum, J. Stat. Phys. 21 (1979) 669; Los Alamos Sci. 1 (1980) 4; Comm. Math. Phys. 77 (1980) 65.
160. M.J. Feigenbaum, J. Stat. Phys. 21 (1979) 669; Los Alamos Sci. 1 (1980) 4; Comm. Math. Phys. 77 (1980) 65.
161. M.J. Feigenbaum, J. Stat. Phys. 21 (1979) 669; Los Alamos Sci. 1 (1980) 4; Comm. Math. Phys. 77 (1980) 65.
162. M.J. Feigenbaum, M.H. Jensen, I. Procaccia, Phys. Rev. Lett. 57 (1986) 1503.
163. A.B. Chhabra, R.V. Jensen, K.R. Sreenivasan, Phys. Rev. A 40 (1989) 4593.
164. M.F. Barnsley, S.G. Demko, Proc. R. Soc. London A 399 (1985) 243.
165. M.F. Barnsley, Fractal Everywhere, Academic Press, New York, 1988.
166. C.R. Handy, G. Mantica, Physica D 43 (1990) 17.
167. A. Arneodo, F. Argoul, E. Bacry, J.F. Muzy, M. Tabard, Fractals 1 (1993) 629.
168. A. Arneodo, F. Argoul, E. Bacry, J.F. Muzy, M. Tabard, Phys. Rev. Lett. 68 (1992) 3456; J. Diff. Eq. Appl. 1 (1995) 117.
169. A. Arneodo, F. Argoul, E. Bacry, J.F. Muzy, M. Tabard, Phys. Rev. Lett. 68 (1992) 3456; J. Diff. Eq. Appl. 1 (1995) 117.
170. A. Arneodo, F. Argoul, J.F. Muzy, M. Tabard, Phys. Lett. A 171 (1992) 31; Physica A 188 (1992) 217.
171. A. Arneodo, F. Argoul, J.F. Muzy, M. Tabard, Phys. Lett. A 171 (1992) 31; Physica A 188 (1992) 217.
172. A. Kuhn, F. Argoul, J.F. Muzy, A. Arneodo, Phys. Rev. Lett. 73 (1994) 2998.