User menu

Wavelet Analysis of the Self-similarity of Diffusion-limited Aggregates and Electrodeposition Clusters

Bibliographic reference Argoul, F. ; Arneodo, A. ; Elezgaray, J. ; Grasseau, G.. Wavelet Analysis of the Self-similarity of Diffusion-limited Aggregates and Electrodeposition Clusters. In: Physical review. A, Atomic, molecular, and optical physics, Vol. 41, no. 10, p. 5537-5560 (1990)
Permanent URL http://hdl.handle.net/2078.1/51787
  1. On Growth and Form: Fractal and Non-Fractal Patterns in Physics (1986)
  2. Fractals in Physics (1986)
  3. Staphys 16 (1986)
  4. The Physics of Structure Formation (1987)
  5. Random Fluctuations and Pattern Growth (1988)
  6. Witten T. A., Sander L. M., Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon, 10.1103/physrevlett.47.1400
  7. Witten T. A., Sander L. M., Diffusion-limited aggregation, 10.1103/physrevb.27.5686
  8. Turkevich Leonid A., Scher Harvey, Occupancy-Probability Scaling in Diffusion-Limited Aggregation, 10.1103/physrevlett.55.1026
  9. Ball R.C., Diffusion limited aggregation and its response to anisotropy, 10.1016/0378-4371(86)90205-0
  10. Halsey Thomas C., Meakin Paul, Procaccia Itamar, Scaling structure of the surface layer of diffusion-limited aggregates, 10.1103/physrevlett.56.854
  11. Matsushita Mitsugu, Honda Katsuya, Toyoki Hiroyasu, Hayakawa Yoshinori, Kondo Horoshi, Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation, 10.1143/jpsj.55.2618
  12. Meakin Paul, Diffusion-controlled cluster formation in 2—6-dimensional space, 10.1103/physreva.27.1495
  13. Meakin Paul, Wasserman Zeida R., Fractal structure of three-dimensional Witten—Sander clusters, 10.1016/0301-0104(84)80071-3
  14. Meakin P., Sander L. M., Comment on "Active Zone of Growing Clusters: Diffusion-Limited Aggregation and the Eden Model", 10.1103/physrevlett.54.2053
  15. Ball R C, Brady R M, Large scale lattice effect in diffusion-limited aggregation, 10.1088/0305-4470/18/13/014
  16. Meakin Paul, Universality, nonuniversality, and the effects of anisotropy on diffusion-limited aggregation, 10.1103/physreva.33.3371
  17. Meakin Paul, Ball Robin C., Ramanlal P., Sander L. M., Structure of large two-dimensional square-lattice diffusion-limited aggregates: Approach to asymptotic behavior, 10.1103/physreva.35.5233
  18. Vicsek Tamás, Pattern Formation in Diffusion-Limited Aggregation, 10.1103/physrevlett.53.2281
  19. Vicsek Tamás, Formation of solidification patterns in aggregation models, 10.1103/physreva.32.3084
  20. Bensimon David, Kadanoff Leo P., Liang Shoudan, Shraiman Boris I., Tang Chao, Viscous flows in two dimensions, 10.1103/revmodphys.58.977
  21. Banavar Jayanth R., Kohmoto Mahito, Roberts James, Aggregate models of pattern formation, 10.1103/physreva.33.2065
  22. Meakin Paul, Family Fereydoon, Vicsek Tama´s, Viscous fingering simulated by off-lattice aggregation, 10.1016/0021-9797(87)90398-5
  23. Tao R., Novotny M. A., Kaski K., Diffusion-limited aggregation with surface tension, 10.1103/physreva.38.1019
  24. Nittmann J, Stanley H E, Non-deterministic approach to anisotropic growth patterns with continuously tunable morphology: the fractal properties of some real snowflakes, 10.1088/0305-4470/20/17/010
  25. Ball Robin C., Brady Robert M., Rossi Giuseppe, Thompson Bernard R., Anisotropy and Cluster Growth by Diffusion-Limited Aggregation, 10.1103/physrevlett.55.1406
  26. Matsushita Mitsugu, Kondo Hiroshi, Diffusion-Limited Aggregation with Tunable Lattice Anisotropy, 10.1143/jpsj.55.2483
  27. Kertesz J, Vicsek T, Diffusion-limited aggregation and regular patterns: fluctuations versus anisotropy, 10.1088/0305-4470/19/5/008
  28. Meakin Paul, Diffusion-limited surface deposition in the limit of large anisotropy, 10.1103/physreva.33.1984
  29. Meakin Paul, Noise-reduced diffusion-limited aggregation, 10.1103/physreva.36.332
  30. Family F, Platt D E, Vicsek T, Deterministic growth model of pattern formation in dendritic solidification, 10.1088/0305-4470/20/17/009
  31. Kolb M, Anisotropic Diffusion Limited Aggregation: From Self-Similarity to Self-Affinity, 10.1209/0295-5075/4/1/014
  32. Meakin Paul, Havlin Shlomo, Fluctuations and distributions in random aggregates, 10.1103/physreva.36.4428
  33. A. Renyi, Probability Theory (1970)
  34. Grassberger Peter, Generalized dimensions of strange attractors, 10.1016/0375-9601(83)90753-3
  35. H. G. E. Hentschel, Physica, 8D, 435 (1983)
  36. P. Grassberger, Physica, 13D, 34 (1984)
  37. Vul E B, Sinai Yakov G, Khanin K M, Feigenbaum universality and the thermodynamic formalism, 10.1070/rm1984v039n03abeh003162
  38. Benzi R, Paladin G, Parisi G, Vulpiani A, On the multifractal nature of fully developed turbulence and chaotic systems, 10.1088/0305-4470/17/18/021
  39. Halsey Thomas C., Jensen Mogens H., Kadanoff Leo P., Procaccia Itamar, Shraiman Boris I., Fractal measures and their singularities: The characterization of strange sets, 10.1103/physreva.33.1141
  40. Collet P., Lebowitz J. L., Porzio A., The dimension spectrum of some dynamical systems, 10.1007/bf01206149
  41. A. Arneodo, Wavelets (1989)
  42. B. B. Mandelbrot, The Fractal Geometry of Nature (1982)
  43. A. Grossmann, Mathematics and Physics, Lectures on Recent Results (1985)
  44. Wavelets (1989)
  45. Goupillaud P., Grossmann A., Morlet J., Cycle-octave and related transforms in seismic signal analysis, 10.1016/0016-7142(84)90025-5
  46. A. Grossmann, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 15, 723 (1984)
  47. Grossmann A., Morlet J., Paul T., Transforms associated to square integrable group representations. I. General results, 10.1063/1.526761
  48. A. Grossmann, Ann. Inst. Henri Poincaré, 45, 293 (1986)
  49. Lemarié-Rieusset Pierre Gilles, Meyer Yves, Ondelettes et bases hilbertiennes, 10.4171/rmi/22
  50. Daubechies Ingrid, Orthonormal bases of compactly supported wavelets, 10.1002/cpa.3160410705
  51. Daubechies Ingrid, Grossmann A., Meyer Y., Painless nonorthogonal expansions, 10.1063/1.527388
  52. I. Daubechies, Proceedings of the VIIIth Congress of Mathematical Physics, Marseille, 1986 (1987)
  53. G. Saracco, Wavelets
  54. R. Kronland-Martinet, Computer Music Journal (1988)
  55. A. Grossmann, Stochastic Processes in Physics and Engineering (1988)
  56. Holschneider Matthias, On the wavelet transformation of fractal objects, 10.1007/bf01019149
  57. Arneodo A., Grasseau G., Holschneider M., Wavelet Transform of Multifractals, 10.1103/physrevlett.61.2281
  58. J. D. Farmer, Physica, 7D, 153 (1983)
  59. Argoul F., Arnéodo A., Grasseau G., Gagne Y., Hopfinger E. J., Frisch U., Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade, 10.1038/338051a0
  60. Real-Space Renormalization, ISBN:9783642818271, 10.1007/978-3-642-81825-7
  61. Gould Harvey, Family Fereydoon, Stanley H. Eugene, Kinetics of Formation of Randomly Branched Aggregates: A Renormalization-Group Approach, 10.1103/physrevlett.50.686
  62. Nakanishi H, Family F, Cell renormalisation of growth processes: 'true' self-avoiding walks and growing animals, 10.1088/0305-4470/17/2/027
  63. Nagatani T, A renormalisation group approach to the scaling structure of diffusion-limited aggregation, 10.1088/0305-4470/20/6/008
  64. Nagatani T, Evolution criterion and renormalisation group for DLA, 10.1088/0305-4470/20/18/057
  65. Nagatani Takashi, Renormalization-group approach to multifractal structure of growth probability distribution in diffusion-limited aggregation, 10.1103/physreva.36.5812
  66. Nagatani Takashi, Fractal structure of drift-diffusion-limited aggregation: Renormalization-group approach, 10.1103/physreva.37.3514
  67. Nagatani Takashi, Convection effect on the diffusion-limited-aggregation fractal: Renormalization-group approach, 10.1103/physreva.37.4461
  68. Pietronero L., Erzan A., Evertsz C., Theory of Fractal Growth, 10.1103/physrevlett.61.861
  69. Nittmann Johann, Stanley H. Eugene, Tip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy, 10.1038/321663a0
  70. Sander L. M., Ramanlal P., Ben-Jacob E., Diffusion-limited aggregation as a deterministic growth process, 10.1103/physreva.32.3160
  71. L. M. Sander, Fractals in Physics
  72. Ramanlal P, Sander L M, Distribution of growth probabilities in fluid flow and diffusion-limited aggregation, 10.1088/0305-4470/21/20/007
  73. R. Murenzi, Wavelets
  74. Argoul F., Arneodo A., Elezgaray J., Grasseau G., Murenzi R., Wavelet transform of fractal aggregates, 10.1016/0375-9601(89)90003-0
  75. Meakin Paul, Scaling of the growth probability measure for fractal structures, 10.1103/physreva.34.710
  76. Meakin Paul, Scaling properties for the growth probability measure and harmonic measure of fractal structures, 10.1103/physreva.35.2234
  77. Amitrano C., Coniglio A., di Liberto F., Growth Probability Distribution in Kinetic Aggregation Processes, 10.1103/physrevlett.57.1016
  78. Meakin Paul, Coniglio Antonio, Stanley H. Eugene, Witten Thomas A., Scaling properties for the surfaces of fractal and nonfractal objects: An infinite hierarchy of critical exponents, 10.1103/physreva.34.3325
  79. Hayakawa Y., Sato S., Matsushita M., Scaling structure of the growth-probability distribution in diffusion-limited aggregation processes, 10.1103/physreva.36.1963
  80. Lee Jysoo, Stanley H. Eugene, Phase Transition in the Multifractal Spectrum of Diffusion-Limited Aggregation, 10.1103/physrevlett.61.2945
  81. Ball Robin, Blunt Martin, Screening in multifractal growth, 10.1103/physreva.39.3591
  82. Ohta Shonosuke, Honjo Haruo, Growth probability distribution in irregular fractal-like crystal growth of ammonium chloride, 10.1103/physrevlett.60.611
  83. Blunt Martin, King Peter, Scaling structure of viscous fingering, 10.1103/physreva.37.3935
  84. L. M. Sander, The Physics of Structure Formation
  85. Grier David G., Kessler David A., Sander L. M., Stability of the dense radial morphology in diffusive pattern formation, 10.1103/physrevlett.59.2315
  86. Grier D., Ben-Jacob E., Clarke Roy, Sander L. M., Morphology and Microstructure in Electrochemical Deposition of Zinc, 10.1103/physrevlett.56.1264
  87. Sawada Yasuji, Dougherty A., Gollub J. P., Dendritic and Fractal Patterns in Electrolytic Metal Deposits, 10.1103/physrevlett.56.1260
  88. Brady R. M., Ball R. C., Fractal growth of copper electrodeposits, 10.1038/309225a0
  89. Matsushita M., Sano M., Hayakawa Y., Honjo H., Sawada Y., Fractal Structures of Zinc Metal Leaves Grown by Electrodeposition, 10.1103/physrevlett.53.286
  90. Matsushita M., Hayakawa Y., Sawada Y., Fractal structure and cluster statistics of zinc-metal trees de- posited on a line electrode, 10.1103/physreva.32.3814
  91. Argoul F., Arneodo A., Grasseau G., Swinney Harry L., Self-Similarity of Diffusion-Limited Aggregates and Electrodeposition Clusters, 10.1103/physrevlett.61.2558
  92. Eckmann J. -P., Ruelle D., Ergodic theory of chaos and strange attractors, 10.1103/revmodphys.57.617
  93. Feigenbaum Mitchell J., Some characterizations of strange sets, 10.1007/bf01011148
  94. Mandelbrot Benoit B., Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, 10.1017/s0022112074000711
  95. Badii R., Politi A., Intrinsic oscillations in measuring the fractal dimension, 10.1016/0375-9601(84)90801-6
  96. Smith L.A., Fournier J.-D., Spiegel E.A., Lacunarity and intermittency in fluid turbulence, 10.1016/0375-9601(86)90695-x
  97. Bessis D., Fournier J. D., Servizi G., Turchetti G., Vaienti S., Mellin transforms of correlation integrals and generalized dimension of strange sets, 10.1103/physreva.36.920
  98. Arneodo A., Grasseau G., Kostelich Eric J., Fractal dimensions and ƒ(α) spectrum of the Hénon attractor, 10.1016/0375-9601(87)90546-9
  99. Argoul F., Arneodo A., Grasseau G., Fractal Dimensions andf(α) Spectrum for Strange Attractors, 10.1002/zamm.19880681017
  100. Grassberger P., Badii R., Politi A., Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors, 10.1007/bf01015324
  101. H. Froehling, Physica, 3D, 605 (1981)
  102. Grassberger Peter, Procaccia Itamar, Characterization of Strange Attractors, 10.1103/physrevlett.50.346
  103. P. Grassberger, Physica, 9D, 189 (1983)
  104. Badii R., Politi A., Hausdorff Dimension and Uniformity Factor of Strange Attractors, 10.1103/physrevlett.52.1661
  105. Radii Remo, Politi Antonio, Statistical description of chaotic attractors: The dimension function, 10.1007/bf01009897
  106. R. Badii, Phys. Lett., 131A, 131 (1988)
  107. B. B. Mandelbrot, Random Fluctuations and Pattern Growth
  108. van de Water Willem, Schram Piet, Generalized dimensions from near-neighbor information, 10.1103/physreva.37.3118
  109. Chhabra Ashvin, Jensen Roderick V., Direct determination of the f(α) singularity spectrum, 10.1103/physrevlett.62.1327
  110. Chhabra Ashvin B., Meneveau Charles, Jensen Roderick V., Sreenivasan K. R., Direct determination of the f(α) singularity spectrum and its application to fully developed turbulence, 10.1103/physreva.40.5284
  111. P. Hanusse, Wavelets
  112. Ghez J. -M., Vaienti S., On the wavelet analysis for multifractal sets, 10.1007/bf01023655
  113. Langer J. S., Instabilities and pattern formation in crystal growth, 10.1103/revmodphys.52.1
  114. Chance and Matter (1987)
  115. Nakaya Ukichiro, Snow Crystals : Natural and Artificial, ISBN:9780674182769, 10.4159/harvard.9780674182769
  116. W. A. Bentley, Snow Crystals (1962)
  117. Vicsek T, Fractal models for diffusion controlled aggregation, 10.1088/0305-4470/16/17/003
  118. Kolb M. , Effects of the growth mechanism on the structure of aggregation clusters, 10.1051/jphyslet:019850046014063100
  119. Meakin Paul, Family Fereydoon, Diverging length scales in diffusion-limited aggregation, 10.1103/physreva.34.2558
  120. Meakin Paul, Multiple-contact diffusion-limited-aggregation model, 10.1103/physreva.33.4199
  121. Nittmann Johann, Daccord Gérard, Stanley H. Eugene, Fractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon, 10.1038/314141a0
  122. Meakin P, The structure of two-dimensional Witten-Sander aggregates, 10.1088/0305-4470/18/11/006
  123. Paterson Lincoln, Radial fingering in a Hele Shaw cell, 10.1017/s0022112081003613
  124. Rauseo S. N., Barnes P. D., Maher J. V., Development of radial fingering patterns, 10.1103/physreva.35.1245
  125. Kopf-Sill Anne R., Homsy G. M., Nonlinear unstable viscous fingers in Hele–Shaw flows. I. Experiments, 10.1063/1.866854
  126. Y. Couder, Random Fluctuations and Pattern Growth
  127. Thomé H., Rabaud M., Hakim V., Couder Y., The Saffman–Taylor instability: From the linear to the circular geometry, 10.1063/1.857493
  128. Daccord Gérard, Nittmann Johann, Stanley H. Eugene, Radial viscous fingers and diffusion-limited aggregation: Fractal dimension and growth sites, 10.1103/physrevlett.56.336
  129. Procaccia Itamar, Zeitak Reuven, Shape of Fractal Growth Patterns: Exactly Solvable Models and Stability Considerations, 10.1103/physrevlett.60.2511
  130. Dimino G. M., Kaufman J. H., Evidence of critical behavior in a random fractal automaton, 10.1103/physrevlett.62.2277
  131. Arnéodo A., Couder Y., Grasseau G., Hakim V., Rabaud M., Uncovering the analytical Saffman-Taylor finger in unstable viscous fingering and diffusion-limited aggregation, 10.1103/physrevlett.63.984
  132. Meakin Paul, Vicsek Tamás, Internal structure of diffusion-limited aggregates, 10.1103/physreva.32.685
  133. Halsey Thomas C., Meakin Paul, Axial inhomogeneity in diffusion-limited aggregation, 10.1103/physreva.32.2546
  134. Universality in Chaos (1984)
  135. Chaos (1984)
  136. H. G. Schuster, Deterministic Chaos (1984)
  137. P. Berge, Order within Chaos (1986)
  138. F. Argoul, Proceedings of the International Workshop on Quantitative Measures of Dynamical Complexity in Nonlinear Systems, Bryn Mawr College, 1989
  139. Freysz E., Pouligny B., Argoul F., Arneodo A., Optical wavelet transform of fractal aggregates, 10.1103/physrevlett.64.745