Percolation: Geometric Phase Transitions
The Center for Polymer Studies at Boston University


[Citation counts listed when above 100.]


  1. H. E. Stanley, R. J. Birgeneau, P. J. Reynolds, and J. F. Nicoll, "Thermally Driven Phase Transitions near the Percolation Threshold in Two Dimensions," J. Phys. C: Solid State 9, L553-560 (1976). PDF [Citations: 106]
  2. H. E. Stanley, "Cluster Shapes at the Percolation Threshold: An Effective Cluster Dimensionality and its Connection with Critical-Point Exponents," J. Phys. A 10, L211-220 (1977). Reproduced in: A. J. Hurd, Fractals (AIP Press, NY). PDF [Citations: 347]
  3. P. J. Reynolds, W. Klein, and H. E. Stanley, "A Real-Space Renormalization Group for Site and Bond Percolation," J. Phys. C: Solid State Phys. 10, L167-L172 (1977). PDF [Citations: 217]
  4. W. Klein, H. E. Stanley, P. J. Reynolds, and A. Coniglio, "Renormalization Group Approach to the Percolation Properties of the Triangular Ising Model," Phys. Rev. Lett. 41, 1145-1148 (1978). PDF
  5. A. Coniglio, H. E. Stanley, and W. Klein, "Site-Bond Correlated-Percolation Problem: A Statistical Mechanical Model of Polymer Gelation," Phys. Rev. Lett. 42, 518-522 (1979). PDF
  6. H. E. Stanley, "A Polychromatic Correlated-Site Percolation Problem with Possible Relevance to the Unusual behavior of Supercooled H2O and D2O," J. Phys. A 12, L329-L337 (1979). PDF
  7. G. Shlifer, W. Klein, P. J. Reynolds, and H. E. Stanley, "Large-Cell Renormalization Group for the Backbone Problem in Percolation," J. Phys. A 12, L169-L174 (1979). PDF
  8. P. J. Reynolds, H. E. Stanley, and W. Klein, "A Large-Cell Monte Carlo Renormalization Group for Percolation," Phys. Rev. B 21, 1223-1245 (1980). PDF [Citations: 350]
  9. H. E. Stanley and J. Teixeira, "Interpretation of The Unusual Behavior of H2O and D2O at Low Temperatures: Tests of a Percolation Model," J. Chem. Phys. 73, 3404-3422 (1980). PDF [Citations: 617]
  10. H. Nakanishi and H. E. Stanley, "Scaling Studies of Percolation Phenomena in Systems of Dimensionality Two to Seven. I. Cluster Numbers," Phys. Rev. B 22, 2466-2488 (1980). PDF
  11. E. T. Gawlinski and H. E. Stanley, "Continuum Percolation in Two Dimensions: Monte Carlo Tests of Scaling and Universality for Non-Interacting Discs," J. Phys. A: Math. Gen. 14, L291-L299 (1981). PDF [Citations: 160]
  12. H. E. Stanley, J. Teixeira, A. Geiger, and R. L. Blumberg, "Interpretation of the Unusual Behavior of H2O and D2O at Low Temperature: Are Concepts of Percolation Relevant to the Puzzle of Liquid Water?" Physica A 106, 260-277 (1981). PDF
  13. R. Pike and H. E. Stanley, "Order Propagation near the Percolation Threshold," J. Phys. A 14, L169 (1981). PDF [Citations: 182]
  14. F. Y. Wu and H. E. Stanley, "Domany-Kinzel Model of Directed Percolation: Formulation as a Random Walk Problem and Some Exact Results," Phys. Rev. Lett. 48, 775-778 (1982). PDF
  15. A. Geiger and H. E. Stanley, "Tests of Universality of Percolation Exponents for a 3-Dimensional Continuum System of Interacting Waterlike Particles," Phys. Rev. Lett. 49, 1895-1898 (1982). PDF
  16. H. E. Stanley, P. Reynolds, S. Redner and F. Family, "Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels," in Real-space renormalization, edited by T. W. Burkhardt and J. M. J. van Leeuwen (Springer-Verlag, 1982). [Citations: 151]
  17. H. E. Stanley and A. Coniglio, "Fractal Structure of the Incipient Infinite Cluster in Percolation," in Percolation Processes and Structures, edited by G. Deutscher, R. Zallen and J. Adler, [Ann. Israel Phys. Soc. 5, 101-120 (1983)].
  18. D. C. Hong and H. E. Stanley, "Cumulant Renormalization Group and its Application to the Incipient Infinite Cluster in Percolation," J. Phys. A 16, L525-L530 (1983). PDF
  19. P. Meakin and H. E. Stanley, "Novel Dimension-Independent Behavior for Diffusive Annihilation on Percolation Fractals," J. Phys. A 17, L173-L178 (1984). PDF
  20. A. Coniglio and H. E. Stanley, "Screening of Deeply Invaginated Clusters and the Critical Behavior of the Random Superconducting Network," Phys. Rev. Lett. 52, 1068-1071 (1984). PDF
  21. H. E. Stanley and A. Coniglio, "Flow in Porous Media: The 'Backbone' Fractal at the Percolation Threshold," Phys. Rev. B 29, 522-524 (1984). PDF
  22. H. J. Herrmann, D. C. Hong, and H. E. Stanley, "Backbone and Elastic Backbone of Percolation Clusters Obtained by the New Method of `Burning'," J. Phys. A Lett. 17, L261-L265 (1984). PDF
  23. I. Majid, D. Ben-Avraham, S. Havlin, and H. E. Stanley, "Exact-Enumeration Approach to Random Walks on Percolation Clusters in Two Dimensions," Phys. Rev. B 30, 1626-1628 (1984). PDF
  24. Z. V. Djordjevic, S. Havlin, H. E. Stanley, and G. H. Weiss, "New Method for Growing Branched Polymers and Large Percolation Clusters below the Percolation Threshold," Phys. Rev. B 30, 478-481 (1984). PDF
  25. D. C. Hong, S. Havlin, H. J. Herrmann, and H. E. Stanley, "Breakdown of Alexander-Orbach Conjecture for Percolation: Exact Enumeration of Random Walks on Percolation Backbones," Phys. Rev. B 30, 4083-4086 (1984). PDF [Citations: 101]
  26. H. J. Herrmann and H. E. Stanley, "Building Blocks of Percolation Clusters: Volatile Fractals," Phys. Rev. Lett. 53, 1121-1124 (1984). PDF [Citations: 116]
  27. S. Havlin, Z. Djordjevic, I. Majid, H. E. Stanley, and G. Weiss, "Relation between `Dynamic' Transport Properties and `Static' Topological Structure for Branched Polymers," Phys. Rev. Lett. 53, 178-181 (1984). PDF
  28. A. Bunde, A. Coniglio, D. C. Hong, and H. E. Stanley, "Transport in a Two-Component Randomly-Composite Material: Scaling Theory and Computer Simulations of Termite Diffusion near the Superconducting Limit," J. Phys. A Lett. 18, L137-L144 (1985). PDF
  29. D. C. Hong, H. E. Stanley, A. Coniglio, and A. Bunde, "Random-Walk Approach to the Two-Component Random-Resistor Mixture: Perturbing away from the Perfect Random Resistor Network and Random Superconducting-Network Limits," Phys. Rev. B 33, 4564-4573 (1986). PDF
  30. A. Coniglio, N. Jan, I. Majid, and H. E. Stanley, "Conformation of a Polymer Chain at the Theta-Prime Point: Connection to the External Perimeter of a Percolation Cluster," Phys. Rev. B 35, 3617-3620 (1987). PDF
  31. H. J. Herrmann and H. E. Stanley, "The Fractal Dimension of the Minimum Path in Two- and Three-Dimensional Percolation," Journal of Physics A 21, L829-L833 (1988). PDF
  32. C.-K. Peng, S. Prakash, H. J. Herrmann, and H. E. Stanley, "Randomness versus Deterministic Chaos: Effect on Invasion Percolation Clusters," Phys. Rev. A 42, 4537-4542 (1990). PDF
  33. R. L. B. Selinger and H. E. Stanley, "Percolation of Interacting Diffusing Particles," Phys. Rev. A 42, 4845-4852 (1990). PDF
  34. T. Nagatani and H. E. Stanley, "Viscous Fingering near Percolation Threshold: Double-Crossover Phenomena," Phys. Rev. A 43, 2963-2969 (1991). PDF
  35. S. Prakash, S. Havlin, M. Schwartz, and H. E. Stanley, "Structural and Dynamical Properties of Long-Range Correlated Percolation," Phys. Rev. A 46, R1724-R1727 (1992). PDF
  36. B. Jovanovic, S. V. Buldyrev, S. Havlin, H. E. Stanley, "Punctuated Equilibrium and 'History Dependent' Percolation," Phys. Rev. E 50, R2403-R2406 (1994). PDF
  37. L. A. N. Amaral, A.-L. Barabasi, S. V. Buldyrev, S. T. Harrington, S. Havlin, R. Sadr, and H. E. Stanley, "Avalanches and the Directed Percolation Depinning Model: Experiments, Simulations and Theory," Phys. Rev. E 51, 4655-4673 (1995). PDF
  38. P. Jensen, A.-L. Barabasi, H. Larralde, S. Havlin, and H. E. Stanley, "Growth and Percolation of Thin Films: A Model Incorporating Deposition, Diffusion and Aggregation," Chaos, Solitons, and Fractals 6, 227-236 (1995). PDF
  39. H. Makse, G. W. Davies, S. Havlin, P. Ivanov, P. R. King, and H. E. Stanley, "Long-Range Correlations in Sandstone Permeability," Phys. Rev. E 54, 3129-3134 (1996). PDF
  40. S. V. Buldyrev, L. A. N. Amaral, A.-L. Barabasi, S. T. Harrington, S. Havlin, R. Sadr and H. E. Stanley, "Avalanches and the Directed Percolation Depinning Model" [Proc. International Conf. on "Future of Fractals"], Fractals 4, 307-319 (1996). PDF
  41. H. Makse, S. Havlin, P. R. King, and H. E. Stanley, "Influence of Spatial Correlations on Permeability and Connectivity of Sandstone" in Disordered Materials and Interfaces [Proc. Symposium of Materials Research Society, 1995], edited by H. Z. Cummins, D. J. Durian, D. L. Johnson, and H. E. Stanley (Materials Research Society, Pittsburgh, 1996), pp. 57-62.
  42. H. A. Makse, S. Havlin, P. Ch. Ivanov, P. R. King, S. Prakash, and H. E. Stanley, "Permeability Fluctuations in Sedimentary Rocks: Connectivity, Permeability, and Spatial Correlations," Physica A 233, 587-605 (1996). PDF
  43. H. Makse, S. Havlin, P. R. King, and H. E. Stanley, "Spontaneous Stratification in Granular Mixtures," Nature 386, 379-382 (1997). PDF [Citations: 196]
  44. J. S. Andrade Jr., D. A. Street, Y. Shibusa, S. Havlin, and H. E. Stanley, "Diffusion and Reaction in Percolating Pore Networks," Phys. Rev. E 55, 772-777 (1997). PDF
  45. H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, "Novel Pattern Formation in Granular Matter," in Stochastic Dynamics, edited by L. Schimansky-Geier and T. Poeschel (Springer, Heidelberg, 1997), pp. 319-333.
  46. H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, "Experimental Studies of Stratification in a Granular Hele-Shaw Cell" in Proc. Minerva Conf., Phil. Mag. 77, 1341-1351 (1998).
  47. H. A. Makse, P. Cizeau, S. Havlin, P. R. King, and H. E. Stanley, "Spontaneous Self-Stratification Without Shaking: 'Potatoes from Mashed Potatoes'" in Physics of Dry Granular Media [Proc. 1997 NATO ASI], edited by H. J. Herrmann, J.-P. Hovi, and S. Luding (Kluwer, Dordrecht, 1998), pp. 671-680.
  48. H. A. Makse, J. S. Andrade, M. Batty, S. Havlin and H. E. Stanley, "Modeling Urban Growth Patterns with Correlated Percolation," Phys. Rev. E 58, 7054-7062 (1998). PDF [Citations: 68]
  49. N. V. Dokholyan, Y. Lee, S. V. Buldyrev, S. Havlin, P. R. King, and H. E. Stanley, "Scaling of the Distribution of Shortest Paths in Percolation," J. Stat. Phys. 93, 603-613 (1998). PDF
  50. N. V. Dokholyan, S. V. Buldyrev, S. Havlin, P. R. King, Y. Lee, and H. E. Stanley, "Distribution of Shortest Paths in Percolation" [Proc. Giessen Conf. on Percolation], Physica A 266, 55-61 (1999). PDF
  51. U. M. S. Costa, J. S. Andrade Jr., H. A. Makse, and H. E. Stanley, "Inertial Effects on Fluid Flow through Disordered Porous Media" [Proc. Giessen Conf. on Percolation], Physica A 266, 420-424 (1999). PDF
  52. P. R. King, J. Andrade, N. V. Dokholyan, S. V. Buldyrev, S. Havlin, Y. Lee, and H. E. Stanley, "Percolation and Oil Recovery" [Proc. Giessen Conf. on Percolation], Physica A 266, 107-114 (1999). PDF
  53. H. E. Stanley, J. S. Andrade Jr., S. Havlin, H. A. Makse, and B. Suki, "Percolation Phenomena: A Broad-Brush Introduction with Some Recent Applications to Porous Media, Liquid Water, and City Growth" [Proc. Giessen Conf. on Percolation], Physica A 266, 5-16 (1999). PDF
  54. H. A. Makse, P. Cizeau, S. Havlin, P. R. King, and H. E. Stanley, "Dynamics of Stratification and Segregation in Two Dimensional Silos" in Slow Dynamics in Complex Systems: Proceedings of the 8th Tohwa University International Symposium, edited by Michio Tokuyama and Irwin Oppenheim (AIP Conference Series, 1999), pp. 53-61.
  55. Y. Lee, J. S. Andrade, S. V. Buldyrev, N. Dokholyan, S. Havlin, P. R. King, G. Paul, and H. E. Stanley, "Traveling Time and Traveling Length for Flow in Porous Media," Phys. Rev. E 60, 3425-3428 (1999). PDF
  56. M. Barthelemy, S. V. Buldyrev, S. Havlin, and H. E. Stanley, "Scaling for the Critical Percolation Backbone," Phys. Rev. E 60, R1123-R1126 (1999). PDF
  57. P. R. King, S. V. Buldyrev, N. V. Dokholyan, S. Havlin, Y. Lee, G. Paul, and H. E. Stanley, "Applications of Statistical Physics to the Oil Industry: Predicting Oil Recovery using Percolation Theory" [Proc. NATO Adv. Res. Workshop, Budapest], Physica A 274, 60-66 (1999). PDF
  58. H. Makse, J. S. Andrade Jr., and H. E. Stanley, "Tracer Dispersion in Correlated Percolation Porous Media," Phys. Rev. E 61, 583-587 (2000). PDF
  59. G. Paul, S. V. Buldyrev, N. V. Dokholyan, S. Havlin, P. R. King, Y. Lee, and H. E. Stanley, "Dependence of Conductance on Percolation Backbone Mass," Phys. Rev. E 61, 3435-3440 (2000). PDF
  60. J. S. Andrade Jr., S. V. Buldyrev, N. Dokholyan, P. R. King, Y. Lee, S. Havlin, and H. E. Stanley, "Flow between Two Sites in Percolation Systems," Phys. Rev. E 62, 8270-8281 (2000). PDF
  61. G. Paul, R. M. Ziff, and H. E. Stanley, "Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for Four and Five Dimensions," Phys. Rev. E 64, 026115 (2001). PDF
  62. P. R. King, S. V. Buldyrev, N. V. Dokholyan, S. Havlin, Y. Lee, G. Paul, H. E. Stanley, and N. Vandesteeg, "Predicting Oil Recovery using Percolation Theory," Petroleum Geoscience 7, S105-S107 (2001).
  63. J. S. Andrade Jr., A. D. Araujo, S. V. Buldyrev, S. Havlin, and H. E. Stanley, "The Dynamics of Viscous Penetration in Percolation Porous Media," Phys. Rev. E 63, 051403 (2001). PDF
  64. L. R. da Silva, G, Paul, S. Havlin, D. R. Baker, and H. E. Stanley, "Distribution of Backbone Mass Between Non-Parallel Lines," Physica A 314, 140-145 (2002). PDF
  65. G. Paul, S. Havlin, and H. E. Stanley, "Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems," Phys. Rev. E 65, 066105 (2002). PDF
  66. G. Paul and H. E. Stanley, "Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold," Phys. Rev. E 65, 056126 (2002). PDF
  67. D. R. Baker, G. Paul, S. Sreenivasan, and H. E. Stanley, Continuum Percolation Threshold for Interpenetrating Squares and Cubes," Phys. Rev. E 66, 046136 (2002). PDF
  68. G. Paul, S. Havlin, and H. E. Stanley, "Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems," Phys. Rev. E 65, 066105 (2002). PDF
  69. R. Consiglio, D. R. Baker, G. Paul and H. E. Stanley, "Continuum Percolation Thresholds for Mixtures of Spheres of Different Sizes," Physica A 319, 49-55 (2003). PDF
  70. P. R. King, S. V. Buldyrev, N. V. Dokholyan, S. Havlin, E. Lopez, G. Paul, and H. E. Stanley, "Using Percolation Theory to Predict Oil Field Performance," Physica A 314, 103-108 (2002). PDF
  71. P. R. King, S. V. Buldyrev, N. V. Dokholyan, S. Havlin, E. Lopez, G. Paul, and H. E. Stanley, "Predicting Oil Recovery Using Percolation Theory" [Proc. IUPAP Statphys21, Cancun], Physica A 306, 376-380 (2002). PDF
  72. S. Sreenivasan, D. R. Baker, G. Paul, and H. E. Stanley, "The Approximate Invariance of the Average Number of Connections for the Continuum Percolation of Squares at Criticality," Physica A 320, 34-40 (2003). PDF
  73. G. Paul and H. E. Stanley, "Fractal Dimension of Three-Blocks in Four-, Five, and Six-dimensional Percolation Systems," Phys. Rev. E 67, 026103 (2003). PDF
  74. Luciano R. da Silva, Gerald Paul, Shlomo Havlin, Don R. Baker and H. E. Stanley, "Scaling of Cluster Mass between Two Lines in 3d Percolation," Physica A 318, 307-318 (2003). PDF
  75. E. Lopez, S. V. Buldyrev, N. V. Dokholyan, L. Goldmakher, S. Havlin, P. R. King, and H. E. Stanley, Postbreakthrough Behavior in Flow through Porous Media," Phys. Rev. E 67, 056314 (2003). PDF
  76. M. Barthelemy, S. V. Buldyrev, S. Havlin, and H. E. Stanley, "Scaling and Finite-Size Effects for the Critical Backbone" inin F. Family, M. Daoud, H. Herrmann, and H. E. Stanley [eds], Scaling and Disordered Systems (World-Scientific Publishers, Singapore, 2002), pp. 19-28. The same paper is also published in: Fractals 11, 19-27 (2003). PDF
  77. R. F. Soares, G. Corso, L. S. Lucena, J. E. Freitas, L. R. da~Silva, G. Paul, and H. E. Stanley, "Distribution of Shortest Paths at Percolation Threshold: Application to Oil Recovery with Multiple Wells," Physica A 343, 739-747 (2004). PDF
  78. R. Consiglio, R. N. A. Zouain, D. R. Baker, G. Paul, and H. E. Stanley, "Symmetry of the Continuum Percolation Threshold in Systems of Two Different Size Objects," Physica A 343, 343-347 (2004). PDF
  79. J. Shao, S. Havlin, and H. E. Stanley, "Dynamic Opinion Model and Invasion Percolation," Phys. Rev. Lett. 103, 018701 (2009). PDF