Percolation: Geometric Phase Transitions |

The Center for Polymer
Studies at Boston
University |

[Citation counts listed when above 100.] |

- 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]** - 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]** - 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]** - 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 - 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 - 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 - 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 - 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]** - 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]** - 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 - 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]** - 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 - R. Pike and H. E. Stanley, "Order Propagation near the Percolation
Threshold," J. Phys. A
**14**, L169 (1981). PDF**[Citations: 182]** - 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 - 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 - 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]** - 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)]. - 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 - P. Meakin and H. E. Stanley, "Novel Dimension-Independent Behavior
for Diffusive Annihilation on Percolation Fractals," J. Phys. A
**17**, L173-L178 (1984). PDF - 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 - 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 - 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 - 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 - 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 - 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]** - H. J. Herrmann and H. E. Stanley, "Building Blocks of
Percolation Clusters: Volatile Fractals," Phys. Rev. Lett.
**53**, 1121-1124 (1984). PDF**[Citations: 116]** - 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 - 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 - 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 - 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 - 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 - 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 - R. L. B. Selinger and H. E. Stanley, "Percolation of
Interacting Diffusing Particles," Phys. Rev. A
**42**, 4845-4852 (1990). PDF - T. Nagatani and H. E. Stanley, "Viscous Fingering near
Percolation Threshold: Double-Crossover Phenomena," Phys. Rev. A
**43**, 2963-2969 (1991). PDF - 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 - B. Jovanovic, S. V. Buldyrev, S. Havlin, H. E. Stanley,
"Punctuated Equilibrium and 'History Dependent' Percolation,"
Phys. Rev. E
**50**, R2403-R2406 (1994). PDF - 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 - 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 - 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 - 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 - 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. - 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 - H. Makse, S. Havlin, P. R. King, and H. E. Stanley, "Spontaneous
Stratification in Granular Mixtures," Nature
**386**, 379-382 (1997). PDF**[Citations: 196]** - 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 - 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. - 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). - 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. - 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]** - 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 - 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 - 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 - 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 - 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 - 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. - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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). - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - J. Shao, S. Havlin, and H. E. Stanley, "Dynamic Opinion Model
and Invasion Percolation," Phys. Rev. Lett.
**103**, 018701 (2009). PDF