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Almeida RAL. Critical Percolation in the Ordering Kinetics of Twisted Nematic Phases. PHYSICAL REVIEW LETTERS 2023; 131:268101. [PMID: 38215366 DOI: 10.1103/physrevlett.131.268101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 11/28/2023] [Indexed: 01/14/2024]
Abstract
I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds toward a broken Z_{2}-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale t_{p}. At this time, exact formulas for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems.
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Affiliation(s)
- Renan A L Almeida
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970, Porto Alegre RS, Brazil
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Taubert F, Fischer R, Groeneveld J, Lehmann S, Müller MS, Rödig E, Wiegand T, Huth A. Global patterns of tropical forest fragmentation. Nature 2018; 554:519-522. [PMID: 29443966 DOI: 10.1038/nature25508] [Citation(s) in RCA: 171] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2017] [Accepted: 01/09/2018] [Indexed: 11/09/2022]
Abstract
Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments-at maximum by a factor of 33 over 50 years-as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.
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Affiliation(s)
- Franziska Taubert
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany
| | - Rico Fischer
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany
| | - Jürgen Groeneveld
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany.,TU Dresden, Institute of Forest Growth and Forest Computer Sciences, PO 1117, 01735 Tharandt, Germany
| | - Sebastian Lehmann
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany
| | - Michael S Müller
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany
| | - Edna Rödig
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany
| | - Thorsten Wiegand
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany.,German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, 04103 Leipzig, Germany
| | - Andreas Huth
- Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, Permoserstrasse 15, 04318 Leipzig, Germany.,German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, 04103 Leipzig, Germany.,University of Osnabrück, Institute of Environmental Systems Research, Barbarastrasse 12, 49076 Osnabrück, Germany
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Roberto GF, Neves LA, Nascimento MZ, Tosta TA, Longo LC, Martins AS, Faria PR. Features based on the percolation theory for quantification of non-Hodgkin lymphomas. Comput Biol Med 2017; 91:135-147. [DOI: 10.1016/j.compbiomed.2017.10.012] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Revised: 10/11/2017] [Accepted: 10/12/2017] [Indexed: 11/26/2022]
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Credidio HF, Moreira AA, Herrmann HJ, Andrade JS. Stochastic Loewner evolution relates anomalous diffusion and anisotropic percolation. Phys Rev E 2016; 93:042124. [PMID: 27176271 DOI: 10.1103/physreve.93.042124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Indexed: 06/05/2023]
Abstract
We disclose the origin of anisotropic percolation perimeters in terms of the stochastic Loewner evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multilayered and directed percolation clusters at criticality are the scaling limits of the Loewner evolution of an anomalous Brownian motion, being superdiffusive and subdiffusive, respectively. The connection between anomalous diffusion and fractal anisotropy is further tested by using long-range power-law correlated time series (fractional Brownian motion) as the driving functions in the evolution process. The fact that the resulting traces are distinctively anisotropic corroborates our hypothesis. Under the conceptual framework of SLE, our study therefore reveals different perspectives for mathematical and physical interpretations of non-Markovian processes in terms of anisotropic paths at criticality and vice versa.
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Affiliation(s)
- Heitor F Credidio
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Brazil
| | - André A Moreira
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Brazil
| | - Hans J Herrmann
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Brazil
- Computational Physics, IfB, ETH Zurich, Stefano-Franscini-Platz 3, CH-8093 Zurich, Switzerland
| | - José S Andrade
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Brazil
- Computational Physics, IfB, ETH Zurich, Stefano-Franscini-Platz 3, CH-8093 Zurich, Switzerland
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Newhall J, Cao J, Milner ST. Lattice model of correlated forces in granular solids near jamming. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052203. [PMID: 23767526 DOI: 10.1103/physreve.87.052203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2012] [Indexed: 06/02/2023]
Abstract
We have devised a lattice model to study force correlations in jamming granular solids in d=2 dimensions. We perform biased Monte Carlo simulations, favoring configurations with more bonds that bear no force, to "starve" the network of bonds and thereby control the distance from the isostatic point J. Increasingly long-ranged correlations are visible as point J is approached, not in the structure of the network of force-bearing bonds but in the spatial extent of perturbations of the force magnitudes consistent with a given starved network. The correlation length so defined diverges as the isostatic point is approached as a power law with an exponent of about ξ~δZ(-5). This divergence is much stronger than for the length scale of "soft modes" observed in jammed systems approaching point J from above.
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Affiliation(s)
- Jillian Newhall
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Ziff RM. Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation. ACTA ACUST UNITED AC 2011. [DOI: 10.1016/j.phpro.2011.06.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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8
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Sicilia A, Arenzon JJ, Bray AJ, Cugliandolo LF. Domain growth morphology in curvature-driven two-dimensional coarsening. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061116. [PMID: 18233823 DOI: 10.1103/physreve.76.061116] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2007] [Indexed: 05/25/2023]
Abstract
We study the distribution of domain areas, areas enclosed by domain boundaries ("hulls"), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, n_{h}(A,t)dA , with enclosed area in the interval (A,A+dA) , is described, for a disordered initial condition, by the scaling function n_{h}(A,t)=2c_{h}(A+lambda_{h}t);{2} , where c_{h}=18pi sqrt[3] approximately 0.023 is a universal constant and lambda_{h} is a material parameter. For a critical initial condition, the same form is obtained, with the same lambda_{h} but with c_{h} replaced by c_{h}2 . For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form n_{d}(A,t)=2c_{d}(lambda_{d}t);{tau'-2}(A+lambda_{d}t);{tau'} , where c_{d} and lambda_{d} are numerically very close to c_{h} and lambda_{h} , respectively, and tau'=18791 approximately 2.055 . For critical initial conditions, one replaces c_{d} by c_{d}2 and the exponent is tau=379187 approximately 2.027 . These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.
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Affiliation(s)
- Alberto Sicilia
- Université Pierre et Marie Curie-Paris VI, LPTHE UMR 7589, 4 Place Jussieu, Paris Cedex 05, France
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Sapoval B. Random fractals built by diffusion and percolation: Intercalation, 1/f and invasion noise. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/13642818908208447] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- B. Sapoval
- a Laboratoire de Physique de la Matière Condensée , Ecole Poly technique , 91128 , Palaiseau , France
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Hul O, Savytskyy N, Tymoshchuk O, Bauch S, Sirko L. Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:066212. [PMID: 16486045 DOI: 10.1103/physreve.72.066212] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2005] [Indexed: 05/06/2023]
Abstract
We study experimentally nodal domains of wave functions (electric field distributions) lying in the regime of Shnirelman ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. For this aim the wave functions of the billiard were measured up to the level number . We show that in the regime of Shnirelman ergodicity wave functions of the chaotic half-circular microwave ray-splitting rough billiard are extended over the whole energy surface and the amplitude distributions are Gaussian. For such ergodic wave functions, the dependence of the number of nodal domains on the level number was found. We show that in the limit the least squares fit of the experimental data yields , which is close to the theoretical prediction . We demonstrate that for higher level numbers the variance of the mean number of nodal domains is scattered around the theoretical limit . We also found that the distribution of the areas of nodal domains has power behavior , where the scaling exponent is equal to . This result is in good agreement with the prediction of percolation theory.
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Affiliation(s)
- Oleh Hul
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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Savytskyy N, Hul O, Sirko L. Experimental investigation of nodal domains in the chaotic microwave rough billiard. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056209. [PMID: 15600730 DOI: 10.1103/physreve.70.056209] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2004] [Indexed: 05/24/2023]
Abstract
We present the results of experimental study of nodal domains of wave functions (electric field distributions) lying in the regime of Shnirelman ergodicity in the chaotic half-circular microwave rough billiard. Nodal domains are regions where a wave function has a definite sign. The wave functions PsiN of the rough billiard were measured up to the level number N=435 . In this way the dependence of the number of nodal domains [symbol: see text]N on the level number N was found. We show that in the limit N-->infinity a least squares fit of the experimental data reveals the asymptotic number of nodal domains [symbol: see text]N/N approximately equal to 0.058+/-0.006 that is close to the theoretical prediction [symbol: see text]N/N approximately equal to 0.062 . We also found that the distributions of the areas s of nodal domains and their perimeters l have power behaviors ns is proportional to s(-tau) and nl is proportional to l(-tau'), where scaling exponents are equal to tau=1.99+/-0.14 and tau'=2.13+/-0.23 , respectively. These results are in a good agreement with the predictions of percolation theory. Finally, we demonstrate that for higher level numbers N approximately equal to 220-435 the signed area distribution oscillates around the theoretical limit SigmaA approximately 0.0386 N(-1) .
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Affiliation(s)
- Nazar Savytskyy
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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Grinchuk PS, Rabinovich OS. Surfaces of percolation systems in lattice problems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046103. [PMID: 12786432 DOI: 10.1103/physreve.67.046103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2002] [Indexed: 05/24/2023]
Abstract
The internal and external surface area of a percolation cluster along with a full surface area of whole percolation system are investigated both analytically and numerically. Numerical simulation is performed by a Monte Carlo method for site and bond problems on square and simple cubic lattices. It is shown that both the external and full surface areas of a percolation cluster as well as the full surface area of the whole percolation system have maxima for a certain share of occupied sites (for the site problem) or permeable bonds (for a bond problem). On the basis of a probabilistic approach, analytical expressions are obtained which relate the surface area of percolation cluster to its density. The last value has been studied in more details at present that allows to analyze the behavior of the above-mentioned surface for various lattices. Two particular technological processes are discussed where the surface area of a percolation cluster plays an important part: generation of electric current in a fuel cell and self-propagating high-temperature synthesis in heterogeneous condensed systems.
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Affiliation(s)
- P S Grinchuk
- A V Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 Petrus Brovka Street, Minsk 220072, Belarus.
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Redinz JA, Martins ML. Roughness exponent in two-dimensional percolation, Potts model, and clock model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:066133. [PMID: 11415199 DOI: 10.1103/physreve.63.066133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2001] [Indexed: 05/23/2023]
Abstract
We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3, and 7) and p=10 clock models as well as from the occupation states for site percolation on the square lattice. The first and second order static phase transitions of the Potts model are located by a sharp change in the value of the roughness exponent alpha characterizing those profiles. The low temperature phase of the Potts model corresponds to flat (alpha approximately 1) profiles, whereas its high temperature phase is associated with rough (alpha approximately 0.5) ones. For the p=10 clock model, in addition to the flat (ferromagnetic) and rough (paramagnetic) profiles, an intermediate rough (0.5<alpha<1) phase-associated with a soft spin-wave one-is observed. Our results for the transition temperatures in the Potts and clock models are in agreement with the static values, showing that this approach is able to detect the phase transitions in these models directly from the spin configurations, without any reference to thermodynamical potentials, order parameters, or response functions. Finally, we show that the roughness exponent alpha is insensitive to geometric critical phenomena.
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Affiliation(s)
- J A Redinz
- Departamento de Física, Universidade Federal de Viçosa, 36571-000, Viçosa, MG, Brazil
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Schakel AM. Percolation, Bose-Einstein condensation, and string proliferation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026115. [PMID: 11308550 DOI: 10.1103/physreve.63.026115] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2000] [Indexed: 05/23/2023]
Abstract
The close analogy between cluster percolation and string proliferation in the context of critical phenomena is studied. Like clusters in percolation theory, closed strings, which can be either finite-temperature worldlines or topological line defects, are described by a distribution parametrized by only two exponents. On approaching the critical point, the string tension vanishes and the loops proliferate, thereby signalling the onset of Bose-Einstein condensation (in the case of worldlines) or the disordering of the ordered state (in the case of vortices). The ideal Bose gas with modified energy spectrum is used as a stepping stone to derive general expressions for the critical exponents in terms of the two exponents parametrizing the loop distribution near criticality.
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Affiliation(s)
- A M Schakel
- Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, Finland
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Ziff RM, Sapoval B. The efficient determination of the percolation threshold by a frontier-generating walk in a gradient. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/19/18/010] [Citation(s) in RCA: 132] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Owczarek AL, Rechnitzer A, Brak R, Guttmann AJ. On the hulls of directed percolation clusters. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/30/19/011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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d'Iribarne C, Rasigni M, Rasigni G. Minimal spanning tree and percolation on mosaics: graph theory and percolation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/32/14/002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Hasmy A, Jullien R. Percolation in cluster-cluster aggregation processes. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:1789-1794. [PMID: 9964440 DOI: 10.1103/physreve.53.1789] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Furuberg L, Måloy KJ, Feder J. Intermittent behavior in slow drainage. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:966-977. [PMID: 9964331 DOI: 10.1103/physreve.53.966] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Sun T, Meakin P, Jossang T. Minimum energy dissipation river networks with fractal boundaries. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:5353-5359. [PMID: 9963266 DOI: 10.1103/physreve.51.5353] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Misra SK, Orhun U. Spin-lattice relaxation of a paramagnetic spin on a magnetically dilute lattice as caused by percolation-limited diffusion. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:10841-10846. [PMID: 10002945 DOI: 10.1103/physrevb.46.10841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Prakash S, Havlin S, Schwartz M, Stanley HE. Structural and dynamical properties of long-range correlated percolation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:R1724-R1727. [PMID: 9908370 DOI: 10.1103/physreva.46.r1724] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bradley RM, Strenski PN, Debierre JM. A growing self-avoiding walk in three dimensions and its relation to percolation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:8513-8524. [PMID: 9906949 DOI: 10.1103/physreva.45.8513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bradley RM, Debierre JM, Strenski PN. Anomalous scaling behavior in percolation with three colors. PHYSICAL REVIEW LETTERS 1992; 68:2332-2335. [PMID: 10045368 DOI: 10.1103/physrevlett.68.2332] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ziff RM, Kong XP, Cohen EG. Lorentz lattice-gas and kinetic-walk model. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:2410-2428. [PMID: 9906223 DOI: 10.1103/physreva.44.2410] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bradley RM, Strenski PN, Debierre JM. Surfaces of percolation clusters in three dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:76-84. [PMID: 9998221 DOI: 10.1103/physrevb.44.76] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sahimi M. Transport, reaction, and fragmentation in evolving porous media. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:5367-5376. [PMID: 9904850 DOI: 10.1103/physreva.43.5367] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Strenski PN, Bradley RM, Debierre JM. Scaling behavior of percolation surfaces in three dimensions. PHYSICAL REVIEW LETTERS 1991; 66:1330-1333. [PMID: 10043178 DOI: 10.1103/physrevlett.66.1330] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Barabási AL, Vicsek T. Tracing a diffusion-limited aggregate: Self-affine versus self-similar scaling. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:6881-6883. [PMID: 9903103 DOI: 10.1103/physreva.41.6881] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Bradley RM. Exact theta point and exponents for two models of polymer chains in two dimensions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:914-922. [PMID: 9903172 DOI: 10.1103/physreva.41.914] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Gouyet JF, Boughaleb Y. Structure of noise generated on diffusion fronts. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:4760-4768. [PMID: 9992471 DOI: 10.1103/physrevb.40.4760] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bradley RM. Exact theta point and exponents for polymer chains on an oriented two-dimensional lattice. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:3738-3740. [PMID: 9901691 DOI: 10.1103/physreva.39.3738] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Poole PH, Coniglio A, Jan N, Stanley HE. Universality classes of the theta and theta ' points. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:495-504. [PMID: 9947179 DOI: 10.1103/physrevb.39.495] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Cutler C, Dawson D. Estimation of dimension for spatially distributed data and related limit theorems. J MULTIVARIATE ANAL 1989. [DOI: 10.1016/0047-259x(89)90100-0] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Sanders DE, Evans JW. Correlated percolation in island-forming processes: Analysis of cooperative filling on a square lattice. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:4186-4197. [PMID: 9900871 DOI: 10.1103/physreva.38.4186] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Pandey RB. Scaling approach for the conductivity in a superconductor-insulator stirred percolating system. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:3792-3795. [PMID: 9900824 DOI: 10.1103/physreva.38.3792] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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