Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs

Gawlinski, E. T.; Stanley, H. Eugene

doi:10.1088/0305-4470/14/8/007

Cited by 261 publications

(108 citation statements)

References 39 publications

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“…11͑c͒, we obtained the fractal dimension d = 1.97Ϯ 0.016 at the percolation point, close to the d = 1.91Ϯ 0.04 result for the continuum percolation of 2D random hard disks. 51 At 28.3°C, the 3500ϫ 10 data points in Fig. 11͑a͒ are not fractal; the 3500 R g 's fluctuate too strongly.…”

Section: F Caged Particle Percolation At the Freezing Pointmentioning

confidence: 91%

Two-dimensional freezing criteria for crystallizing colloidal monolayers

Wang

Alsayed

Yodh

et al. 2010

The Journal of Chemical Physics

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Recommended CitationWang, Z., Alsayed, A. M., Yodh, A. G., & Han, Y. (2010). Two-dimensional freezing criteria for crystallizing colloidal monolayers. Retrieved from http://repository.upenn.edu/physics_papers/32 Two-dimensional freezing criteria for crystallizing colloidal monolayers AbstractVideo microscopy was employed to explore crystallization of colloidal monolayers composed of diametertunable microgel spheres. Two-dimensional (2D) colloidal liquids were frozen homogenously into polycrystalline solids, and four 2D criteria for freezing were experimentally tested in thermal systems for the first time: the Hansen-Verlet freezing rule, the Löwen-Palberg-Simon dynamical freezing criterion, and two other rules based, respectively, on the split shoulder of the radial distribution function and on the distribution of the shape factor of Voronoi polygons. Importantly, these freezing criteria, usually applied in the context of single crystals, were demonstrated to apply to the formation of polycrystalline solids. At the freezing point, we also observed a peak in the fluctuations of the orientational order parameter and a percolation transition associated with caged particles. Speculation about these percolated clusters of caged particles casts light on solidification mechanisms and dynamic heterogeneity in freezing. Video microscopy was employed to explore crystallization of colloidal monolayers composed of diameter-tunable microgel spheres. Two-dimensional ͑2D͒ colloidal liquids were frozen homogenously into polycrystalline solids, and four 2D criteria for freezing were experimentally tested in thermal systems for the first time: the Hansen-Verlet freezing rule, the Löwen-PalbergSimon dynamical freezing criterion, and two other rules based, respectively, on the split shoulder of the radial distribution function and on the distribution of the shape factor of Voronoi polygons. Importantly, these freezing criteria, usually applied in the context of single crystals, were demonstrated to apply to the formation of polycrystalline solids. At the freezing point, we also observed a peak in the fluctuations of the orientational order parameter and a percolation transition associated with caged particles. Speculation about these percolated clusters of caged particles casts light on solidification mechanisms and dynamic heterogeneity in freezing.

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Section: F Caged Particle Percolation At the Freezing Pointmentioning

confidence: 91%

Two-dimensional freezing criteria for crystallizing colloidal monolayers

Wang

Alsayed

Yodh

et al. 2010

The Journal of Chemical Physics

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“…[33]. Tunneling processes [37,38] and related soft percolation problems [39] have been studied for some time, but it has only recently been demonstrated [33,40,41] that when tunneling is allowed the system conductance depends exponentially on surface coverage p below the percolation threshold, p c = 0.676336 [42] and that for p > p c the system conductance obeys the power law:…”

Section: Simulation Detailsmentioning

confidence: 99%

Neuromorphic behavior in percolating nanoparticle films

Fostner

Brown

2015

Phys. Rev. E

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We show that the complex connectivity of percolating networks of nanoparticles provides a natural solid-state system in which bottom-up assembly provides a route to realization of neuromorphic behavior. Below the percolation threshold the networks comprise groups of particles separated by tunnel gaps; an applied voltage causes atomic scale wires to form in the gaps, and we show that the avalanche of switching events that occurs is similar to potentiation in biological neural systems. We characterize the level of potentiation in the percolating system as a function of the surface coverage of nanoparticles and other experimentally relevant variables, and compare our results with those from biological systems. The complex percolating structure and the electric field driven switching mechanism provide several potential advantages in comparison to previously reported solid-state neuromorphic systems.

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“…H o w e v e r , w e n e e d t o t h e p e r c o l a t i o n threshold as it depends on the details of the system. Examples of applying percolation theory to uncorrelated (or even correlated) continuum systems that check the universality and determination of the percolation threshold of different models can be found elsewhere [Gawlinski and Stanley, 1981;Lee and Torquato., 1990;King, 1990;Berkowitz, 1995;Lorenz and Ziff, 2001;Baker et al, 2002].…”

Section: Percolation Theorymentioning

confidence: 99%