Monte Carlo experiment for the two-dimensional site percolation network

Yuge, Y; Onizuka, Kotaro

doi:10.1088/0022-3719/11/18/005

Cited by 38 publications

(15 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Traditionally, the conductivity behavior using the percolation theory has been modeled based on assuming a network of resistances [34][35][36][37][38][39][40]. In one experimental work, Last and Thouless [41] peppered a conducting sheet of colloidal graphite paper of a finite resistance with holes (the resistance of holes is infinity, analogous to our microgels), according to coordinates obtained using a random number generator.…”

Section: Modeling Approachmentioning

confidence: 99%

“…It is seen that the observed conductivity tapers off to zero when the fractional concentration of holes reaches 0.4. This experiment was modeled by Yuge and Onizuka [40] using a two-dimensional (2-D) resistor network consisting of two kinds of special unit resistor with different conductances, Kl and K2. The resistors are placed at random as shown in Figure 48.…”

Section: Modeling Approachmentioning

confidence: 99%

“…The resistors are placed at random as shown in Figure 48. Yuge and Onizuka [40] designed and studied such a 200 x 200 site random-resistor network. A simulation of Last and Thouless' experiment [41] by making Kl as unity (as in graphite) and K2 as zero (as in holes) yielded the critical fraction of Kl to be 0.591, and K2 to be 0.409.…”

Section: Modeling Approachmentioning

confidence: 99%

See 2 more Smart Citations

Vinyl-Ester (VE) Cure Characterization Via Direct Current Sensors

Fink¹

2001

View full text Add to dashboard Cite

.High-performance thermosetting composites typically consist of a high-modulus fibrous material embedded in a thermosetting polymer matrix. The behavior of the resulting composite depends on the properties of the reinforcement, the interphase, and the matrix. Vinyl-ester (VE) resins are relatively low-cost matrix resins used in liquid molding of large structures such as contiguous vehicle huUs. In liquid-molding processes, quality-control sensors can ensure resin impregnation of the preform and cure of the resin after infiltration. For these purposes, SMARTweave (SW), based on direct current (DC) sensing, is used as an in-situ flow-front detection and curemonitoring system. SW measures change in the ionic conductivity with cure, which can then be related to the material properties like viscosity and degree of cure. This enables in-situ measurement of degree of cure and viscosity development during cure from SW measurements. This report builds on previous modeling work that assumed a direct dependence of DC resistance on the resin viscosity, limiting the use of such models beyond gelation. This report presents a continuum model based on free volume theory to describe ionic conductivity through gelation to vitrification.

show abstract

Section: Modeling Approachmentioning

confidence: 99%

Section: Modeling Approachmentioning

confidence: 99%

See 1 more Smart Citation

Vinyl-Ester (VE) Cure Characterization Via Direct Current Sensors

Fink¹

2001

View full text Add to dashboard Cite

show abstract

“…These asymptotic values for both Figures (3) and (4) are vanishingly small for site fractions below the critical percolation values, 0.59 and 0.50 respectively. Infinite lattice conductivities [13] shown on the right-hand side of Figure ( f(x,À,). Some of the occupied sites in the top and bottom row may not belong to a current carrying path.…”

Section: Monte Carlo Lattice Conductivity Calculationsmentioning

confidence: 99%

“…The conductivity of an infinite lattice of random fibers will vanish below the critical percolation fiber volume fractions [7,8] A major difficulty with using random lattice literature values [3,4,[7][8][9][10][11][12][13] for percolation and conductivity for a single ply of unidirectional graphite/epoxy composite is that the previous theory was addressed solely to understanding the infinite lattice. The previous Jiterature results for the conductivity [10][11][12][13] of random lattices only apply to a single ply very large in both width and thickness whereas in practical applications the single ply is sometimes only a few fiber diameters thick. In this paper, we have calculated the distribution of the electrical potentials V; for each occupied fiber site i for very wide random lattices of various thicknesses and the corresponding lattice conductivity from an iteration of Kirchoff's equation.…”

mentioning

confidence: 99%

Random Lattice Electrical Conductivity Calculations for a Graphite/Epoxy Ply of Finite Thickness

Strieder

Joy

1982

Journal of Composite Materials

View full text Add to dashboard Cite

A single ply of unidirectional graphite/epoxy composite is modeled by both a two-dimensional Cartesian square and a close packed triangular lattice of fibers of infinite width and finite thickness. All fiber cross-sections are cir cular (of the same diameter) and those fibers with centers located at adjacent points on the lattice will contact at the midpoint. From these contacts con duction paths are formed across the latice. To generate randomness, the cir cular fiber cross-sections are removed at random from the lattice, leaving va cant sites of insulating matrix material, until a certain fiber fraction is reached. Lattice conductivities are calculated for both models at various fiber fractions and lattice thicknesses. Good agreement is obtained when the asymptotic conductivity versus thickness curves are compared with ex perimental data.

show abstract

Lattice Gas Automata Simulation of 2D Site-Percolation Diffusion: Configuration Dependence of the Theoretically Expected Crossover of Diffusion Regime

Ghaemi¹,

Rezaei‐Ghaleh

Asgari

2008

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Theoretical analysis of random walk on percolation lattices has predicted that, at the occupied site concentrations of above the threshold value, a characteristic crossover between an initial sub-diffusion to a final classical diffusion behavior should occur. In this study, we have employed the lattice gas automata model to simulate random walk over a square 2D site-percolation lattice. Quite good result was obtained for the critical exponent of diffusion coefficient. The random walker was found to obey the anomalous sub-diffusion regime, with the exponent decreasing when the occupied site concentration decreases. The expected crossover between diffusion regimes was observed in a configuration-dependent manner, but the averaging over the ensemble of lattice configurations removed any manifestation of such crossovers. This may have been originated from the removal of short-scale inhomogeneities in percolation lattices occurring after ensemble averaging.

show abstract

Monte Carlo experiment for the two-dimensional site percolation network

Cited by 38 publications

References 16 publications

Vinyl-Ester (VE) Cure Characterization Via Direct Current Sensors

Vinyl-Ester (VE) Cure Characterization Via Direct Current Sensors

Random Lattice Electrical Conductivity Calculations for a Graphite/Epoxy Ply of Finite Thickness

Lattice Gas Automata Simulation of 2D Site-Percolation Diffusion: Configuration Dependence of the Theoretically Expected Crossover of Diffusion Regime

Contact Info

Product

Resources

About