Percolation of binary disk systems: Modeling and theory

Meeks, Kelsey; Tencer, John; Pantoya, Michelle L.

doi:10.1103/PhysRevE.95.012118

Title: Percolation of binary disk systems: Modeling and theory

Abstract

The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This paper utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and compared to previously published correlations. Finally, a set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.

Authors:

Meeks, Kelsey ^[1]; Tencer, John ^[2]; Pantoya, Michelle L. ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Texas Tech Univ., Lubbock, TX (United States). Mechanical Engineering Dept.
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Texas Tech Univ., Lubbock, TX (United States). Mechanical Engineering Dept.

Publication Date:: 2017-01-12

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); US Army Research Office (ARO)

Contributing Org.:: Texas Tech Univ., Lubbock, TX (United States)

OSTI Identifier:: 1343061

Alternate Identifier(s):: OSTI ID: 1339186

Report Number(s):: SAND2016-6744J
Journal ID: ISSN 2470-0045; 645220; TRN: US1700999

Grant/Contract Number:: AC04-94AL85000; W911NF-11-1-0439

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review E

Additional Journal Information:: Journal Volume: 95; Journal Issue: 1; Journal ID: ISSN 2470-0045

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

Citation Formats


                    Meeks, Kelsey, Tencer, John, and Pantoya, Michelle L. Percolation of binary disk systems: Modeling and theory.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevE.95.012118.

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                    Meeks, Kelsey, Tencer, John, & Pantoya, Michelle L. Percolation of binary disk systems: Modeling and theory.  United States.  https://doi.org/10.1103/PhysRevE.95.012118

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                    Meeks, Kelsey, Tencer, John, and Pantoya, Michelle L. Thu .  
"Percolation of binary disk systems: Modeling and theory".  United States.  https://doi.org/10.1103/PhysRevE.95.012118.  https://www.osti.gov/servlets/purl/1343061.

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@article{osti_1343061,

  title        = {Percolation of binary disk systems: Modeling and theory},

  author       = {Meeks, Kelsey and Tencer, John and Pantoya, Michelle L.},

  abstractNote = {The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This paper utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and compared to previously published correlations. Finally, a set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.},

  doi          = {10.1103/PhysRevE.95.012118},

  journal      = {Physical Review E},

  number       = 1,

  volume       = 95,

  place        = {United States},

  year         = {2017},

  month        = {1}

}

Copy to clipboard

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Works referencing / citing this record:

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Title: Percolation of binary disk systems: Modeling and theory

Abstract

Citation Formats

Continuum percolation of overlapping disks with a distribution of radii having a power-law tail journal, August 2013

Continuum percolation thresholds for mixtures of spheres of different sizes journal, March 2003

Finite-size effects in continuum percolation journal, September 1989

Universality and cluster structures in continuum models of percolation with two different radius distributions journal, September 1993

Geometrical percolation threshold of overlapping ellipsoids journal, July 1995

Continuum percolation thresholds in two dimensions journal, December 2012

Percolation of phases in a three-dimensional cement paste microstructural model journal, March 1991

Advanced susceptors for microwave heating of energetic materials journal, January 2016

Polynomial-Time Data Reduction for the Subset Interconnection Design Problem journal, January 2015

Finite-size scaling in stick percolation journal, October 2009

Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs journal, August 1981

Site- and bond-percolation thresholds in K n , n -based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies journal, April 2016

Monte Carlo study of correlated continuum percolation: Universality and percolation thresholds journal, May 1990

Efficient measurement of the percolation threshold for fully penetrable discs journal, October 2000

Continuum percolation with discs having a distribution of radii journal, August 1984

Critical phenomena in complex networks journal, October 2008

Continuum percolation with steps in an annulus journal, November 2004

Combustion synthesis of advanced materials: Part I. Reaction parameters journal, January 1995

Estimation of percolation thresholds via percolation in inhomogeneous media journal, January 2003

Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses journal, August 2012

Critical Density in Percolation Processes journal, November 1970

Polyaniline–titania solid electrolyte for new generation photovoltaic single-layer devices journal, April 2012

Percolation on a Continuum and the Localization-Delocalization Transition in Amorphous Semiconductors journal, December 1971

Continuum Percolation of Rods journal, April 1985

Excluded volume and its relation to the onset of percolation journal, October 1984

Measurement of the percolation threshold for fully penetrable disks of different radii journal, May 2001

Symmetry of the continuum percolation threshold in systems of two different size objects journal, November 2004

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis journal, June 2010

On the critical density for continuum percolation of spheres of variable radii journal, August 1997

Application of percolation theory to microtomography of structured media: Percolation threshold, critical exponents, and upscaling journal, January 2011

Thermal conductivity and latent heat thermal energy storage characteristics of paraffin/expanded graphite composite as phase change material journal, June 2007

Anomalous voltage distribution of random resistor networks and a new model for the backbone at the percolation threshold journal, April 1985

Efficient Monte Carlo Algorithm and High-Precision Results for Percolation journal, November 2000

Random Plane Networks journal, December 1961

Fast Monte Carlo algorithm for site or bond percolation journal, June 2001

Estimation of microwave penetration distance and complex permittivity of graphite by measurement of permittivity and direct current conductivity of graphite powder mixtures journal, February 2015

Asymmetry in the percolation thresholds of fully penetrable disks with two different radii journal, November 2007

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes journal, January 2010

Transport and diffusion in three-dimensional composite media journal, June 1994

Topological estimation of percolation thresholds journal, January 2008

Spanning probability in 2D percolation journal, November 1992

Effect of nanofiller shape on effective thermal conductivity of fluoropolymer composites journal, October 2015

Continuum percolation threshold for interpenetrating squares and cubes journal, October 2002

Nonuniversality and continuity of the critical covered volume fraction in continuum percolation journal, April 1994

Long-range correlated percolation and flow and transport in heterogeneous porous media journal, September 1994

Flexible h-BN foam sheets for multifunctional electronic packaging materials with ultrahigh thermostability journal, January 2018

Percolation thresholds for discorectangles: Numerical estimation for a range of aspect ratios journal, February 2020

Continuum percolation of overlapping disks with a distribution of radii having a power-law tail
journal, August 2013

Continuum percolation thresholds for mixtures of spheres of different sizes
journal, March 2003

Finite-size effects in continuum percolation
journal, September 1989

Universality and cluster structures in continuum models of percolation with two different radius distributions
journal, September 1993

Geometrical percolation threshold of overlapping ellipsoids
journal, July 1995

Continuum percolation thresholds in two dimensions
journal, December 2012

Percolation of phases in a three-dimensional cement paste microstructural model
journal, March 1991

Advanced susceptors for microwave heating of energetic materials
journal, January 2016

Polynomial-Time Data Reduction for the Subset Interconnection Design Problem
journal, January 2015

Finite-size scaling in stick percolation
journal, October 2009

Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs
journal, August 1981

Site- and bond-percolation thresholds in $K_{n, n}$ -based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies
journal, April 2016

Monte Carlo study of correlated continuum percolation: Universality and percolation thresholds
journal, May 1990

Efficient measurement of the percolation threshold for fully penetrable discs
journal, October 2000

Continuum percolation with discs having a distribution of radii
journal, August 1984

Critical phenomena in complex networks
journal, October 2008

Continuum percolation with steps in an annulus
journal, November 2004

Combustion synthesis of advanced materials: Part I. Reaction parameters
journal, January 1995

Estimation of percolation thresholds via percolation in inhomogeneous media
journal, January 2003

Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses
journal, August 2012

Critical Density in Percolation Processes
journal, November 1970

Polyaniline–titania solid electrolyte for new generation photovoltaic single-layer devices
journal, April 2012

Percolation on a Continuum and the Localization-Delocalization Transition in Amorphous Semiconductors
journal, December 1971

Continuum Percolation of Rods
journal, April 1985

Excluded volume and its relation to the onset of percolation
journal, October 1984

Measurement of the percolation threshold for fully penetrable disks of different radii
journal, May 2001

Symmetry of the continuum percolation threshold in systems of two different size objects
journal, November 2004

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis
journal, June 2010

On the critical density for continuum percolation of spheres of variable radii
journal, August 1997

Application of percolation theory to microtomography of structured media: Percolation threshold, critical exponents, and upscaling
journal, January 2011

Thermal conductivity and latent heat thermal energy storage characteristics of paraffin/expanded graphite composite as phase change material
journal, June 2007

Anomalous voltage distribution of random resistor networks and a new model for the backbone at the percolation threshold
journal, April 1985

Efficient Monte Carlo Algorithm and High-Precision Results for Percolation
journal, November 2000

Random Plane Networks
journal, December 1961

Fast Monte Carlo algorithm for site or bond percolation
journal, June 2001

Estimation of microwave penetration distance and complex permittivity of graphite by measurement of permittivity and direct current conductivity of graphite powder mixtures
journal, February 2015

Asymmetry in the percolation thresholds of fully penetrable disks with two different radii
journal, November 2007

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes
journal, January 2010

Transport and diffusion in three-dimensional composite media
journal, June 1994

Topological estimation of percolation thresholds
journal, January 2008

Spanning probability in 2D percolation
journal, November 1992

Effect of nanofiller shape on effective thermal conductivity of fluoropolymer composites
journal, October 2015

Continuum percolation threshold for interpenetrating squares and cubes
journal, October 2002

Nonuniversality and continuity of the critical covered volume fraction in continuum percolation
journal, April 1994

Long-range correlated percolation and flow and transport in heterogeneous porous media
journal, September 1994

Flexible h-BN foam sheets for multifunctional electronic packaging materials with ultrahigh thermostability
journal, January 2018

Percolation thresholds for discorectangles: Numerical estimation for a range of aspect ratios
journal, February 2020