Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation.

We investigate the effective conductivity ($\sigma_e$) of a class of amorphous media defined by the level-cut of a Gaussian random field. The three point solid-solid correlation function is derived and utilised in the evaluation of the Beran-Milton bounds. Simulations are used to calculate $\sigma_e$ for a variety of fields and volume fractions at several different conductivity contrasts. Relatively large differences in $\sigma_e$ are observed between the Gaussian media and the identical overlapping sphere model used previously as a `model' amorphous medium. In contrast $\sigma_e$ shows little variability between different Gaussian media.

• Publication year

  1995

• Venue

  Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

• Publication date

  1995-05-01

• Fields of study

  Medicine, Materials Science, Physics

• Identifiers
  DOI 10.1103/PhysRevE.51.4141arXiv cond-mat/0004462PMID 9963124
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Coarse-graining procedure to generate and analyze heterogeneous materials: Theory.

  1993cited by this paper
• Ductile-brittle transition in random porous Au.

  1992cited by this paper
• Flow, conduction, and a characteristic length in periodic bicontinuous porous media.

  1991cited by this paper
• Scattering properties of the leveled-wave model of random morphologies.

  1991cited by this paper
• Numerical recipes

  1990cited by this paper
• n-point probability functions for a lattice model of heterogeneous media.

  1990cited by this paper
• Recent Advances in Engineering Science

  1989cited by this paper
• Scattering properties of a model bicontinuous structure with a well defined length scale.

  1987cited by this paper
• Effective properties of two-phase disordered composite media: II. Evaluation of bounds on the conductivity and bulk modulus of dispersions of impenetrable spheres.

  1986cited by this paper
• Handbook of Mathematical Functions.

  1966cited by this paper

• Structural tuning of nanoporous metal via electrodeposition

  2026cites this paper
• Effective transport and mechanical properties of two-phase materials across the order-disorder spectrum

  2025cites this paper
• Towards a physically and microstructure-based equation for the evolution of the specific surface area in snow

  2025cites this paper
• Computational Intelligence in Stochastic Reconstruction of Porous Microstructures for Image-Based Poro/Micro-Mechanical Modeling

  2025cites this paper
• Explicit total Lagrangian material point method with implicit frictional-contact model for soft granular materials

  2024cites this paper
• Accurate prediction of discontinuous crack paths in random porous media via a generative deep learning model

  2024cites this paper
• Simulated diffusion spreadability for characterizing the structure and transport properties of two-phase materials

  2023cites this paper
• The nonlinear elastic response of bicontinuous rubber blends

  2023cites this paper
• Mechanically-grown morphogenesis of Voronoi-type materials: Computer design, 3D-printing and experiments

  2022cites this paper
• Multi-Scale Modeling of the Thermo-Mechanical Behavior of Cast Iron

  2022cites this paper
• Pore-scale modeling of complex transport phenomena in porous media

  2022cites this paper
• Inelastic neutron scattering analysis with time-dependent Gaussian-field models.

  2021cites this paper
• Self-supervised optimization of random material microstructures in the small-data regime

  2021cites this paper
• Characterization of anisotropic Gaussian random fields by Minkowski tensors

  2021cites this paper
• Local Hydraulic Resistance in Heterogeneous Porous Media

  2021cites this paper
• Reconstruction, optimization, and design of heterogeneous materials and media: Basic principles, computational algorithms, and applications

  2021cites this paper
• Thermo-elasto-plastic phase-field modelling of mechanical behaviours of sintered nano-silver with randomly distributed micro-pores

  2021cites this paper
• Topology optimization under microscale uncertainty using stochastic gradients

  2021cites this paper
• Quantifying the effect of two-point correlations on the effective elasticity of specific classes of random porous materials with and without connectivity

  2021cites this paper
• Microstructural design of tunable elastoplastic two-phase random heterogeneous materials

  2021cites this paper
• The microstructural dependence of ionic transport in bi-continuous nanoporous metal

  2021cites this paper
• Chord-distribution functions and Rice formulae. Application to random media.

  2021cites this paper
• The pore geometry of pharmaceutical coatings: statistical modelling, characterization methods and transport prediction

  2020cites this paper
• Stochastic models of dense or hollow nanoparticles and their scattering properties.

  2020cites this paper
• Binary Random Fields

  2020cites this paper
• Floating tracer clustering in divergent random flows modulated by an unsteady mesoscale ocean field

  2020cites this paper
• Method of evaluation of permeability properties of heterogeneous media based on voxel models

  2020cites this paper
• Tensile strength of granular aggregates: Stress chains across particle phase versus stress concentration by pores.

  2020cites this paper
• Modelling Material Microstructure Using the Perlin Noise Function

  2020cites this paper
• Ferropericlase Control of Lower Mantle Rheology: Impact of Phase Morphology

  2020cites this paper
• Multiscale Modeling of Cohesive-Frictional Strength Properties in Cementitious Materials

  2020cites this paper
• On the excursion area of perturbed Gaussian fields

  2019cites this paper
• Effective transport properties of conformal Voronoi-bounded columns via recurrent boundary element expansions

  2019cites this paper
• Effective elastic properties of 3D stochastic bicontinuous composites

  2019influential citation
• Simulations of Non-Gaussian Property Fields Based on the Apparent Properties of Statistical Volume Elements

  2019cites this paper
• Clustering of floating tracers in weakly divergent velocity fields.

  2019cites this paper
• Hyperuniform states of matter

  2018cites this paper
• Random field finite element models with cohesive-frictional interactions of a hardened cement paste microstructure

  2018cites this paper
• Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques

  2018cites this paper
• Thermoelastic Analysis of Porous Media Using a Multiscale Asymptotic Expansion Homogenization Method

  2018cites this paper
• Recurrent approach to effective material properties with application to anisotropic binarized random fields

  2018cites this paper
• Prediction of diffusive transport through polymer films from characteristics of the pore geometry

  2018cites this paper
• Stochastic analysis of capillary condensation in disordered mesopores.

  2018cites this paper
• Stochastic models of disordered mesoporous materials for small-angle scattering analysis and more

  2018cites this paper
• A Computational-Experimental Method to Determine the Effective Diffusivity of Asphalt Concrete

  2017cites this paper
• A three‐dimensional statistical model for imaged microstructures of porous polymer films

  2017cites this paper
• Impact of diffusion on surface clustering in random hydrodynamic flows.

  2017cites this paper
• Characteristic Analysis of Particulate Composites According to a Random Microstructure

  2017cites this paper
• A novel PCA-based microstructure descriptor for heterogeneous material design

  2017cites this paper
• Random scalar fields and hyperuniformity

  2017cites this paper
• Probabilistic Reduced-Order Modeling for Stochastic Partial Differential Equations

  2017cites this paper
• Statistical methods for mechanical characterization of randomly reinforced media

  2017influential citation
• Concurrent design of quasi-random photonic nanostructures

  2017cites this paper
• Microstructure statistics–property relations of silver particle-based interconnects

  2017influential citation
• Regional analysis techniques for integrating experimental and numerical measurements of transport properties of reservoir rocks

  2017cites this paper
• Microstructure statistics – property relations of silver particle-based interconnects

  2017influential citation
• Statistical reconstruction and Karhunen–Loève expansion for multiphase random media

  2016cites this paper
• Bio-inspired design strategy of quasi-random structures for optimal light control

  2016cites this paper
• Stochastic shale permeability matching: Three-dimensional characterization and modeling

  2016cites this paper
• Hyperuniformity and its generalizations.

  2016cites this paper
• Characterization and Design of Functional Quasi-Random Nanostructured Materials Using Spectral Density Function

  2016cites this paper
• Implicit frictional-contact model for soft particle systems

  2015cites this paper
• Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure

  2015cites this paper
• Multigrid hierarchical simulated annealing method for reconstructing heterogeneous media.

  2015cites this paper
• Explicit numerical simulation of microfluidic liquid flows in micro-packed bed

  2015cites this paper
• Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function.

  2015cites this paper
• Generation of Spatially Correlated Network Models of Porous Media

  2015cites this paper
• Stochastic reconstruction using multiple correlation functions with different-phase-neighbor-based pixel selection.

  2014cites this paper
• Statistical reconstruction of two-phase random media

  2014cites this paper
• Reconstruction of the 3D representative volume element from the generalized two-point correlation function

  2014cites this paper
• On the experimental design of the material microstructures

  2014influential citation
• Rock-typing Using The Complete Set Of Additive Morphological Descriptors

  2013influential citation
• Structure and dynamics of wireless communication systems

  2013cites this paper
• Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization

  2013cites this paper
• Analytical estimation of distance–disorientation function of the material microstructure

  2013cites this paper
• Cross-correlation function for accurate reconstruction of heterogeneous media.

  2013cites this paper
• Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty

  2013cites this paper
• Topology of evolving pore networks

  2012cites this paper
• Thermal characterization of materials using Karhunen–Loève decomposition techniques – Part II. Heterogeneous materials

  2012cites this paper
• Homogenization and thermoelastic analysis of heterogenous materials with regular and random microstructures

  2012cites this paper
• Tensile strength and fracture of cemented granular aggregates

  2012cites this paper
• Microstructure Sensitive Design for Performance Optimization

  2012cites this paper
• Three-dimensional midpoint displacement algorithm for the generation of fractal porous media

  2012cites this paper
• Chord-length distribution functions and Rice formulae. Application to random media

  2012cites this paper
• How fast can the chord length distribution decay?

  2011cites this paper
• Improved reconstructions of random media using dilation and erosion processes.

  2011cites this paper
• STOCHASTIC DESIGN AND CONTROL IN RANDOM HETEROGENEOUS MATERIALS

  2011cites this paper
• Developments in the theory and applications of the variability response function concept

  2011cites this paper
• Simulating mechanical behavior of porous materials by homogenization method

  2011cites this paper
• Combined impact of microstructure and mechanical stress on the electrical resistivity of PdHc thin films

  2011cites this paper
• Chord-length distribution functions and Rice formulae. Application to random media

  2011cites this paper
• Multiscale thermoelastic analysis of random heterogeneous materials. Part I: Microstructure characterization and homogenization of material properties

  2010cites this paper
• Multiscale thermoelastic analysis of random heterogeneous materials: Part II: Direct micromechanical failure analysis and multiscale simulations

  2010cites this paper
• Transient multiscale thermoelastic analysis of functionally graded materials

  2010cites this paper
• Stochastic reconstruction of the microstructure of equilibrium form snow and computation of effective elastic properties

  2010cites this paper
• Multiscale investigation of random heterogeneous media in materials and earth sciences

  2010influential citation
• Optimal Design of Heterogeneous Materials

  2010cites this paper
• The response of an elastic three-dimensional half-space to random correlated displacement perturbations on the boundary

  2010cites this paper
• Boolean reconstructions of complex materials: Integral geometric approach.

  2009cites this paper
• Towards precise prediction of transport properties from synthetic computer tomography of reconstructed porous media.

  2009cites this paper