0000000000117175
AUTHOR
B. Biswal
Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model.
The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for ‘‘fat’’ stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.
Quantitative prediction of effective material properties of heterogeneous media
Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic app…
Stochastic multiscale model for carbonate rocks.
A multiscale model for the diagenesis of carbonate rocks is proposed. It captures important pore scale characteristics of carbonate rocks: wide range of length scales in the pore diameters; large variability in the permeability; and strong dependence of the geometrical and transport parameters on the resolution. A pore scale microstructure of an oolithic dolostone with generic diagenetic features is successfully generated. The continuum representation of a reconstructed cubic sample of sidelength $2\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ contains roughly $42\ifmmode\times\else\texttimes\fi{}{10}^{6}$ crystallites and pore diameters varying over many decades. Petrophysical parameters are com…
Exact and approximate calculations for the conductivity of sandstones
We analyze a three-dimensional pore space reconstruction of Fontainebleau sandstone and calculate from it the eective conductivity using local porosity theory. We compare this result with an exact calculation of the eective conductivity that solves directly the disordered Laplace equation. The prediction of local porosity theory is in good quantitative agreement with the exact result. c 1999 Elsevier Science B.V. All rights reserved.
Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the Two-Dimensional Ising Model
We report multicanonical Monte Carlo simulations of the tails of the order-parameter distribution of the two-dimensional Ising model for fixed boundary conditions. Clear numerical evidence for "fat" stretched exponential tails is found below the critical temperature, indicating the possible presence of fat tails at the critical temperature.
Quantitative Analysis of Experimental and Synthetic Microstructures for Sedimentary Rock
A quantitative comparison between the experimental microstructure of a sedimentary rock and three theoretical models for the same rock is presented. The microstructure of the rock sample (Fontainebleau sandstone) was obtained by microtomography. Two of the models are stochastic models based on correlation function reconstruction, and one model is based on sedimentation, compaction and diagenesis combined with input from petrographic analysis. The porosity of all models closely match that of the experimental sample and two models have also the same two point correlation function as the experimental sample. We compute quantitative differences and similarities between the various microstructur…
Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone
Abstract A stochastic geometrical modeling technique is used to reconstruct a laboratory scale Fontainebleau sandstone with a sidelength of 1.5 cm. The model reconstruction is based on crystallite properties and diagenetic parameters determined from two-dimensional images. The three-dimensional pore scale microstructure of the sandstone is represented by a list of quartz crystallites defined geometrically and placed in the continuum. This allows generation of synthetic μ -CT images of the rock model at arbitrary resolutions. Quantitative microstructure comparison based on Minkowski functionals, two-point correlation function and local porosity theory indicates that this modeling technique c…
Quantitative comparison of mean field mixing laws for conductivity and dielectric constants of porous media
Abstract Exact numerical solution of the electrostatic disordered potential problem is carried out for four fully discretized three-dimensional experimental reconstructions of sedimentary rocks. The measured effective macroscopic dielectric constants and electrical conductivities are compared with parameter-free predictions from several mean field type theories. All these theories give agreeable results for low contrast between the media. Predictions from local porosity theory, however, match for the entire range of contrast.