Simulation of Multidimensional Binary Random Fields with Application to Modeling of Two-Phase Random Media
Publication: Journal of Engineering Mechanics
Volume 132, Issue 6
Abstract
This paper proposes a methodology for simulation of binary random fields with application to the problem of generating sample realizations of two-phase random media. The methodology is based on the concept of nonlinear transformations with memory of Gaussian random fields. The simulation is performed according to the autocorrelation function of the binary field which contains considerable information about the microstructural characteristics of the medium. The determination of the probabilistic characteristics of the underlying Gaussian field is achieved through an iterative procedure that was introduced in a previous paper by the same authors in one dimension and is extended here to multiple dimensions. Limiting cases and alternative mappings are also presented. The capabilities of the methodology are demonstrated in a series of examples.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Science Foundation under collaborative Grant No. NSFCMS-0084533/0084547, with Dr. Ken Chong as Program Director.
References
Berk, N. (1991). “Scattering properties of leveled-wave model for random morphologies.” Phys. Rev. A, 44(9), 5069–5079.
Cule, D., and Torquato, S. (1999). “Generating random media from limited microstructural information via stochastic optimization.” J. Appl. Phys., 86, 3428.
Grigoriu, M. (1995). Applied non-Gaussian processes, Prentice-Hall, Upper Saddle River, N.J.
Koutsourelakis, P. (2002). “A methodology to generate samples of two-phase random media.” Ph.D. thesis, Princeton Univ., Princeton, N.J.
Koutsourelakis, P., and Deodatis, G. (2005). “Simulation of binary random fields with applications to two-phase random media.” J. Eng. Mech., 131(4), 397–412.
Roberts, A. (1997). “Statistical reconstruction of three-dimensional porous media from two-dimensional images.” Phys. Rev. E, 56(3), 3203–3212.
Roberts, A., and Teubner, M. (1995). “Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation.” Phys. Rev. E, 51(5), 4141–4153.
Rozman, M., and Utz, M. (2001). “Efficient reconstruction of multiphase morphologies from correlation functions.” Phys. Rev. E, 63, 066701.
Rozman, M., and Utz, M. (2002). “Uniqueness of reconstruction of multiphase morphologies from two-point correlation functions.” Phys. Rev. Lett., 89(13), 135501.
Sheehan, N., and Torquato, S. (2001). “Generating microstructures with specified correlation functions.” J. Appl. Phys., 89, 53.
Shinozuka, M., and Deodatis, G. (1996). “Simulation of multi-dimensional stochastic processes by spectral representation.” Appl. Mech. Rev., 49(1), 29–53.
Torquato, M. (2002). Random heterogeneous materials. Springer, Berlin.
Yeong, C., and Torquato, S. (1998). “Reconstructing random media I and II.” Phys. Rev. E, 58(1), 224–233.
Information & Authors
Information
Published In
Copyright
© 2006 ASCE.
History
Received: Dec 28, 2004
Accepted: Aug 23, 2005
Published online: Jun 1, 2006
Published in print: Jun 2006
Notes
Note. Associate Editor: Arvid Naess
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.