Simulation of binary random fields with applications to two-phase random media

Journal of Engineering Mechanics

Volumn 131, Issue 4, 2005, Pages 397-412

  Koutsourelakis, Phaedon Stelios ^a   Deodatis, George ^b  

^a UNIVERSITY OF INNSBRUCK   (Austria)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Gaussian process; Material properties; Random processes; Simulation

Indexed keywords

ALGORITHMS; MAPPING; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR SYSTEMS; PROBABILITY;

AUTOCORRELATION FUNCTIONS; BINARY RANDOM FIELDS; GAUSSIAN SAMPLE FUNCTIONS; TWO-PHASE RANDOM MEDIA;

COMPUTER SIMULATION;

MATHEMATICAL ANALYSIS;

EID: 16344382608     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(2005)131:4(397)     Document Type: Article

References (29)

1. Berk, N. F. (1991). "Scattering properties of the leveled-wave model of random morphologies." Phys. Rev. A, 44(8), 5069-5079.
2. Berryman, J. G. (1986). "Relationship between specific surface area and spatial correlation functions for anisotropic media." J. Math. Phys. 28, 244-245.
3. Berryman, J. G. (1997). "Planar spatial correlations, anisotropy and specific surface area of stationary random porous media." J. Appl. Phys., 83(3), 1685-1693.
4. Cule, D., and Torquato, S. (1999). "Generating random media from limited microstructural information." J. Appl. Phys., 86(6), 3428-3437.
5. Debye, P., Anderson, H. R., and Brumberger, H. (1957). "Scattering by an imhomogeneous solid." J. Appl. Phys., 28, 679-683.
6. Deodatis, G., and Koutsourelakis, S. (2002). "A methodology to generate sample realizations of two-phase random media." Proc., 5th World Congress on Computational Mechanics H. A. Mang, F.R G. Rammerstorfer, and J. Eberhardsteiner, eds., Vienna, Austria, ISBN 3-9501554-0-6 .
7. Genz, A. (1992). "Numerical computation of multivariate normal probabilities." J. Comput. Graph. Stat., 1, 141-149.
8. Genz, A., and Kwong, K.-S. (2000). "Numerical evaluation of singular multivariate normal distributions." J. Stat. Comput. Simul., 68(1), 1-21.
9. Grigoriu, M. (1995). Applied Non-Gaussian Processes, Prentice-Hall, Englewood Cliffs, N.J.
10. Koutsourelakis, P.-S. (2002). "A method to generate samples of two-phase random media." PhD thesis, Princeton Univ., Princeton , N.J.
11. Koutsourelakis, S., and Deodatis, G. (2002). "A methodology to simulate the clustering of inclusions in two-phase random media." Proc., 4th Int. Conf. on Computational Stochastic Mechanics, Corfu, Greece, 325-333.
12. Koutsourelakis, P. S., and Deodatis, G. (2003). "Simulation of binary random fields: Application to random media." Applications of Statistics and Probability in Civil Engineering, Proc., 9th ICASP, A. Der Kiureghian, S. Madanat, and J. M. Pestana, eds., San Francisco, 337-343.
13. Leadbetter, M. R. (1972). "Point processes generated by level crossings." Proc., Conf. on Stochastic Point Processes: Statistical Analysis, Theory, and Applications, IBM Research Center, Yorktown Heights, N.Y., 1971, Wiley-Interscience, New York, 436-467.
14. Papoulis, A. (1962). The Fourier integral and its applications, McGraw-Hill, New York.
15. Quintanilla, J., and Torquato, S. (1996). "Microstructure and conductivity of hierarchical laminate composites." Phys. Rev. E, 53(5), 4368-4369.
16. Ripley, B. D. (1981). Spatial Statistics, Wiley, Hoboken, N.J.
17. Roberts, A. P. (1997). "Statistical reconstruction of three-dimensional porous media from two-dimensional images." Phys. Rev. E, 56(3), 3203-3212.
18. Roberts, A. P., and Knackstedt, M. A. (1996). "Structure-property correlations in model composite materials." Phys. Rev. E, 54(3), 2313-2328.
19. Roberts, A. P., and Teubner, M. (1995). "Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation." Phys. Rev. E, 51(5), 4141-4153.
20. Rozman, M. G., and Utz, M. (2001). "Efficient reconstruction of multi-phase morphologies from correlation functions." Phys. Rev. E 63(1), 1-8.
21. Sheehan, N., and Torquato, S. (2001). "Generating microstructures with specified correlation functions." J. Appl. Phys., 89(1), 53-60.
22. Shinozuka, M., and Deodatis, G. (1991). " Simulation of stochastic processes by spectral representation." Appl. Mech. Rev., 44(4), 191-204.
23. Sinai, Y. (2001). Lecture notes on random processes, Princeton Univ. Press, Princeton, N.J.
24. Tong, Y. L. (1990). The multivariate normal distribution, Springer, New York.
25. Van Marcke, E. (1983). Random fields: Analysis and synthesis, MIT Press, Cambridge, Mass.
26. Yeong, C. L. Y., and Torquato, S. (1998a). "Reconstructing random media." Phys. Rev. E, 57(1), 495-506.
27. Yeong, C. L. Y., and Torquato, S. (1998b). "Reconstructing random media II. Three-dimensional media from two-dimensional cuts." Phys. Rev. E 58(1), 224-233.
28. Ylvisaker, N. D. (1965). "The expected number of zeros of a stationary Gaussian process." Ann. Math. Stat., 36(3), 1043-1046.
29. Zerva, A. (1992). "Seismic ground motion simulations from a class of spatial variability models." Earthquake Eng. Struct. Dyn., 21(4), 351-361.