A reduced concurrent memory access method to accelerate the computation of the lineal path function on large microstructures
Authors: Bissaker Edward , Lamichhane Bishnu , Jenkins David 
Published: May 2024

The Concurrent Reduced Memory Access method (CRMA) is a scalable memory-efficient Monte Carlo method for computing the lineal path function. It addresses an inherent memory bottleneck of lineal path function algorithms by utilising known properties of the two-point correlation function to reduce the number of voxels where the phase value must be evaluated. The CRMA method reduces the computation time and improves the scalability characteristics of the traditional lineal path function Monte Carlo methods. CRMA also provides additional information useful for analysing microstructures since the two-point correlation function is computed as part of the method. The CRMA method offers an efficient, scalable and extendable solution for computing the lineal path function.
References

A. A. Agra, A. Nicolodi, B. D. Flores, I. V. Flores, G. L. R. da Silva, A. C. F. Vilela, and E. Osório. Automated procedure for coke microstructural characterization in imagej software aiming industrial application. Fuel 304, 121374 (2021). doi: 10.1016/j.fuel.2021.121374
J. Baruchel, P. Bleuet, A. Bravin, P. Coan, E. Lima, A. Madsen, W. Ludwig, P. Pernot, and J. Susini. Advances in synchrotron hard X-ray based imaging. Comptes Rendus Physique 9.5-6 (2008), pp. 624–641. doi: 10.1016/j.crhy.2007.08.003
J. E. Bresenham. Algorithm for computer control of a digital plotter. IBM Sys. J. 4.1 (1965), pp. 25–30. doi: 10.1147/sj.41.0025
D. T. Fullwood, S. R. Kalidindi, S. R. Niezgoda, A. Fast, and N. Hampson. Gradient-based microstructure reconstructions from distributions using fast Fourier transforms. Mat. Sci. Eng.: A 494.1-2 (2008), pp. 68–72. doi: 10.1016/j.msea.2007.10.087
J. Gajdošík, J. Zeman, and M. Šejnoha. Qualitative analysis of fiber composite microstructure: Influence of boundary conditions. Prob. Eng. Mech. 21.4 (2006), pp. 317–329. doi: 10.1016/j.probengmech.2005.11.006
E. Y. Guo, N. Chawla, T. Jing, S. Torquato, and Y. Jiao. Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method. Mat. Character. 89 (2014), pp. 33–42. doi: 10.1016/j.matchar.2013.12.011
J. Havelka, A. Kučerová, and J. Sýkora. Compression and reconstruction of random microstructures using accelerated lineal path function. Comput. Mat. Sci. 122 (2016), pp. 102–117. doi: 10.1016/j.commatsci.2016.04.044
J. H. Kinney and M. C. Nichols. X-ray tomographic microscopy (XTM) using synchrotron radiation. Ann. Rev. Mat. Sci. 22.1 (1992), pp. 121–152. doi: 10.1146/annurev.ms.22.080192.001005
D. Kirk and W.-m. W. Hwu. Programming massively parallel processors: A hands-on approach. Morgan Kaufmann, 2016. url: https://shop.elsevier.com/books/programming-massively-parallel-processors/kirk/978-0-12-811986-0
J. Kováčik. Correlation between Young’s modulus and porosity in porous materials. J. Matt. Sci. Lett. 18.13 (1999), pp. 1007–1010. doi: 10.1023/A:1006669914946
J. Kukunas. Power and performance: Software analysis and optimization. Morgan Kaufmann, 2015. url: https://www.sciencedirect.com/book/9780128007266/power-and-performance
D. S. Li, M. A. Tschopp, M. Khaleel, and X. Sun. Comparison of reconstructed spatial microstructure images using different statistical descriptors. Comput. Mat. Sci. 51.1 (2012), pp. 437–444. doi: 10.1016/j.commatsci.2011.07.056
H. Lomas, D. R. Jenkins, M. R. Mahoney, R. Pearce, R. Roest, K. Steel, and S. Mayo. Examining mechanisms of metallurgical coke fracture using micro-CT imaging and analysis. Fuel Process. Tech. 155 (2017), pp. 183–190. doi: 10.1016/j.fuproc.2016.05.039
B. Lu and S. Torquato. Lineal-path function for random heterogeneous materials. Phys. Rev. A 45.2 (1992), pp. 922–929. doi: 10.1103/PhysRevA.45.922
N. Otsu. A threshold selection method from gray-level histograms. IEEE Trans. Sys., Man. Cyber. 9.1 (1979), pp. 62–66. doi: 10.1109/TSMC.1979.4310076
H. Singh, A. M. Gokhale, S. I. Lieberman, and S. Tamirisakandala. Image based computations of lineal path probability distributions for microstructure representation. Mat. Sci. Eng.: A 474.1-2 (2008), pp. 104–111. doi: 10.1016/j.msea.2007.03.099
M. S. Talukdar, O. Torsaeter, and M. A. Ioannidis. Stochastic reconstruction of particulate media from two-dimensional images. J. Colloid Interface Sci. 248.2 (2002), pp. 419–428. doi: 10.1006/jcis.2001.8064
S. Torquato. Microstructure characterization and bulk properties of disordered two-phase media. J. Stat. Phys. 45.5 (1986), pp. 843–873. doi: 10.1007/BF01020577
D. M. Turner, S. R. Niezgoda, and S. R. Kalidindi. Efficient computation of the angularly resolved chord length distributions and lineal path functions in large microstructure datasets. Mod. Sim. Mat. Sci. Eng. 24.7, 075002 (2016). doi: 10.1088/0965-0393/24/7/075002
C. L. Y. Yeong and S. Torquato. Reconstructing random media. Phys. Rev. E 57.1 (1998), pp. 495–506. doi: 10.1103/PhysRevE.57.495
J. Zeman. Analysis of composite materials with random microstructure. Czech Technical University, Faculty of Civil Engineering, 2003. url: https://katalog.cbvk.cz/arl-cbvk/en/detail-cbvk_us_cat-0288377-Analysis-of-composite-materials-with-random- microstructure/