90
S. Ghosh et al.
39. Y. Jiao, F.H. Stillinger, S. Torquato, Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E 76(3), 031110 (2007)
40. Y. Jiao, E. Padilla, N. Chawla, Modeling and predicting microstructure evolution in lead/tin
alloy via correlation functions and stochastic material reconstruction. Acta Mat. 61(9), 3370–
3377 (2013)
41. G. Saheli, H. Garmestani, B.L. Adams, Microstructure design of a two phase composite using
two-point correlation functions. J. Comput.-Aided Mater. Des. 11(2), 103–115 (2004)
42. S. Torquato, G. Stell, Microstructure of two-phase random media. I. the n-point probability
functions. J. Chem. Phys. 77(4), 2071–2077 (1982)
43. J. MacSleyne, M.D. Uchic, J.P. Simmons, M. De Graef, Three-dimensional analysis of
secondary γ ’ precipitates in René-88 dt and UMF-20 superalloys. Acta Mat. 57(20), 6251–
6267 (2009)
44. M. Kühbach, G. Gottstein, L.A. Barrales-Mora, A statistical ensemble cellular automaton
microstructure model for primary recrystallization. Acta Mater. 107, 366–376 (2016)
45. C. Schwarze, R.D. Kamachali, M. Kühbach, C. Mießen, M. Tegeler, L. Barrales-Mora,
I. Steinbach, G. Gottstein, Computationally efficient phase-field simulation studies using RVE
sampling and statistical analysis. Comp. Mater. Sci. 147, 204–216 (2018)
46. W. Lenthe, Twin Related Domains in Polycrystalline Nickel-Base Superalloys: 3D Structure
and Fatigue. Ph.D. thesis, University of California- Santa Barbara (2017)
47. M. Pinz, G. Weber, S. Ghosh, Generating 3D virtual microstructures and statistically equivalent
representative volume elements for intragranular nickel-based superalloy microstructures.
Submitted 2019.
48. M.P. Echlin, A. Mottura, C.J. Torbet, T.M. Pollock, A new TriBeam system for threedimensional multimodal materials analysis. Rev. Sci. Instrum. 83(2), 023701 (2012)
49. F. Meyer. Topographic distance and watershed lines. Signal Process. 38(1), 113–125 (1994)
50. S.J. Ahn, W. Rauh, H.-J. Warnecke, Least-squares orthogonal distances fitting of circle, sphere,
ellipse, hyperbola, and parabola. Pattern Recogn. 34(12), 2283–2303 (2001)
51. D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (AddisonWesley, Reading, 1989)
52. W.W. Daniel, Kolmogorov-Smirnov One-Sample Test (PWS-Kent, Boston, 1990)
53. Simulation Modeling Suite (Simmetrix Inc., 2015). http://www.simmetrix.com/
54. G. Casella, C.P. Robert, M.T. Wells, Generalized Accept-Reject Sampling Schemes Lecture
Notes: Monograph Series 45(Institute of Mathematical Statistics. Wiley StatsRef: Statistics
Reference Online, John Wiley & Sons Ltd.), 342–347 (2004)
55. J.K. Mackenzie, 2nd Paper on statistics associated with the random disorientation of cubes.
Biometrika 45, 229–240 (1958)
56. Z. Alam, D. Eastman, M. Jo, K. Hemker, Development of a high-temperature tensile tester
for micromechanical characterization of materials supporting meso-scale ICME models. JOM
68(11), 2754–2760 (2016)
57. J.C. Stinville, N. Vanderesse, F. Bridier, P. Bocher, T.M. Pollock, High resolution mapping of
strain localization near twin boundaries in a nickel-based superalloy. Acta Mat. 98(1), 29–42
(2015)
S. Ghosh et al.
39. Y. Jiao, F.H. Stillinger, S. Torquato, Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E 76(3), 031110 (2007)
40. Y. Jiao, E. Padilla, N. Chawla, Modeling and predicting microstructure evolution in lead/tin
alloy via correlation functions and stochastic material reconstruction. Acta Mat. 61(9), 3370–
3377 (2013)
41. G. Saheli, H. Garmestani, B.L. Adams, Microstructure design of a two phase composite using
two-point correlation functions. J. Comput.-Aided Mater. Des. 11(2), 103–115 (2004)
42. S. Torquato, G. Stell, Microstructure of two-phase random media. I. the n-point probability
functions. J. Chem. Phys. 77(4), 2071–2077 (1982)
43. J. MacSleyne, M.D. Uchic, J.P. Simmons, M. De Graef, Three-dimensional analysis of
secondary γ ’ precipitates in René-88 dt and UMF-20 superalloys. Acta Mat. 57(20), 6251–
6267 (2009)
44. M. Kühbach, G. Gottstein, L.A. Barrales-Mora, A statistical ensemble cellular automaton
microstructure model for primary recrystallization. Acta Mater. 107, 366–376 (2016)
45. C. Schwarze, R.D. Kamachali, M. Kühbach, C. Mießen, M. Tegeler, L. Barrales-Mora,
I. Steinbach, G. Gottstein, Computationally efficient phase-field simulation studies using RVE
sampling and statistical analysis. Comp. Mater. Sci. 147, 204–216 (2018)
46. W. Lenthe, Twin Related Domains in Polycrystalline Nickel-Base Superalloys: 3D Structure
and Fatigue. Ph.D. thesis, University of California- Santa Barbara (2017)
47. M. Pinz, G. Weber, S. Ghosh, Generating 3D virtual microstructures and statistically equivalent
representative volume elements for intragranular nickel-based superalloy microstructures.
Submitted 2019.
48. M.P. Echlin, A. Mottura, C.J. Torbet, T.M. Pollock, A new TriBeam system for threedimensional multimodal materials analysis. Rev. Sci. Instrum. 83(2), 023701 (2012)
49. F. Meyer. Topographic distance and watershed lines. Signal Process. 38(1), 113–125 (1994)
50. S.J. Ahn, W. Rauh, H.-J. Warnecke, Least-squares orthogonal distances fitting of circle, sphere,
ellipse, hyperbola, and parabola. Pattern Recogn. 34(12), 2283–2303 (2001)
51. D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (AddisonWesley, Reading, 1989)
52. W.W. Daniel, Kolmogorov-Smirnov One-Sample Test (PWS-Kent, Boston, 1990)
53. Simulation Modeling Suite (Simmetrix Inc., 2015). http://www.simmetrix.com/
54. G. Casella, C.P. Robert, M.T. Wells, Generalized Accept-Reject Sampling Schemes Lecture
Notes: Monograph Series 45(Institute of Mathematical Statistics. Wiley StatsRef: Statistics
Reference Online, John Wiley & Sons Ltd.), 342–347 (2004)
55. J.K. Mackenzie, 2nd Paper on statistics associated with the random disorientation of cubes.
Biometrika 45, 229–240 (1958)
56. Z. Alam, D. Eastman, M. Jo, K. Hemker, Development of a high-temperature tensile tester
for micromechanical characterization of materials supporting meso-scale ICME models. JOM
68(11), 2754–2760 (2016)
57. J.C. Stinville, N. Vanderesse, F. Bridier, P. Bocher, T.M. Pollock, High resolution mapping of
strain localization near twin boundaries in a nickel-based superalloy. Acta Mat. 98(1), 29–42
(2015)