1. Bishop, P.J., Lior, N., Lavine, A., Flik, M., Karwe, M.V., Bergman, T.L., Beckermann, C., and Charmchi, M., Transport Phenomena in Materials Processing, HTD-Vol. 146, ASME, New York, 1990.

2. Advani, S.G., and Beckermann, C., Heat and Mass Transfer in Solidification Processing, ASME, New York, HTD-Vol. 175, MD-Vol. 25, 1991; also in ASME J. Eng. Materials and Technology, Vol. 115, No. 1, 1993.

3. Beckermann, C., Bertram, L.A., Pien, S.J., and Smelser, R.E., Micro/Macro Scale Phenomena in Solidification, ASME, New York, HTD-Vol. 218, AMD-Vol. 139, 1992.

4. Beckermann, C., Wang, H.P., Bertram, M.A., Sohal, M.S., and Guceri, S.I., Transport Phenomena in Solidification, ASME, New York, HTD-Vol. 284, AMD-Vol. 182, 1994.

5. Thomas, B.G., and Beckermann, C., Modeling of Casting, Welding and Advanced Solidification Processes VIII, TMS, Warrendale, PA, 1998 (1,267 pages).

6. Rappaz, M., Beckermann, C., and Trivedi, R., Solidification Processes and Microstructures: A Symposium in Honor of Prof. W. Kurz, TMS, Warrendale, PA, 2004 (432 pages).

2. Beckermann, C., Viskanta, R., and Ramadhyani, S., "A Numerical Study of Non-Darcian Natural Convection in a Vertical Enclosure Filled with a Porous Medium," Numerical Heat Transfer, Vol. 10, 1987, pp. 557-570.

3. Beckermann, C., and Viskanta, R., "Forced Convection Boundary Layer Flow and Heat Transfer Along a Flat Plate Embedded in a Porous Medium," Int. J. Heat Mass Transfer, Vol. 30, 1987, pp. 1547-1551.

4. Beckermann, C., Ramadhyani, S., and Viskanta, R., "Natural Convection Flow and Heat Transfer Between a Fluid and a Porous Layer Inside a Rectangular Enclosure," ASME J. Heat Transfer, Vol. 109, pp. 363-370, 1987.

5. Beckermann, C., Viskanta, R., and Ramadhyani, S., "Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layers," J. Fluid Mechanics, Vol. 186, 1988, pp. 257-284.

6. Beckermann, C. and Viskanta, R., "Natural Convection Solid/Liquid Phase Change in Porous Media," Int. J. Heat Mass Transfer, Vol. 31, 1988, pp. 35-46.

7. Wolff, F., Beckermann, C., and Viskanta, R., "Natural Convection of Liquid Metals in Vertical Cavities," Experimental Thermal and Fluid Science, Vol. 1, 1988, pp. 83-91.

8. Beckermann, C., and Viskanta, R., "Double-Diffusive Convection during Dendritic Solidification of a Binary Mixture," PhysicoChemical Hydrodynamics, Vol.10, 1988, pp. 195-213.

9. Beckermann, C., and Viskanta, R., "Double-Diffusive Convection Due to Melting," Int. J. Heat Mass Transfer, Vol. 31, 1988, pp. 2077-2089.

10. Beckermann, C., and Viskanta, R., "An Experimental Study of Melting of Binary Mixtures with Double-Diffusive Convection in the Liquid," Experimental Thermal and Fluid Science, Vol. 2, 1989, pp. 17-26.

11. Offhaus, C., Beckermann, C., and Goldschmidt, V.W., "Effect of Flueway Baffle Emissivity on the Performance of a Gas Fired Water Heater," ASHRAE Transactions, Vol. 95, pt. 1, 1989, pp. 281-283.

12. Beckermann, C., and Viskanta, R., "An Experimental Study of Solidification of Binary Mixtures with Double-Diffusive Convection in the Liquid," Chemical Engineering Communications, Vol. 85, 1989, pp. 135-156.

13. Beckermann, C., "A General Correlation for Melting in Enclosures," ASME J. Heat Transfer, Vol. 111, pp. 1111-1115, 1989.

14. Beckermann, C., and Viskanta, R., "Effect of Solid Subcooling on Natural Convection Melting of a Pure Metal," ASME J. Heat Transfer, Vol. 111, 1989, pp. 416-424.

16. Ellinger, E.A., and Beckermann, C., "On the Effect of Porous Layers on Melting Heat Transfer in an Enclosure," Experimental Thermal and Fluid Science, Vol. 4, 1991, pp. 619-629.

17. Ni, J., and Beckermann, C., "A Volume-Averaged Two-Phase Model for Solidification Transport Phenomena," Metall. Trans. B, Vol. 22B, 1991, pp. 349-361.

18. Schneider, M.C., and Beckermann, C., "Effects of Simplified Enthalpy Functions on the Prediction of Heat Transfer During Solidification of a Lead-Tin Alloy," J. Appl. Math. Modeling, Vol. 15, 1991, pp. 596-605.

19. Smith, T.F., Beckermann, C., and Weber, S.W., "Coupled Conduction, Natural Convection, and Radiation in an Electronic Chassis," ASME J. Electronic Packaging, Vol. 113, 1991, pp. 382-391.

20. Ni, J., and Beckermann, C., "Natural Convection in a Vertical Enclosure Filled with Anisotropic Porous Media," ASME J. Heat Transfer, Vol. 113, 1991, pp. 1033-1037.

21. Beckermann, C., Fan, C., and Mihailovic, J., "Numerical Simulations of Double-Diffusive Convection in a Hele-Shaw Cell," Int. Video Journal of Engineering Research, Vol. 1, 1991, pp. 71-82.

22. Beckermann, C., and Viskanta, R., "Mathematical Modeling of Transport Phenomena During Alloy Solidification," Appl. Mechanics Reviews, Vol. 46, 1993, pp. 1-27.

23. Wang, C.Y., and Beckermann, C., "A Two-Phase Mixture Model of Liquid-Gas Flow and Heat Transfer in Capillary Porous Media, Part I: Model Formulation," Int. J. Heat Mass Transfer, Vol. 36, 1993, pp. 2747-2758.

24. Wang, C.Y., and Beckermann, C., "A Two-Phase Mixture Model of Liquid-Gas Flow and Heat Transfer in Capillary Porous Media, Part II: Application to Pressure-Driven Boiling Flow Adjacent to a Vertical Heated Plate," Int. J. Heat Mass Transfer, Vol. 36, 1993, pp. 2759-2768.

25. Beckermann, C., and Smith, T.F., "Incorporation of Internal Surface Radiant Exchange in the Finite Volume Method," Numerical Heat Transfer, Part B, Vol. 23, 1993, pp. 127-133.

26. Reddy, A.V., and Beckermann, C., "Measurements of Metal-Mold Interfacial Heat Transfer Coefficients during Solidification of Sn and Sn-Pb Alloys," Experimental Heat Transfer, Vol. 6, 1993, pp. 111-129.

27. Wang, C.Y., and Beckermann, C., "Single- vs. Dual-Scale Volume Averaging for Heterogeneous Multiphase Systems," Int. J. Multiphase Flow, Vol. 19, 1993, pp. 397-407.

28. Smith, T.F., Beckermann, C., and Adams, C.C., "A Numerical Simulation Model to Study the Thermal Performance of Windows," ASHRAE Transactions: Symposia, DE-93-4-4, 1993, pp. 585-596.

29. Feller, R. and Beckermann, C., "Modeling of the Globulitic Solidification of a Binary Metal Alloy," Int. Comm. Heat Mass Transfer, Vol. 20, 1993, pp. 311-322.

30. Ni, J., and Beckermann, C., "Modeling of Globulitic Alloy Solidification with Convection," J. Materials Processing and Manufacturing Science, Vol. 2, 1993, pp. 217-231.

31. Wang, C.Y., and Beckermann, C., "A Multiphase Solute Diffusion Model for Dendritic Alloy Solidification," Metall. Trans. A, Vol. 24A, 1993, pp. 2787-2802.

32. de Groh III, H.C., Weidman, P.D., Zakhem, D., Ahuja, S., and Beckermann, C., "Calculation of Dendrite Settling Velocities Using a Porous Envelope," Metall. Trans. B, Vol. 24B, 1993, pp. 749-753.

33. Wang, C.Y., and Beckermann, C., "A Unified Solute Diffusion Model for Columnar and Equiaxed Dendritic Alloy Solidification," Mater. Sci. Eng. A, Vol. 171A, 1993, pp. 199-211.

34. Wang, C.Y., Beckermann, C., and Fan, C., "A Numerical Study of Boiling and Natural Convection in Capillary Porous Media Using the Two-Phase Mixture Model," Numerical Heat Transfer, Part A, Vol. 26, 1994, pp. 375-398.

35. Beckermann, C., Smith, T.F., and Pospichal, B., "Use of a Two-Dimensional Simulation Model in the Thermal Analysis of a Multi-Board Electronic Module," ASME J. Electronic Packaging, Vol. 116, 1994, pp. 126-133.

36. Wang, C.Y., and Beckermann, C., "Prediction of Columnar to Equiaxed Transition During Diffusion-Controlled Dendritic Alloy Solidification," Metall.Trans. A, Vol. 25A, 1994, pp. 1081-1093.

37. Ni, J., and Beckermann, C., "Numerical Simulation of Alloy Solidification by a Two-Phase Model," Acta Metallurgica Sinica, Vol. 30, No. 9, 1994, pp. 385-392.

38. Wang, C.Y., Beckermann, C., and Fan, C., "Transient Natural Convection and Boiling in a Porous Layer Heated from Below," Heat Transfer 1994, Proceedings of the 10th International Heat Transfer Conference, ed. G.F. Hewitt, Vol. 5, 1994, pp. 411-416.

39. Beckermann, C., and Wang, C.Y., "Incorporating Interfacial Phenomena in Solidification Models," JOM, Vol. 46, No. 1, 1994, pp. 42-47.

40. Wang, C.Y., Ahuja, S., Beckermann, C. and de Groh III, H.C., "Multiparticle Interfacial Drag in Equiaxed Solidification," Metall. Trans. B, Vol. 26B, 1995, pp. 111-119.

41. Mihailovic, J., and Beckermann, C., "Development of a Two-Dimensional Liquid Species Concentration Measurement Technique Based on Absorptiometry," Experimental Thermal and Fluid Science, Vol. 10, 1995, pp. 113-123.

42. Wang, C.Y., and Beckermann, C., "Boundary Layer Analysis of Buoyancy-Driven Two-Phase Flow in Capillary Porous Media," ASME J. Heat Transfer, Vol. 117, 1995, pp. 1082-1087.

43. Schneider, M.C., and Beckermann, C., "A Numerical Study of the Combined Effects of Microsegregation, Mushy Zone Permeability, and Contraction Driven Flow on Macrosegregation and Eutectic Formation in Binary Alloy Solidification," Int. J. Heat Mass Transfer, Vol. 38, 1995, pp. 3455-3473.

44. Schneider, M.C., and Beckermann, C., "Formation of Macrosegregation by Multicomponent Thermosolutal Convection during Solidification of Steel," Metall. Mater. Trans. A, Vol. 26A, 1995, pp. 2373-2388.

45. Beckermann, C., and Schneider, M.C., "Simulation of Micro-/Macrosegregation During the Solidification of a Low-Alloy Steel," ISIJ International, Vol. 35, No. 6, 1995, pp. 1300-1307.

46. Wang, C.Y., and Beckermann, C., "Equiaxed Dendritic Solidification with Convection: Part 1. Multi-Scale /-Phase Modeling," Metall. Mater. Trans. A, Vol. 27A, 1996, pp. 2754-2764.

47. Wang, C.Y., and Beckermann, C., "Equiaxed Dendritic Solidification with Convection: Part 2. Numerical Simulations for an Al-4wt% Cu Alloy," Metall. Mater. Trans. A, Vol. 27A, 1996, pp. 2765-2783.

48. Beckermann, C., and Wang, C.Y., "Equiaxed Dendritic Solidification with Convection: Part 3. Comparisons with NH₄Cl-H₂O Experiments," Metall. Mater. Trans. A, Vol. 27A, 1996, pp. 2784-2795.

49. Beckermann, C., and Ni, J., "Simulations of Sedimentation in Equiaxed Alloy Solidification," Int. Comm. Heat Mass Transfer, Vol. 23, 1996, pp. 315-324.

50. Beckermann, C., "Modeling Segregation and Grain Structure Development in Equiaxed Solidification with Convection," JOM, Vol. 49, No. 3, 1997, pp. 13-17.

51. Ramani, A., and Beckermann, C., "Dendrite Tip Growth Velocities of Settling NH₄Cl Equiaxed Crystals," Scripta Materialia, Vol. 36, 1997, pp. 633-638.

52. Feller, R.J., and Beckermann, C., "Solidification of Metal-Matrix Composites with Convection," Metall. Mater. Trans. B, Vol. 28B, 1997, pp. 1165-1183.

53. Reddy, A.V., and Beckermann, C., "Modeling of Macrosegregation Due to Thermosolutal Convection and Contraction Driven Flow in Direct Chill Continuous Casting of an Al-Cu Round Ingot," Metall. Mater. Trans. B, Vol. 28B, 1997, pp. 479-489.

54. Schneider, M.C., Gu, J.P., Beckermann, C., Boettinger, W.J., and Kattner, U.R., "Modeling of Micro- and Macrosegregation and Freckle Formation in Single-Crystal Nickel-Base Superalloy Directional Solidification," Metall. Mater. Trans. A, Vol. 28A, 1997, pp. 1517-1531.

55. Gu, J.P., Beckermann, C., and Giamei, A.F., "Motion and Remelting of Dendrite Fragments during Directional Solidification of a Nickel-Base Superalloy," Metall. Mater. Trans. A, Vol. 28A, 1997, pp. 1533-1542.

56. Jensen, D.H., Beckermann, C., Fischer, G.W., and Srinivasan, V., "Implementing Casting Design Software: Costs, Strategies, and Realized Benefits," AFS Transactions, Vol. 97-87, 1997, pp. 877-882.

57. Tong, X., and Beckermann, C., "A Diffusion Boundary Layer Model of Microsegregation," J. Crystal Growth, Vol. 187, 1998, pp. 289-302.

58. Li, Q., and Beckermann, C., "Scaling Behavior of Three-Dimensional Dendrites," Physical Review E, Vol. 57, 1998, pp. 3176-3188.

59. Tong, X., and Beckermann, C., "Integral Solutions of Diffusion-Controlled Dendrite Tip Growth," Int. J. Heat Mass Transfer, Vol. 41, 1998, pp. 4025-4029.

60. Hardin, R.A., and Beckermann, C., "Current State of Casting Yield: Results of 1997 SFSA Survey," AFS Transactions,Vol. 98-66, 1998, pp. 633-642.

61. Pines, V., Chait, A., Zlatowski, M., and Beckermann, C., "Equiaxed Dendritic Solidification in Supercooled Melts," J. Crystal Growth, Vol. 197, 1999, pp. 355-363.

62. Steinbach, I., Beckermann, C., Kauerauf, B., Li, Q., and Guo, J., "Three-Dimensional Modeling of Equiaxed Dendritic Growth on a Mesoscopic Scale," Acta Materialia, Vol. 47, 1999, pp. 971-982.

63. Voller, V.R., and Beckermann, C., "A Unified Model of Microsegregation and Coarsening," Metall. Mater. Trans. A, Vol. 30A, 1999, pp. 2183-2189.

64. Gu, J.P., and Beckermann, C., "Simulation of Convection and Macrosegregation in a Large Steel Ingot," Metall. Mater. Trans. A, Vol. 30A, 1999, pp. 1357-1366.

65. Hardin, R., Shen, X., Gu, J.P., and Beckermann, C., "Use of the Niyama Criterion to Predict ASTM X-ray Levels and to Develop Improved Feeding Rules for Steel Casting," AFS Transactions, Vol. 107, Paper No. 99-62, 1999, pp. 433-440.

66. Beckermann, C., Diepers, H.J., Steinbach, I., Karma, A., and Tong, X., "Modeling Melt Convection in Phase-Field Simulations of Solidification," J. Computational Physics, Vol. 154, 1999, pp. 468-496.

67. Li, Q., and Beckermann, C., "Evolution of Sidebranch Structure in Free Dendritic Growth," Acta Materialia, Vol. 47, 1999, pp. 2345-2356.

68. Diepers, H.J., Beckermann, C., and Steinbach, I., "Simulation of Convection and Ripening in a Binary Alloy Mush Using the Phase-Field Method," Acta Materialia, Vol. 47, 1999, pp. 3663-3678.

69. Voller, V.R., and Beckermann, C., "Approximate Models of Microsegregation with Coarsening," Metall. Mater. Trans. A, Vol. 30A, 1999, pp. 3016-3019.

70. Tong, X., Beckermann, C., and Karma, A., "Velocity and Shape Selection of Dendritic Crystals in a Forced Flow," Physical Review E, Vol. 61, 2000, pp. R49-R52.

71. Beckermann, C., Gu, J.P., and Boettinger, W.J., "Development of a Freckle Predictor via Rayleigh Number Method for Single-Crystal Nickel-Base Superalloy Castings," Metall. Mater. Trans. A, Vol. 31A, 2000, pp. 2545-2557.

72. Hardin, R.A., Ou, S., Carlson, K., and Beckermann, C., "Relationship between the Niyama Criterion and Radiographic Testing in Steel Casting," AFS Transactions, Vol. 108, Paper No. 00-86, 2000, pp. 53-62.

73. Yu, Y., Lu, Y., Zhang, Z., Yang, G., Karma, A., and Beckermann, C., "Progress in Numerical Simulation of Solidification Microstructure using Phase-Field Method," Zhuzao/Foundry, Vol. 49, 2000, pp. 507-511.

74. Ceynar, D.L., and Beckermann, C., "Measurement of the Density of Succinonitrile-Acetone Alloys," J. Crystal Growth, Vol. 222, 2001, pp. 380-391.

75. Tong, X., Beckermann, C., Karma, A., and Li, Q., "Phase-Field Simulations of Dendritic Crystal Growth in a Forced Flow," Physical Review E, Vol. 63, 2001, pp. 061601-1 to 0.61601-16.

76. Ratke, L., and Beckermann, C., "Concurrent Growth and Coarsening of Spheres," Acta Materialia, Vol. 49, 2001, pp. 4041-4054.

77. Beckermann, C., Li, Q., and Tong, X., "Microstructure Evolution in Equiaxed Dendritic Growth," Science and Technology of Advanced Materials, Vol. 2, 2001, pp. 117-126.

78. Carlson, K., Ou, S., Hardin, R., and Beckermann, C., "Analysis of ASTM X-Ray Shrinkage Rating for Steel Castings," Int. J. Cast Metals Research, Vol. 14, 2001, pp. 169-183.

79. Yu, Y.M., Yang, G.C., Zhao, D.W., Lu, Y., Karma, A., and Beckermann, C., "Numerical Simulation of Dendritic Growth in Undercooled Melt Using Phase-Field Approach," Acta Physica Sinica, Vol. 50, 2001, pp. 2423-2428.

80. Shen, H.F., and Beckermann, C., "An Experimental Study of Deformation of a Columnar Dendritic Mushy Zone Using a Transparent Succinonitrile-Acetone Alloy," Metall. Mater. Trans. B, Vol. 33B, 2002, pp. 69-78.

81. Shen, H.F., Hardin, R.A., MacKenzie, R.,and Beckermann, C., "Simulation using Realistic Spray Cooling for the Continuous Casting of Multi-Component Steel," J. Materials Science and Technology, Vol. 18, 2002, pp. 311-314.

82. Li, Q., and Beckermann, C., "Modeling of Free Dendritic Growth of Succinonitrile-Acetone Alloys with Thermosolutal Melt Convection," J. Crystal Growth, Vol. 236, 2002, pp. 482-498.

83. Shen, H.F., and Beckermann, C., "Experiment Study on the Mush Deformation and Solute Redistribution," Acta Metallurgica Sinica, Vol. 38, 2002, pp. 352-358.

84. Beckermann, C., "Modelling of Macrosegregation: Applications and Future Needs," Int. Mater. Rev., Vol. 47, 2002, pp. 243-261.

85. Carlson, K.D., Ou, S., Hardin, R.A., and Beckermann, C., "Development of New Feeding Distance Rules Using Casting Simulation; Part I: Methodology," Metall. Mater. Trans. B, Vol. 33B, 2002, pp. 731-740.

86. Ou, S., Carlson, K.D., Hardin, R.A., and Beckermann, C., "Development of New Feeding Distance Rules Using Casting Simulation; Part II: The New Rules," Metall. Mater. Trans. B, Vol. 33B, 2002, pp. 741-755.

87. Rerko, R.S., de Groh III, H.C., and Beckermann, C., "Effect of Melt Convection and Solid Transport on Macrosegregation and Grain Structure in Equiaxed Al-Cu Alloys," Mater. Sci. Eng. A, Vol. 347, 2003, pp. 186-197.

88. Ramirez, J.C., and Beckermann, C., "Evaluation of a Rayleigh Number Based Freckle Criterion for Pb-Sn and Ni-base Superalloys," Metall. Mater. Trans. A, Vol. 34A, 2003, pp. 1525-1536.

89. Guo, J., and Beckermann, C., "Three-Dimensional Simulation of Freckle Formation During Binary Alloy Solidification: Effect of Mesh Spacing," Numerical Heat Transfer, Part A: Applications, Vol. 44, 2003, pp. 559-576.

90. Hardin, R.A., Liu, K., Kapoor, A., and Beckermann, C., "A Transient Simulation and Dynamic Spray Cooling Control Model for Continuous Steel Casting," Metall. Mater. Trans. B, Vol. 34B, 2003, pp. 297-306.

91. Martorano, M.A., Beckermann, C., and Gandin, Ch.-A., "A Solutal Interaction Mechanism for the Columnar-to-Equiaxed Transition in Alloy Solidification," Metall. Mater. Trans. A, Vol. 34A, 2003, pp. 1657-1674. Correction to Equations in Appendix:

92. Rizzo, E.M. da S., Santos, R. Gomes dos, and Beckermann, C., "Modeling of Solidification and Mushy Zone Deformation of Alloys," J. Bras. Soc. Mech. Sci., Vol. 25, 2003, pp. 180-184.

93. Ramirez, J.C., Beckermann, C., Karma, A., and Diepers, H.-J., "Phase-field Modeling of Binary Alloy Solidification with Coupled Heat and Solute Diffusion," Physical Review E, Vol. 69, 2004, pp. 051607-1 to 051607-16.

94. Sigl, K.M., Hardin, R.A., Stephens, R.I., and Beckermann, C., "Fatigue of 8630 Cast Steel in the Presence of Porosity," Int. J. Cast Metals Research, Vol. 17, 2004, pp. 130-146.

95. Sun, Y., and Beckermann, C., "Diffuse Interface Modeling of Two-Phase Flow Based on Averaging: Mass and Momentum Equations," Physica D, Vol. 198, 2004, pp. 281-308.

96. Ou, S., Carlson, K.D., and Beckermann, C., "Feeding and Risering of High-Alloy Steel Castings," Metall. Mater. Trans. B, Vol. 36B, 2005, pp. 97-116.

97. Steinbach, I., Diepers, H.-J., and Beckermann, C., "Transient Growth and Interaction of Equiaxed Dendrites," J. Crystal Growth, Vol. 275, 2005, pp. 624-638.

98. Ramirez, J.C., and Beckermann, C., "Examination of Binary Alloy Free Dendritic Growth Theories with a Phase-Field Model," Acta Materialia, Vol. 53, 2005, pp. 1721-1736.

99. Lu, Y., Beckermann, C., and Ramirez, J.C., "Three-Dimensional Phase-Field Simulations of the Effect of Convection on Free Dendritic Growth," J. Crystal Growth, Vol. 280, 2005, pp. 320-334.

100. Ramirez, J.C., and Beckermann, C., "Simulation of Binary Alloy Free Dendritic Growth with a Phase-Field Model," Trans. Indian Inst. Met., Vol. 58, 2005, pp. 525-530.

101. Carlson, K.D., Ou, S., and Beckermann, C., "Feeding of High-Nickel Alloy Castings," Metall. Mater. Trans. B, Vol. 36B, 2005, pp. 843-856.

102. Monroe, C., and Beckermann, C., "Development of a Hot Tear Indicator for Steel Castings," Mater. Sci. Eng. A, Vol. 413-414, 2005, pp. 30-36.

103. Blair, M., Monroe, R., Beckermann, C., Hardin, R., Carlson, K., and Monroe, C., "Predicting the Occurrence and Effects of Defects in Castings," JOM, Vol. 57, No. 5, 2005, pp. 29-34.

104. Badillo, A., and Beckermann, C., "Phase-Field Simulation of the Columnar-to-Equiaxed Transition in Alloy Solidification," Acta Materialia, Vol. 54, 2006, pp. 2015-2026.

105. Carlson, K.D., Lin, Z., Beckermann, C., Mazurkevich, G., and Schneider, M.C., "Modeling of Porosity Formation in Aluminum Alloys," Materials Science Forum, Vols. 519-521, 2006, pp. 1699-1706.

106. Wang, L., and Beckermann, C., "Prediction of Reoxidation Inclusion Composition in Casting of Steel," Metall. Mater. Trans. B, Vol. 37B, 2006, pp. 571-588.

107. Sun, Y., and Beckermann, C., "Sharp Interface Tracking Using the Phase-Field Equation," J. Computational Physics, Vol. 220, 2007, pp. 626-653.

108. Carlson, K.D., Lin, Z., and Beckermann, C., "Modeling the Effect of Finite-Rate Hydrogen Diffusion on Porosity Formation in Aluminum Alloys," Metall. Mater. Trans. B, Vol. 38B, 2007, pp. 541-555.

109. Deegan, P.T., Stephens, R.I., Hardin, R.A., and Beckermann, C., "The Effect of Porosity on the Fatigue Life of 8630 Cast Steel," AFS Transactions, Vol. 115, Paper No. 07-120, 2007, pp. 787-803.

110. Badillo, A., Ceynar, D.L., and Beckermann, C., "Growth of Equiaxed Dendritic Crystals Settling in an Undercooled Melt, Part 1: Tip Kinetics," J. Crystal Growth, Vol. 309, 2007, pp. 197-215.

111. Badillo, A., Ceynar, D.L., and Beckermann, C., "Growth of Equiaxed Dendritic Crystals Settling in an Undercooled Melt, Part 2: Internal Solid Fraction," J. Crystal Growth, Vol. 309, 2007, pp. 216-224.

112. Hardin, R.A., and Beckermann, C., "Effect of Porosity on the Stiffness of Cast Steel," Metall. Mater. Trans. A, Vol. 38A, 2007, pp. 2992-3006.

113. Brooks, B.E., Beckermann, C., and Richards, V.L., "Prediction of Burn-on and Mould Penetration in Steel Casting Using Simulation," Int. J. Cast Metals Research, Vol. 20, 2007, pp. 177-190.

114. Peters, F., Voigt, R., Ou, S.Z., and Beckermann, C., "Effect of Mould Expansion on Pattern Allowances in Sand Casting of Steel," Int. J. Cast Metals Research, Vol. 20, 2007, pp. 275-287.

115. Pokorny, M., Monroe, C., Beckermann, C., Bichler, L., and Ravindran, C., "Prediction of Hot Tear Formation in a Magnesium Alloy Permanent Mold Casting," Int. J. Metalcasting, Vol. 2, No. 4, 2008, pp. 41-53.

116. Sun, Y., and Beckermann, C., "A Two-Phase Diffuse-Interface Model for Hele-Shaw Flows with Large Property Contrasts," Physica D, Vol. 237, 2008, pp. 3089-3098, 2008.

117. Carlson, K.D., and Beckermann, C., "Prediction of Shrinkage Pore Volume Fraction Using a Dimensionless Niyama Criterion," Metall. Mater. Trans. A, Vol. 40A, 2009, pp. 163-175.

118. Hardin, R.A., and Beckermann, C., "Prediction of the Fatigue Life of Cast Steel Containing Shrinkage Porosity," Metall. Mater. Trans. A, Vol. 40A, 2009, pp. 581-597.

119. Asta, M., Beckermann, C., Karma, A., Kurz, W., Napolitano, R., Plapp, M., Purdy, G., Rappaz, M., and Trivedi, R., "Solidification Microstructures and Solid-State Parallels: Recent Developments, Future Directions," Acta Materialia, Vol. 57, 2009, pp. 941-971.

120. Blair, M., Monroe, R., Hardin, R., and Beckermann, C., "A New Standard for Radiographic Acceptance Criteria for Steel Castings," AFS Transactions, Vol. 117, Paper No. 09-118, 2009, pp. 765-775.

121. Sun, Y., and Beckermann, C., "Effect of Solid-Liquid Density Change on Dendrite Tip Velocity and Shape Selection," J. Crystal Growth, Vol. 311, 2009, pp. 4447-4453.

122. Carlson, K.D., and Beckermann, C., "Authors' Reply to Discussion of "Prediction of Shrinkage Pore Volume Fraction Using a Dimensionless Niyama Criterion," Metall. Mater. Trans. A, Vol. 40A, 2009, pp. 3054-3055.

123. Sun, Y., and Beckermann, C., "Phase-Field Modeling of Bubble Growth and Flow in a Hele-Shaw Cell," Int. J. Heat Mass Transfer, Vol. 53, 2010, pp. 2969-2978.

124. Melendez, A.J., Carlson, K.D., and Beckermann, C., "Modelling of Reoxidation Inclusion Formation in Steel Sand Casting," Int. J. Cast Metals Research, Vol. 23, 2010, pp. 278-288.

125. Thole, J., and Beckermann, C., "Measurement of Elastic Modulus of PUNB Bonded Sand as a Function of Temperature," Int. J. Metalcasting, Vol. 4, No. 4, 2010, pp. 7-18.

126. Pokorny, M.G., Monroe, C.A., Beckermann, C., Zhen, Z., and Hort, N., "Simulation of Stresses During Casting of Binary Magnesium-Aluminum Alloys," Metall. Mater. Trans. A, Vol. 41A, 2010, pp. 3196-3207.

127. Delaleau, P., Beckermann, C., Mathiesen, R.H., and Arnberg, L., "Mesoscopic Simulation of Dendritic Growth Observed in X-ray Video Microscopy During Directional Solidification of Al-Cu Alloys," ISIJ International, Vol. 50, 2010, pp. 1886-1894.

128. Melendez, A.J., and Beckermann, C., "Measurements of Dendrite Tip Growth and Sidebranching in Succinonitrile-Acetone Alloys, " J. Crystal Growth, Vol. 340, 2012, pp. 175-189.

129. Carlson, K.D., and Beckermann, C., "Determination of Solid Fraction-Temperature Relation and Latent Heat Using Full Scale Casting Experiments: Application to Corrosion Resistant Steels and Nickel Based Alloys," Int. J. Cast Metals Research, Vol. 25, 2012, pp. 75-92.

130. Samuels, G., and Beckermann, C., "Measurement of Gas Evolution from PUNB Bonded Sand as a Function of Temperature," Int. J. Metalcasting, Vol. 6, No. 2, 2012, pp. 23-40.

131. Yamaguchi, M., and Beckermann, C., "Simulation of Solid Deformation During Solidification: Compression of a Single Dendrite," Acta Materialia, Vol. 61, 2013, pp. 4053-4065.

132. Yamaguchi, M., and Beckermann, C., "Simulation of Solid Deformation During Solidification: Shearing and Compression of Polycrystalline Structures," Acta Materialia, Vol. 61, 2013, pp. 2268-2280.

133. Torabi Rad, M., Kotas, P., and Beckermann, C., "Rayleigh Number Criterion for Formation of A-Segregates in Steel Castings and Ingots," Metall. Mater. Trans. A, Vol. 44A, 2013, pp. 4266-4281.

134. Hardin, R.A., and Beckermann, C., "Effect of Porosity on Deformation, Damage, and Fracture of Cast Steel," Metall. Mater. Trans. A, Vol. 44A, 2013, pp. 5316-5332.

135. Yamaguchi, M., and Beckermann, C., "Direct Numerical Simulation of Solid Deformation During Dendritic Solidification," JOM, Vol. 66, No. 8, 2014, pp. 1431-1438.

136. Monroe, C., and Beckermann, C., "Prediction of Hot Tearing Using a Dimensionless Niyama Criterion," JOM, Vol. 66, No. 8, 2014, pp. 1439-1445.

137. Hardin, R.A., Choi, K.K., Gaul, N.J., and Beckermann, C., "Reliability Based Casting Process Design Optimisation," Int. J. Cast Metals Research, Vol. 28, 2015, pp. 181-192.

138. Neumann-Heyme, H., Eckert, K., and Beckermann, C., "Dendrite Fragmentation in Alloy Solidification due to Sidearm Pinch-Off," Physical Review E, Vol. 92, 2015, 060401(R). Supplementary Information.

139. Souhar, Y., De Felice, V. F., Beckermann, C., Combeau, H., and Založnik, M., "Three-Dimensional Mesoscopic Modeling of Equiaxed Dendritic Solidification of a Binary Alloy," Comput. Mater. Sci., Vol. 112, 2016, pp. 304-317.

140. Galles, D., and Beckermann, C., "In-Situ Measurement and Prediction of Stresses and Strains during Casting of Steel," Metall. Mater. Trans. A, Vol. 47A, 2016, pp. 811-829.

141. Williams, T.J., Hardin, R.A., and Beckermann, C., "Thermophysical Properties and Performance of Riser Sleeves for Steel Castings," Int. J. Metalcasting, Vol. 10, 2016, pp. 535-555.

142. Khalajzadeh, V., Carlson, K.D., Backman, D.G., and Beckermann, C., "A Pore-Centric Model for Combined Shrinkage and Gas Porosity in Alloy Solidification," Metall. Mater. Trans. A, Vol. 48A, 2017, pp. 1797-1816.

143. Galles, D., and Beckermann, C., "Prediction of Distortions and Pattern Allowances during Sand Casting of a Steel Bracket," Int. J. Cast Metals Research, Vol. 30, 2017, pp. 133-147.

144. Zimmermann, G., Sturz, L., Nguyen-Thi, H., Mangelinck-Noel, N., Li, Y.Z., Gandin, C.-A., Fleurisson, R., Guillemont, G., McFadden, S., Mooney, R.P., Voorhees, P., Roosz, A., Ronafoeldi, A., Beckermann, C., Karma, A., Chen, C.-H., Warnken, N., Gruen, G.-U., Grohn, M., Poitrault, I., Pehl, T., Nagy, I., Todt, D., Minster, O., Sillikens, W., "Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project," JOM, Vol. 69, No. 8, 2017, pp. 1269-1279.

145. Neumann-Heyme, H., Eckert, K., and Beckermann, C., "General Evolution Equation for the Specific Interface Area of Dendrites during Alloy Solidification," Acta Materialia, Vol. 140, 2017, pp. 87-96.

146. Galles, D., and Beckermann, C., "Effect of Sand Dilation on Distortions and Pattern Allowances during Steel Sand Casting," Int. J. Cast Metals Research, Vol. 30, 2017, pp. 257-275.

147. Majidi, S.H., and Beckermann, C., "Modelling of Air Entrainment During Pouring of Metal Castings," Int. J. Cast Metals Research, Vol. 30, 2017, pp. 301-315.

148. Neumann-Heyme, H., Shevchenko, N., Lei, Z., Eckert, K., Keplinger, O., Grenzer, J., Beckermann, C., and Eckert, S., "Coarsening Evolution of Dendritic Sidearms: From Synchrotron Experiments to Quantitative Modeling," Acta Materialia, Vol. 146, 2018, pp. 176-186.

149. Archer, L., Hardin, R.A., and Beckermann, C., "Counter-Gravity Sand Casting of Steel with Pressurization During Solidification," Int. J. Metalcasting, Vol. 12, 2018, pp. 596-606.

150. Weidt, M., Hardin, R.A., Garb, C., Rosc, J., Brunner, R., and Beckermann, C., "Prediction of Porosity Characteristics of Aluminium Castings Based on X-ray CT Measurements," Int. J. Cast Metals Research, Vol. 31, 2018, pp. 289-307.

151. Majidi, S.H., Griffin, J., and Beckermann, C., "Simulation of Air Entrainment during Mold Filling: Comparison with Water Modeling Experiments," Metall. Mater. Trans. B, Vol. 49B, 2018, pp. 2599-2610.

152. Khalajzadeh, V., Goettsch, D.D., and Beckermann, C., "Real-time X-ray Radiography and Computational Modeling of Shrinkage Porosity Formation in Aluminum Alloy Castings," Metall. Mater. Trans. A, Vol. 50A, 2019, pp. 757-771.

153. Phillion, A.B., Shuai, S., Guo, E., Wang, J., Jing, T., Ren, Z., Neumann-Heyme, H., Beckermann, C., and Lee, P.D., "Corrigendum to “Synchrotron Tomographic Quantification of the Influence of Zn Concentration on Dendritic Growth in Mg-Zn Alloys” [Acta Mater. 156 (2018) 287-296]," Acta Materialia, Vol. 165, 2019, pp. 751-752.

154. Torabi Rad, M., Založnik, M., Combeau, H., and Beckermann, C., "Upscaling Mesoscopic Simulation Results to Develop Constitutive Relations for Macroscopic Modeling of Equiaxed Dendritic Solidification," Materialia, Vol. 5, 2019, 100231.

155. Majidi, S.H., and Beckermann, C., "Effect of Pouring Conditions and Gating System Design on Air Entrainment During Mold Filling," Int. J. Metalcasting, Vol. 13, 2019, pp. 255-272.

156. Galles, D., Lu, J., and Beckermann, C., "Determination of Pattern Allowances for Steel Castings Using the Finite Element Inverse Deformation Analysis," Int. J. Cast Metals Research, Vol. 32, 2019, pp. 123-134.

157. Torabi Rad, M., and Beckermann, C., "A Truncated-Scheil-Type Model for Columnar Solidification of Binary Alloys in the Presence of Melt Convection," Materialia, Vol. 7, 2019, 100364.

4. House, J.M., Beckermann, C., and Smith, T.F., "Natural Convection in a Square Enclosure Containing an Obstruction," in Heat Transfer in Convective Flows, ed. R.K. Sha, ASME, New York, HTD-Vol. 107, 1989, pp. 289-297.

5. Ni, J., and Beckermann, C., "Natural Convection in Vertical Enclosures Filled with Anisotropic Porous Media," in Natural Circulation in Single-Phase and Two-Phase Flow, eds. F.B. Cheung and M.S. El-Genk, ASME, New York, HTD-Vol. 115, 1989, pp. 15-21.

6. Ellinger, E.A., and Beckermann, C., "Solid/Liquid Phase Change in an Enclosure Partially Occupied by a Porous Medium," in Transport Phenomena in Materials Processing, eds. M. Charmchi et al., ASME, New York, HTD-Vol. 132, 1990, pp. 9-16.

7. Ni, J., and Beckermann, C., "A Two-phase Model for Mass, Momentum, Heat, and Species Transport During Solidification," in Transport Phenomena in Materials Processing, eds. M. Charmchi et al., ASME, New York, HTD-Vol. 132, 1990, pp. 45-56.

8. Beckermann, C., and Ni, J., "Modeling of Macro- and Microscopic Transport Phenomena During Solidification," in ICHMT International Symposium on Manufacturing and Materials Processing, ed. W. Aung, Begell House, New York, NY, Vol. 1, 1991, pp. 179-195.

9. Ni, J., Feller, R.J., and Beckermann, C., "A Two-Phase Model for Transport Phenomena During Solidification," in Modeling of Casting, Welding and Advanced Solidification Processes-V, eds. M. Rappaz, M.R. Ozgu, K.W. Makin, TMS, Warrendale, PA, 1991, pp. 675-682.

10. Beckermann, C., and Fan, C., "Application of Flux-Corrected Transport (FCT) to Double-Diffusive Convection in Porous Media," in Heat Transfer in Unsteady Flows, eds. L.S. Yao and J. O'Brian, ASME, New York, HTD-Vol. 158, 1991, pp. 19-26.

11. Beckermann, C., and Ni, J., "Modeling of Equiaxed Solidification with Convection," in First International Conference on Transport Phenomena in Processing, ed. S.I. Guceri, Technovic Pub. Comp., Lancester, PA, 1993, pp. 308-317.

12. Schneider, M.C., and Beckermann, C., "Simulation of Columnar Dendritic Solidification of a Pb-Sn Alloy," in Interactive Dynamics of Convection and Solidification, eds. S.H. Davies, H.E. Huppert, U. Müller and M.G. Worster, NATO AS1 Series E., Vol. 219, Klumer Academic Pub., Dordrecht, Netherlands, 1992, pp. 195-197.

13. Ahuja, S., Beckermann, C., Zakhem, R., Weidman, P.D., and deGroh III, H.C., "Drag Coefficient of an Equiaxed Dendrite Settling in an Infinite Medium," in Micro/Macro Scale Phenomena in Solidification, eds. C. Beckermann et al., ASME, New York, HTD-Vol. 218, 1992, pp. 85-91.

14. Wang, C.Y., and Beckermann, C., "A Multiphase Micro-Macroscopic Model of Solute Diffusion in Dendritic Alloy Solidification," in Micro/Macro Scale Phenomena in Solidification, eds. C. Beckermann et al., ASME, New York, HTD-Vol. 218, 1992, pp. 43-57.

15. Beckermann, C., "Water Modeling of Steel Flow, Air Entrainment and Filtration," in Proceedings of the 46th SFSA Technical and Operating Conference, Paper No. 3.6, Steel Founders' Society of America, Chicago, IL, 1992.

16. Beckermann, C., "Modeling of Transport Phenomena in Mushy Zones," (invited keynote lecture) in Modeling of Casting, Welding and Advanced Solidification Processes-VI, eds. T.S. Piwonka, V. Voller, L. Katgerman, TMS, Warrendale, PA, 1993, pp. 181-192.

17. Beckermann, C., and Wang, C.Y., "Multiphase/Multiscale Modeling of Dendritic Alloy Solidification," in Modeling of Coarsening and Grain Growth, eds. S.P. Marsh and C.S. Pande, TMS, Warrendale, PA, 1993, pp. 55-70.

18. Ni, J., Beckermann, C., and Smith, T.F., "Effect of an Electromagnetic Field on Natural Convection in Porous Media," in Fundamentals of Heat Transfer in Electromagnetic, Electrostatic, and Acoustic Fields, eds. Y. Bayazitoglu and V.S. Arpaci, ASME, New York, HTD-Vol. 248, 1993, pp. 23-33.

19. Wang, C.Y., Beckermann, C., and Fan, C., "A New Approach to Two-phase Transport in Porous Media: The Two-Phase Mixture Model," in Multiphase Transport in Porous Media, eds. R.R. Eaton, M. Kaviany, M.P. Sharma, K.S. Udell and K. Vafai, ASME, New York, FED-Vol. 173, HTD-Vol. 265, 1993, pp. 1-13.

20. Beckermann, C., and Fischer, G.W., "Vehicle and Heavy Equipment Integrated Product and Process Development (IPPD) Technology Development: Casting Process Simulation," in Proceedings of the 47th SFSA Technical and Operating Conference, Paper No. 3.6, Steel Founders' Society of America, Chicago, IL, 1993.

21. Blair, M., Monroe, R.W., and Beckermann, C., "The Effect of Pour Time and Head Height on Air Entrainment," in Proceedings of the 47th SFSA Technical and Operating Conference, Paper No. 1.11, Steel Founders' Society of America, Chicago, IL, 1993.

22. Beckermann, C., Feller, R.J., Irwin, T., Müller-Späth, H., and Wang, C.Y., "Visualization of Sedimentation and Thermosolutal Convection During Equiaxed Alloy Solidification," 32nd AIAA Aerospace Sciences Meeting, AIAA Paper No. 94-0570, 1994.

23. Monroe, R.W., Blair, M., Bates, C.E., and Beckermann, C., "Dross and Inclusions in Iron and Steel Castings," in Proceedings of the BCIRA International Conference, England, April 1994.

24. Schneider, M.C., and Beckermann, C., "Simulation of the Solidification of a Pb-Sn Alloy with Consideration of Microsegregation and Contraction Driven Flow," in Transport Phenomena in Solidification, eds. C. Beckermann et al., ASME, New York, HTD-Vol. 284, 1994, pp. 43-58.

25. Wang, C.Y., and Beckermann, C., "Multi-Scale/-Phase Modeling of Dendritic Alloy Solidification," in Transport Phenomena in Solidification, eds. C. Beckermann et al., ASME, New York, HTD-Vol. 284, 1994, pp. 75-95.

26. Jain, S.C., and Beckermann, C., "Analysis of Water Modeling of Air Entrainment," in Proceedings of the 48th SFSA Technical and Operating Conference, Paper No. 1.4, Steel Founders' Society of America, Chicago, IL, 1994.

27. Reddy, A.V., and Beckermann, C., "Simulation of the Effects of Thermosolutal Convection, Shrinkage Induced Flow and Solid Transport on Macrosegregation and Equiaxed Grain Size Distribution in a DC Continuous Cast Al-Cu Round Ingot," in Materials Processing in the Computer Age - II, eds. V.R. Voller, S.P. Marsh and N. El-Kaddah, TMS, Warrendale, PA, 1995, pp. 89-102.

28. Wang, C.Y., and Beckermann, C., "Computer Simulations of Microstructural Development in Dendritic Alloy Solidification with Convection," in Materials Processing in the Computer Age - II, eds. V.R. Voller, S.P. Marsh and N. El-Kaddah, TMS, Warrendale, PA, 1995, pp. 129-143.

29. Boehmer, W., Schneider, M.C., Beckermann, C., and Sahm, P.R., "Combined Experimental and Numerical Investigation of the Formation of Macrosegregation during Multicomponent Steel Solidification," in Modeling of Casting, Welding, and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, 1995, pp. 697-624.

30. Wang, C.Y., and Beckermann, C., "Modeling of Combined Melt Convection and Solid Transport during Equiaxed Dendritic Solidification," in Modeling of Casting, Welding, and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, 1995, pp. 549-556.

31. Beckermann, C., and Wang, C.Y., "Multi-Phase/-Scale Modeling of Transport Phenomena in Alloy Solidification," in Annual Review of Heat Transfer VI, ed. C.L. Tien, Begell House, New York, NY, Vol. 6, 1995, pp. 115-198.

32. Jensen, D.H., Beckermann, C., Fischer, G.W., and Srinivasan, V., "Capabilities and Integration Potential of Current Casting Design Software," in Proceedings of the 49th SFSA Technical and Operating Conference, Paper No. 3.6, Steel Founders' Society of America, Chicago, IL, 1995.

33. Beckermann, C., and Wang, C.Y., "Modeling of Microstructure Formation in Alloy Solidification with Convection," in Solidification Science and Processing, eds. I. Ohnaka and D.M. Stefanescu, TMS, Warrendale, PA, 1996, pp. 99-110.

34. Feller, R.J., and Beckermann, C., "Modeling of Multiphase Transport During Solidification of Metal-Matrix Particulate Composites," in Transport Phenomena in Materials Processing and Manufacturing, eds. A.S. Lavine et al., ASME, New York, HTD-Vol. 336, FED-Vol. 240, 1996, pp. 305-312.

35. Feller, R.J., and Beckermann, C., "Simulation of Cast Metal-Matrix Particulate Composite Solidification with Convection," in Processing, Properties, and Applications of Cast Metal Matrix Composites, ed. P.K. Rohatgi, TMS, Warrendale, PA, 1996, pp. 1-19.

36. Beckermann, C., and Schneider, M.C., "Simulation of Convection and Macrosegregation in Steel Casting," in Proceedings of the 50th SFSA Technical and Operating Conference, Paper No. 4.2, Steel Founders' Society of America, Chicago, IL, 1996.

37. Gu, J.P., Schneider, M.C., Beckermann, C., Boettinger, W.J., and Kattner, U.R., "Prediction of Freckles during Directional Solidification of Nickel-Base Superalloy through a Macroscopic Multicomponent Solidification Model," in Modeling of Casting and Solidification Processes 1996 (MCS3-’96), eds. Liu Baicheng and Jing Tao, Int. Academic Publishers, Beijing, China, 1996, pp. 198-203.

38. Diepers, H.J., Beckermann, C., and Steinbach, I., "A Phase-Field Method for Alloy Solidification with Convection," in Solidification Processing 1997, eds. J. Beech and H. Jones, Dept. Engineering Materials, The University of Sheffield, Sheffield, UK, 1997, pp. 426-430.

39. Reddy, A.V., Kothe, D.B., and Beckermann, C., "High-Resolution FV Parallel Simulations of Mould Filling and Binary Alloy Solidification on Unstructured 3-D Meshes," in Solidification Processing 1997, eds. J. Beech and H. Jones, Dept. Engineering Materials, The University of Sheffield, Sheffield, UK, 1997, pp. 83-87.

40. Hardin, R.A., and Beckermann, C., "Heat Transfer and Solidification Modeling in the Continous Casting of Multi-Component Steels," in Proceedings of the ASME 1997 National Heat Transfer Conference, Vol. 9, ASME, New York, HTD-Vol. 347, 1997, pp. 9-20.

41. Hardin, R.A., and Beckermann, C., "The Current State of Casting Yield: Results from the 1997 SFSA Yield Survey," in Proceedings of the 51st SFSA Technical and Operating Conference, Paper No. 3.5, Steel Founders' Society of America, Chicago, IL, 1997.

42. Beckermann, C., Shen, X., Hardin, R.A., and Gu, J., "A Computational Study of Feeding Rules and Yield Improvement Techniques," in Proceedings of the 51st SFSA Technical and Operating Conference, Paper No. 3.9, Steel Founders' Society of America, Chicago, IL, 1997.

43. Steinbach, I., Kauerauf, B., Beckermann, C., and Guo, J., "Modeling of the Growth and Interactions of Equiaxed Dendrites on a Mesoscopic Scale," in Solidification 1998, eds. S.P. Marsh et al., TMS, Warrendale, PA, 1998. pp. 5-14.

44. Tong, X., Beckermann, C., and Karma, A., "Phase Field Simulation of Dendritic Growth with Convection," in Modeling of Casting, Welding and Advanced Solidification Processes VIII, eds. B.G. Thomas and C. Beckermann, TMS, Warrendale, PA, 1998, pp. 613-620.

45. Diepers, H.J., Beckermann, C., and Steinbach, I., "Modeling of Convection-Influenced Coarsening of a Binary Alloy Mush Using the Phase-Field Method," in Modeling of Casting, Welding and Advanced Solidification Processes VIII, eds. B.G. Thomas and C. Beckermann, TMS, Warrendale, PA, 1998, pp. 565-572.

46. Schneider, M.C., Beckermann, C., Lipinski, D.M., and Schaefer, W., "Macrosegregation Formation During Solidification of Complex Steel Castings: 3-D Numerical Simulation and Experimental Comparison," in Modeling of Casting, Welding and Advanced Solidification Processes VIII, eds. B.G. Thomas and C. Beckermann, TMS, Warrendale, PA, 1998, pp. 257-264.

47. Steinbach, I., Kauerauf, B., Beckermann, C., Guo, J., and Li, Q., "Three-Dimensional Modeling of Equiaxed Dendritic Growth on a Mesoscopic Scale," in Modeling of Casting, Welding and Advanced Solidification Processes VIII, eds. B.G. Thomas and C. Beckermann, TMS, Warrendale, PA, 1998, pp. 573-580.

48. Hardin, R., Shen, X., Gu, J.P., and Beckermann, C., "Progress in the Development of Improved Feeding Rules for the Risering of Steel Castings," in Proceedings of the 52nd SFSA Technical and Operating Conference, Paper No. 4.4, Steel Founders' Society of America, Chicago, IL, 1998.

49. Schneider, M.C., Beckermann, C., Lipinski, D.M., and Schaefer, W., "Macrosegregation Formation during Solidification of Complex Steel Castings: 3-D Numerical Simulation and Experimental Comparison," in Proceedings of V Congreso Internacional de Materiales y XX Encuentro de Investigacion Metalurgica, eds. M. Martinez et al., Satillo, Coahuila, Mexico, 1998, pp. 1-10.

50. Li, Q., and Beckermann, C., "Evolution of Sidebranch Spacings in Three-Dimensional Dendritic Growth," in Solidification 1999, eds. W.H. Hofmeister et al., TMS, Warrendale, PA, 1999, pp. 111-120.

51. Gu, J.P., and Beckermann, C., "Simulation of Convection and Macrosegregation in a Large Steel Ingot," in Fluid Flow Phenomena in Metals Processing, eds. N. El-Kaddah et al., TMS, Warrendale, PA, 1999, pp. 379-386.

52. Beckermann, C., Li, Q., and Tong, X., "Microstructure Evolution in Equiaxed Dendritic Growth," 5th IUMRS Int. Conf. On Advanced Materials, Beijing, China, 1999, Vol.2, pg.307.

53. Beckermann, C., "Modeling of Segregation and Grain Structure in Alloy Solidification with Melt Convection and Solid Movement," in Cutting Edge of Computer Simulation of Solidification and Casting, eds. I. Ohnaka and H. Yasuda, ISIJ, Japan, 1999, pp.69-82.

54. Hardin, R.A., Ou, S., Carlson, K., and Beckermann, C., "Relationship between Casting Simulation and Radiographic Testing: Results from the SFSA Plate Casting Trials," in Proceedings of the 53rd SFSA Technical and Operating Conference, Paper No. 4.5, Steel Founders' Society of America, Chicago, IL, 1999.

55. Hardin, R.A., Liu, K., and Beckermann, C., "Development of a Model for Transient Simulation and Control of a Continuous Slab Caster," in Materials Processing in the Computer Age III, eds. V.R. Voller and H. Henein, TMS, Warrendale , PA, 2000, pp. 61-74.

56. Hardin, R.A., Shen, H., and Beckermann, C., "Heat Transfer Modeling of Continuous Steel Slab Casters Using Realistic Spray Patterns," in Modeling of Casting, Welding and Advanced Solidification Processes IX, eds. P.R. Sahm et al., Shaker Verlag, Aachen, Germany, 2000, pp. 729-736.

57. Carlson, K., Ou, S., Hardin, R.A., and Beckermann, C., "Analysis of ASTM X-Ray Shrinkage Rating for Steel Castings," in Proceedings of the 54th SFSA Technical and Operating Conference, Paper No. 1.6, Steel Founders' Society of America, Chicago, IL, 2000.

58. Ou, S., Carlson, K., Blair, M., Jones, G., Hardin, R.A., and Beckermann, C., "Yield Improvement Case Study: Stacked Spring Caps," in Proceedings of the 54th SFSA Technical and Operating Conference, Paper No. 2.4, Steel Founders' Society of America, Chicago, IL, 2000.

59. Smith, D., Faivre, T., Ou, S., Carlson, K., Hardin, R.A., and Beckermann, C., "Application of New Feeding Rules to Risering of Steel Castings," in Proceedings of the 54th SFSA Technical and Operating Conference, Paper No. 2.1, Steel Founders' Society of America, Chicago, IL, 2000.

60. Beckermann, C., "Modeling of Macrosegregation: Past, Present and Future," in Proceedings of the Merton C. Flemings Symposium on Solidification and Materials Processing, eds. R. Abbashian, H. Brody, and A. Mortensen, TMS, Warrendale, PA, 2001, pp. 297-310.

61. Beckermann, C., "Modeling of Solidification: From Dendrites to Castings," in Proceedings of the 2001 National Heat Transfer Conference, eds. T.L. Bergman and C.B. Panchal, ASME, NY, 2001, NHTC2001-20262.

62. Tong, X., Beckermann, C., and Karma, A., "Velocity and Shape Selection of Dendritic Crystals in a Forced Flow," in Interactive Dynamics of Convection and Solidification, eds. P. Ehrhard et al., Kluwer Academic Publishers, Netherlands, 2001, pp. 47-56.

63. Beckermann, C., Tong, X., and Karma, A., "Phase-Field Simulations of Convective Effects in Solidification Microstructure Development," in The Science of Casting and Solidification, eds. D.M. Stefanescu et al., Editura Lux Libris, Brasov, Romania, 2001, pp. 100-109.

64. Carlson, K., Ou, S., Hardin, R., and Beckermann, C., "Development of a Methodology to Predict and Prevent Leakers Caused by Microporosity in Steel Castings," in Proceedings of the 55th SFSA Technical and Operating Conference, Paper No. 3.7, Steel Founders' Society of America, Chicago, IL, 2001.

65. Hardin, R., Hays, T., and Beckermann, C., "Pressurized Riser Casting Trials," in Proceedings of the 55th SFSA Technical and Operating Conference, Paper No. 3.8, Steel Founders' Society of America, Chicago, IL, 2001.

66. Beckermann, C., "Macrosegregation," in Encyclopedia of Materials: Science and Technology, eds. K.H.J. Bushow et al., Elsevier Science, NY, 2001, pp. 4733-4739.

67. Lu, Y., Beckermann, C., and Karma, A., "Convection Effects in Three-Dimensional Dendritic Growth," in Mat. Res. Soc. Symp. Proc., Vol. 701, 2002, T2.2.1-T2.2.10.

68. Boettinger, W.J., Warren, J.A., Beckermann, C., and Karma, A., "Phase-Field Simulation of Solidification," Annual Review of Materials Research, Vol. 32, 2002, pp. 163-194.

69. Carlson, K.D., Lin, Z., Hardin, R., and Beckermann, C., "Modeling of Porosity Formation and Feeding Flow in Steel Casting," in Proceedings of the 56th SFSA Technical and Operating Conference, Paper No. 4.4, Steel Founders' Society of America, Chicago, IL, 2002.

70. Hardin, R., and Beckermann, C., "Effect of Shrinkage on Service Performance of Steel Castings," in Proceedings of the 56th SFSA Technical and Operating Conference, Paper No. 4.5, Steel Founders' Society of America, Chicago, IL, 2002.

71. Lu, Y., Beckermann, C., and Karma, A., "Convection Effects in Three-Dimensional Dendritic Growth," in Proceedings of IMECE 2002, ASME, NY, 2002, Paper No. IMECE2002-32838.

72. Ramirez, J.C., and Beckermann, C., "Quantitative Modeling of Binary Alloy Solidification with Coupled Heat and Solute Diffusion via the Phase-Field Method," in 41st AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 6-9, 2003, Paper No. AIAA 2003-816.

73. Carlson, K.D., Lin, Z., Hardin, R.A., Beckermann, C., Mazurkevich, G., and Schneider, M.C., "Modeling of Porosity Formation and Feeding Flow in Steel Casting," in Modeling of Casting, Welding and Advanced Solidification Processes X, eds. D.M. Stefanescu et al., TMS, Warrendale, PA, 2003, pp. 295-302.

74. Sigl, K.M., Hardin, R., Stephens, R.I., and Beckermann, C., "Fatigue of 8630 Cast Steel in the Presence of Shrinkage Porosity," in Proceedings of the 57th SFSA Technical and Operating Conference, Paper No. 3.5, Steel Founders' Society of America, Chicago, IL, 2003.

75. Bryant, R., Carlson, K.D., Ou, S., and Beckermann, C., "Tilt Pour Trials and Analysis," in Proceedings of the 57th SFSA Technical and Operating Conference, Paper No. 2.6, Steel Founders' Society of America, Chicago, IL, 2003.

76. Ou, S., and Beckermann, C., "Simulation of Dimensional Changes in Steel Casting," in Proceedings of the 57th SFSA Technical and Operating Conference, Paper No. 4.3, Steel Founders' Society of America, Chicago, IL, 2003.

77. Carlson, K.D., Ou, S., and Beckermann, C., "Feeding and Risering of High Alloy Steel Castings," in Proceedings of the 57th SFSA Technical and Operating Conference, Paper No. 4.5, Steel Founders' Society of America, Chicago, IL, 2003.

78. Ramirez, J.C., and Beckermann, C., "Examination of Binary Alloy Free Dendritic Growth Theories with a Phase-Field Model," in Solidification Processes and Microstructures - A Symposium in Honor of Wilfried Kurz, eds. M. Rappaz, C. Beckermann, and R. Trivedi, TMS, Warrendale, PA, 2004, pp. 373-378.

79. Sun, Y., and Beckermann, C., "A Diffuse Interface Model for Two-Phase Flows Based on Averaging," in Multiphase Phenomena and CFD Modeling and Simulation in Materials Processes, eds. L. Nastac and B.Q. Li, TMS, Warrendale, PA, 2004, pp. 109-118.

80. Carlson, K.D., and Beckermann, C., "Modeling of Reoxidation Inclusion Formation During Filling of Steel Castings," in Proceedings of the 58th SFSA Technical and Operating Conference, Paper No. 4.6, Steel Founders' Society of America, Chicago, IL, 2004.

81. Carlson, K.D., Ou, S., and Beckermann, C., "Feeding of Nickel-Based Alloys," in Proceedings of the 58th SFSA Technical and Operating Conference, Paper No. 3.3, Steel Founders' Society of America, Chicago, IL, 2004.

82. Monroe, C., and Beckermann, C., "Development of a Hot Tear Indicator for Use in Casting Simulation," in Proceedings of the 58th SFSA Technical and Operating Conference, Paper No. 3.1, Steel Founders' Society of America, Chicago, IL, 2004.

83. Hardin, R.A., and Beckermann, C., "Effect of Porosity on Mechanical Properties of 8630 Cast Steel," in Proceedings of the 58th SFSA Technical and Operating Conference, Paper No. 4.4, Steel Founders' Society of America, Chicago, IL, 2004.

84. Sun, Y., and Beckermann, C., "Phase-Field Simulation of Solidification with Density Change," in Proceedings of the ASME Heat Transfer Division - 2004, ASME, New York, NY, HTD-Vol. 375-3, 2004, pp. 519-525 (Paper No. IMECE2004-60875).

85. Blair, M., Monroe, R., Beckermann, C., Hardin, R., Carlson, K., Monroe, C., and Griffin, J., "Designing Reliable Castings," in Shape Casting: The John Campbell Symposium, eds. M. Tiryakioglu and P.N. Crepeau, TMS, Warrendale, PA, 2005, pp. 63-72.

86. Carlson, K.D., and Beckermann, C., "Modeling of Reoxidation Inclusion Formation During Filling of Steel Castings," in Defect Formation, Detection, and Elimination During Casting, Welding, and Solidification (Proceedings of a Symposium Sponsored by Materials Science & Technology 2005), eds. M.L.C. Clemens et al., TMS, Warrendale, PA, 2005, pp. 35-46.

87. Monroe, C., and Beckermann, C., "Development of a Hot Tear Indicator for Steel Castings," in Defect Formation, Detection, and Elimination During Casting, Welding, and Solidification (Proceedings of a Symposium Sponsored by Materials Science & Technology 2005), eds. M.L.C. Clemens et al., TMS, Warrendale, PA, 2005, pp. 47-56.

88. Sun, Y., and Beckermann, C., "Phase-Field Simulation of Two-Phase Micro-Flows in a Hele-Shaw Cell," in Computational Methods in Multiphase Flow III, eds. A.A. Mammoli and C.A. Brebbia, WIT Press, Southampton, UK, 2005, pp. 147-157.

89. Hardin, R.A., and Beckermann, C., "Simulation of Heat Treatment Distortion," in Proceedings of the 59th SFSA Technical and Operating Conference, Paper No. 3.3, Steel Founders' Society of America, Chicago, IL, 2005.

90. Wang, L., and Beckermann, C., "Prediction of Reoxidation Inclusion Composition in Casting of Steel," in Proceedings of the 59th SFSA Technical and Operating Conference, Paper No. 4.4, Steel Founders' Society of America, Chicago, IL, 2005.

91. Gradman, J.J., Stephens, R.I., Hardin, R.A., and Beckermann, C., "Comparison of Fatigue Behavior for Centrifugally Cast and Keel Block Cast Steel," in Proceedings of the 59th SFSA Technical and Operating Conference, Paper No. 3.1, Steel Founders' Society of America, Chicago, IL, 2005.

92. Carlson, K.D., Lin, Z., Beckermann, C., Mazurkevich, G., and Schneider, M.C., "Simulation of Porosity Formation in Aluminum Casting," in Simulation of Aluminum Shape Casting Processing: From Alloy Design to Mechanical Properties, eds. Q. Wang, M.J.M. Krane, and P.D. Lee, TMS, Warrendale, PA, 2006, pp. 133-142.

93. Carlson, K.D., Lin, Z., Beckermann, C., Mazurkevich, G., and Schneider, M.C., "Modeling of Porosity Formation in Aluminum Alloys," in Modeling of Casting, Welding and Advanced Solidification Processes XI, eds. C.A. Gandin and M. Bellet, TMS, Warrendale, PA, 2006, pp. 627-634.

94. Hardin, R.A., Huff, R.K., and Beckermann, C., "Integrated Design of Steel Castings for Service Performance," in Modeling of Casting, Welding and Advanced Solidification Processes XI, eds. C.A. Gandin and M. Bellet, TMS, Warrendale, PA, 2006, pp. 653-660.

95. Hardin, R.A., and Beckermann, C., "Simulation of the Mechanical Performance of Cast Steel with Porosity: Static Properties," in Proceedings of the 60th SFSA Technical and Operating Conference, Paper No. 4.3, Steel Founders' Society of America, Chicago, IL, 2006.

96. Brooks, B.E., and Beckermann, C., "Prediction of Burn-on and Mold Penetration in Steel Casting Using Simulation," in Proceedings of the 60th SFSA Technical and Operating Conference, Paper No. 5.3, Steel Founders' Society of America, Chicago, IL, 2006.

97. Monroe, C., and Beckermann, C., "Simulation of Hot Tearing and Distortion During Casting of Steel: Comparison with Experiments," in Proceedings of the 60th SFSA Technical and Operating Conference, Paper No. 5.7, Steel Founders' Society of America, Chicago, IL, 2006.

98. Badillo, A., and Beckermann, C., "Growth of Equiaxed Dendritic Crystals Settling in an Undercooled Melt, " in Solidification Processing 2007, ed. H. Jones, Dept. Engineering Materials, The University of Sheffield, Sheffield, UK, 2007, pp. 176-180.

99. Hardin, R.A., and Beckermann, C., "Prediction of Fatigue Life of Cast Steel in the Presence of Porosity," in Proceedings of the 61st SFSA Technical and Operating Conference, Paper No. 5.8, Steel Founders' Society of America, Chicago, IL, 2007.

100. Monroe, C., and Beckermann, C., "Deformation During Casting of Steel: Mold and Material Properties," in Proceedings of the 61st SFSA Technical and Operating Conference, Paper No. 5.6, Steel Founders' Society of America, Chicago, IL, 2007.

101. Jain, N., Carlson, K.D., and Beckermann, C., "Round Robin Study to Assess Variations in Casting Simulation Niyama Criterion Predictions," in Proceedings of the 61st SFSA Technical and Operating Conference, Paper No. 5.5, Steel Founders' Society of America, Chicago, IL, 2007.

102. Brooks, B.E., and Beckermann, C., "Prediction of Heat Treatment Distortion of Cast Steel C-Rings," in Proceedings of the 61st SFSA Technical and Operating Conference, Paper No. 4.5, Steel Founders' Society of America, Chicago, IL, 2007.

103. Melendez, A.J., Carlson, K.D., and Beckermann, C., "Simulation of Reoxidation Inclusion Formation in Steel Casting," in Proceedings of the 61st SFSA Technical and Operating Conference, Paper No. 3.8, Steel Founders' Society of America, Chicago, IL, 2007.

104. Blair, M., Monroe, R., Hardin, R.A., and Beckermann, C., "A New Standard for Radiographic Acceptance Criteria for Steel Castings," in Proceedings of the 62nd SFSA Technical and Operating Conference, Paper No. 5.5, Steel Founders' Society of America, Chicago, IL, 2008.

105. Carlson, K.D., and Beckermann, C., "Use of the Niyama Criterion to Predict Shrinkage-Related Leaks in High-Nickel Steel and Nickel-Based Alloy Castings," in Proceedings of the 62nd SFSA Technical and Operating Conference, Paper No. 5.6, Steel Founders' Society of America, Chicago, IL, 2008.

106. Beckermann, C., "Macrosegregation," in ASM Handbook, Volume 15: Casting, ed. S. Viswanathan, ASM International, Materials Park, OH, 2009, pp. 348-352.

107. Pokorny, M.G., Monroe, C.A., and Beckermann, C., "Prediction of Deformation and Hot Tear Formation Using a Viscoplastic Model with Damage," in Shape Casting: The 3rd International Symposium, eds. J. Campbell, P.N. Crepeau and M. Tiryakioglu, TMS, Warrendale, PA, 2009, pp. 265-272.

108. Monroe, C.A., Beckermann, C., and Klinkhammer, J., "Simulation of Deformation and Hot Tear Formation Using a Visco-Plastic Model with Damage," in Modeling of Casting, Welding, and Advanced Solidification Processes - XII, eds. S.L. Cockcroft and D.M. Maijer, TMS, Warrendale, PA, 2009, pp. 313-320.

109. Lin, Z., Monroe, C.A., Huff, R.K., and Beckermann, C., "Prediction of Hot Tear Defects in Steel Castings Using a Damage Based Model," in Modeling of Casting, Welding, and Advanced Solidification Processes - XII, eds. S.L. Cockcroft and D.M. Maijer, TMS, Warrendale, PA, 2009, pp. 329-336.

110. Melendez, Z., Carlson, K.D., Beckermann, C., and Schneider, M.C., "Modeling of Reoxidation Inclusion Formation in Steel Sand Casting," in Modeling of Casting, Welding, and Advanced Solidification Processes - XII, eds. S.L. Cockcroft and D.M. Maijer, TMS, Warrendale, PA, 2009, pp. 393-400.

111. Delaleau, P., Mathiesen, R.H., Schaffer, P.L., Arnberg, L., and Beckermann, C., "Modeling and In-situ X-ray Video Microscopy of Confined Equiaxed Grain Growth and Buoyant Motion in Al-Cu," in Modeling of Casting, Welding, and Advanced Solidification Processes - XII, eds. S.L. Cockcroft and D.M. Maijer, TMS, Warrendale, PA, 2009, pp. 643-649.

112. Hardin, R.A., and Beckermann, C., "Integrated Design of Steel Castings: Case Studies," in Proceedings of the 63rd SFSA Technical and Operating Conference, Paper No. 2.3, Steel Founders' Society of America, Chicago, IL, 2009.

113. Hardin, R.A., and Beckermann, C., "A New Standard for Radiographic Acceptance Criteria for Steel Castings: Gage R&R Study," in Proceedings of the 63rd SFSA Technical and Operating Conference, Paper No. 2.6, Steel Founders' Society of America, Chicago, IL, 2009.

114. Thole, J., and Beckermann, C., "Measurement of Elastic Modulus of PUNB Bonded Sand as a Function of Temperature," in Proceedings of the 63rd SFSA Technical and Operating Conference, Paper No. 4.7, Steel Founders' Society of America, Chicago, IL, 2009.

115. Carlson, K.D., Melendez, A.J., and Beckermann, "Modeling of Reoxidation Inclusion Formation in Steel Sand Casting," in Proceedings of the 63rd SFSA Technical and Operating Conference, Paper No. 5.6, Steel Founders' Society of America, Chicago, IL, 2009.

116. Pokorny, M.G., Monroe, C.A., Beckermann, C., Zhen, Z., and Hort, N., "Simulation of Stresses During Casting of Binary Magnesium-Aluminum Alloys," in Magnesium Technology 2010, eds. S.R. Agnew et al., TMS, Warrendale, PA, 2010, pp. 401-407.

117. Hardin, R.A., and Beckermann, C., "Validation and Gage R&R Studies of a New Radiography Standard for Steel Castings," in Proceedings of the 64th SFSA Technical and Operating Conference, Paper No. 2.6, Steel Founders' Society of America, Chicago, IL, 2010.

118. Carlson, K.D., and Beckermann, C., "Prediction of Riser Carbon Macrosegregation due to Shrinkage Flow in Steel Casting," in Proceedings of the 64th SFSA Technical and Operating Conference, Paper No. 3.2, Steel Founders' Society of America, Chicago, IL, 2010.

119. Carlson, K.D., and Beckermann, C., "Development of Thermophysical Property Datasets, Benchmark Niyama Results, and A Simulation Qualification Procedure," in Proceedings of the 64th SFSA Technical and Operating Conference, Paper No. 5.5, Steel Founders' Society of America, Chicago, IL, 2010.

120. Carlson, K.D., Beckermann, C., Jekl, J., and Berkmortel, R., "Simulation of Porosity and Hot Tears in a Squeeze Cast Magnesium Control Arm," in Magnesium Technology 2011, eds. W.H. Sillekens et al., TMS, Warrendale, PA, 2011, pp. 93-100.

121. Hardin, R., Du, P., and Beckermann, C., "Three-dimensional Simulation of Heat Transfer and Stresses in a Steel Slab Caster, " in Proceedings of the 4th International Conference on Modelling and Simulation of Metallurgical Processes in Steelmaking, Paper No. STSI-71, Steel Institute VDEh, Duesseldorf, Germany, 2011.

122. Hardin, R.A., and Beckermann, C., "Measurement and Prediction of Mechanical Behavior of Cast Steel Plates with Centerline Porosity," in Proceedings of the 65th SFSA Technical and Operating Conference, Paper No. 5.4, Steel Founders' Society of America, Chicago, IL, 2011.

123. Galles, D., Monroe, C., and Beckermann, C., "Measurement and Prediction of Stresses during Casting of a Steel Bar," in Proceedings of the 65th SFSA Technical and Operating Conference, Paper No. 5.5, Steel Founders' Society of America, Chicago, IL, 2011.

124. Samuels, G., and Beckermann, C., "Measurement of Gas Evolution from PUNB Bonded Sand as a Function of Temperature," in Proceedings of the 65th SFSA Technical and Operating Conference, Paper No. 5.6, Steel Founders' Society of America, Chicago, IL, 2011.

125. Hardin, R.A., and Beckermann, C., "Effect of Porosity on Deformation, Damage, and Fracture of Cast Steel," in Supplemental Proceedings: Volume 2: Materials Properties, Characterization, and Modeling, TMS, Warrendale, PA, 2012, pp. 217-224.

126. Hardin, R.A., and Beckermann, C., "Integrated Design of Castings: Effect of Porosity on Mechanical Performance," IOP Conf. Series: Materials Science and Engineering, Vol. 33, 2012, 012069 (8 pages).

127. Galles, D., Monroe, C.A., and Beckermann, C., "Measurement and Simulation of Deformation and Stresses in Steel Casting," IOP Conf. Series: Materials Science and Engineering, Vol. 33, 2012, 012049 (8 pages).

128. Sturz, L., Zimmermann, G., Gandin, C.A., Billia, B., Mangelinck, N., Nguyen-Thi, H., Browne, D.J., Mirihanage, W.U., Voss, D., Beckermann, C., and Karma, A., "ISS-Experiments of Columnar-to-Equiaxed Transition in Solidification Processing," in Materials Research in Microgravity 2012: Proceedings of a Symposium held at the 141st TMS 2012 Annual Meeting and Exhibition, eds. R. Hyers et al., NASA/CP-2012-217466, 2012, pp. 56-62.

129. Hardin, R.A., and Beckermann, C., "Simulations of the Effect of Section Size and Cooling on Sigma Phase Formation in Duplex Stainless Steels," in Proceedings of the 66th SFSA Technical and Operating Conference, Paper No. 3.6, Steel Founders' Society of America, Chicago, IL, 2012.

130. Galles, D., and Beckermann, C., "Measurement and Simulation of Distortion of a Steel Bracket Casting," in Proceedings of the 66th SFSA Technical and Operating Conference, Paper No. 5.2, Steel Founders' Society of America, Chicago, IL, 2012.

131. Carlson, K.D., and Beckermann, C., "Sensitivity of Steel Casting Simulation Results to Alloy Property Datasets," in Proceedings of the 66th SFSA Technical and Operating Conference, Paper No. 5.3, Steel Founders' Society of America, Chicago, IL, 2012.

132. Torabi Rad, M., Kotas, P., and Beckermann, C., "Rayleigh Number Criterion for Formation of A-Segregates in Steel Castings and Ingots," in Proceedings of the 66th SFSA Technical and Operating Conference, Paper No. 5.4, Steel Founders' Society of America, Chicago, IL, 2012.

133. Hardin, R.A., Williams, T.J., and Beckermann, C., "Riser Sleeve Properties for Steel Castings and the Effect of Sleeve Type on Casting Yield," in Proceedings of the 67th SFSA Technical and Operating Conference, Paper No. 5.2, Steel Founders' Society of America, Chicago, IL, 2013.

134. Williams, T.J., Galles, D., and Beckermann, C., "Translating Water Spray Cooling of a Steel Bar Sand Casting," in Proceedings of the 67th SFSA Technical and Operating Conference, Paper No. 5.4, Steel Founders' Society of America, Chicago, IL, 2013.

135. Galles, D., and Beckermann, C., "Distortion of a Steel Cylinder Casting with a Core," in Proceedings of the 67th SFSA Technical and Operating Conference, Paper No. 5.8, Steel Founders' Society of America, Chicago, IL, 2013.

136. Hardin, R., Choi, K.K., and Beckermann, C., "Reliability-Based Casting Process Design Optimization," in Shape Casting: The 5th International Symposium, eds. M. Tiryakioglu, J. Campbell, and G. Byczynski, TMS, Warrendale, PA, 2014, pp. 19-26.

137. Williams, T.J., Hardin, R.A., and Beckermann, C., "Thermophysical Properties for ASK Chemical and Exochem Riser Sleeves for Steel Castings," in Proceedings of the 68th SFSA Technical and Operating Conference, Paper No. 4.6, Steel Founders' Society of America, Chicago, IL, 2014.

138. Zimmermann, G., Sturz, L., Billia, B., Mangelinck-Noël, N., Liu, D.R., Nguyen Thi, H., Bergeon, N., Gandin, Ch.-A., Browne, D.J., Beckermann, Ch., Tourret, D., and Karma, A., "Columnar-to-Equiaxed Transition in Solidification Processing of AlSi7 Alloys in Microgravity – The CETSOL Project," Materials Science Forum, Vols. 790-791, 2014, pp. 12-21.

139. Monroe, R., Blair, M., and Beckermann, C., "Reducing Leaks in Cast Pump and Valve Bodies using Solidification Simulation," in Corrosion 2014, Paper No. NACE-2014-3928, NACE International, San Antonio, TX, 2014.

140. Galles, D., and Beckermann, C., "Effect of Sand Dilation on Core Expansion during Steel Casting," IOP Conf. Series: Materials Science and Engineering, Vol. 84, 2015, 012022 (8 pages).

141. Neumann-Heyme, H., Eckert, K., and Beckermann, C., "Evolution of Specific Interface Area in Dendritic Alloy Solidification," IOP Conf. Series: Materials Science and Engineering, Vol. 84, 2015, 012072 (7 pages).

142. Guo, J., Beckermann, C., Carlson, K., Hirvo, D., Bell, K., Moreland, T., Gu, J., Clews, J., Scott, S., Couturier, G., and Backman, D., "Microporosity Prediction and Validation for Ni-based Superalloy Castings," IOP Conf. Series: Materials Science and Engineering, Vol. 84, 2015, 012003 (6 pages).

143. Williams, T.J., Hardin, R.A., and Beckermann, C., "Characterization of the Thermophysical Properties of Riser Sleeve Materials and Analysis of Riser Sleeve Performance," in Proceedings of the 69th SFSA Technical and Operating Conference, Paper No. 5.9, Steel Founders' Society of America, Chicago, IL, 2015.

144. Galles, D., and Beckermann, C., "Simulation of Distortions and Pattern Allowances for a Production Steel Casting," in Proceedings of the 69th SFSA Technical and Operating Conference, Paper No. 3.7, Steel Founders' Society of America, Chicago, IL, 2015.

145. Beckermann, C., Neumann-Heyme, H., and Eckert, K., "Evolution of the Specific Solid-Liquid Interface Area in Directional Solidification," in Frontiers in Solidification: TMS MPMD Symposium in Honor of Michel Rappaz, eds. W. Kurz, J. Dantzig, A. Karma, J. Hoyt, EPFL Materials Science, Lausanne, Switzerland, 2016, pp. 53-57.

146. Založnik, M., Souhar, Y., Beckermann, C., and Combeau, H., "Upscaling from Mesoscopic to Macroscopic Solidification Models by Volume Averaging," in Frontiers in Solidification: TMS MPMD Symposium in Honor of Michel Rappaz, eds. W. Kurz, J. Dantzig, A. Karma, J. Hoyt, EPFL Materials Science, Lausanne, Switzerland, 2016, pp. 59-63.

147. Torabi Rad, M., and Beckermann, C., "Validation of a Model for the Columnar to Equiaxed Transition with Melt Convection," in CFD Modeling and Simulation in Materials Processing 2016, eds. L. Nastac et al., TMS, John Wiley & Sons Inc., Hoboken, NJ, 2016, pp. 85-92.

148. Khalajzadeh, V., Goettsch, D. D., and Beckermann, C., "Real-Time Radiography and Modeling of Porosity Formation in an A356 Aluminum Alloy Wedge Casting," in Shape Casting: 6th International Symposium, eds. M. Tiryakioglu, M, Jolly, and G. Byczynski, TMS, John Wiley & Sons Inc., Hoboken, NJ, 2016, pp. 35-42.

149. Galles, D., and Beckermann, C., “Modeling of Distortion of a Steel Bracket Sand Casting,” in Shape Casting: 6th International Symposium, eds. M. Tiryakioglu, M. Jolly, and G. Byczynski, TMS, John Wiley & Sons Inc., Hoboken, NJ, 2016, pp. 35-42.

150. Souhar, Y., De Felice, V.F., Založnik, M., Combeau, H., and Beckermann, C., "The Role of the Stagnant-Film Thickness in Mesoscopic Modeling of Equiaxed Grain Envelopes," IOP Conf. Series: Materials Science and Engineering, Vol. 117, 2016, 012014 (6 pages).

151. Majidi, S.H., and Beckermann, C., "Modeling of Air Entrainment During Pouring of Steel Castings," in Proceedings of the 70th SFSA Technical and Operating Conference, Paper No. 4.8, Steel Founders' Society of America, Chicago, IL, 2016.

152. Hardin, R.A., and Beckermann, C., "Effect of Cooling Rate and Microporosity on Mechanical Performance of a High Strength Steel," in Proceedings of the 70th SFSA Technical and Operating Conference, Paper No. 5.2, Steel Founders' Society of America, Chicago, IL, 2016.

153. Neumann-Heyme, H., Eckert, K., and Beckermann, C., "Evolution of the Interfacial Area in Dendritic Solidification," in Proceedings of the 6th Decennial International Conference on Solidification Processing, ed. Z. Fan, BCAST, Brunel University, London, UK, 2017, pp. 193-196.

154. Neumann-Heyme, H., Shevchenko, N., Eckert, K., Grenzer, J., Beckermann, C., and Eckert, S., "Synchrotron X-ray Imaging and Numerical Modelling of Dendritic Sidebranch Evolution during Coarsening," in Proceedings of the 6th Decennial International Conference on Solidification Processing, ed. Z. Fan, BCAST, Brunel University, London, UK, 2017, pp. 214-217.

155. Zimmermann, G., Sturz, L., Nguyen-Thi, H., Mangelinck-Noel, N., Li, Y.Z., Liu, D.-R., Gandin, C.-A., Fleurisson, R., Guillemont, G., McFadden, S., Mooney, R.P., Voorhees, P., Roosz, A., Ronafoeldi, A., Beckermann, C., Karma, A., Warnken, N., Saad, A., Gruen, G.-U., Grohn, M., Poitrault, I., Pehl, T., Nagy, I., Todt, D., Minster, O., and Sillikens, W., "Columnar and Equiaxed Solidification in a Microgravity Environment – The CETSOL Project," in Proceedings of the 6th Decennial International Conference on Solidification Processing, ed. Z. Fan, BCAST, Brunel University, London, UK, 2017, pp. 288-291.

156. Torabi Rad, M., Založnik, M., Combeau, H., and Beckermann, C., “Constitutive Relations for Macroscopic Modelling of Equiaxed Solidification,” in Proceedings of the 6th Decennial International Conference on Solidification Processing, ed. Z. Fan, BCAST, Brunel University, London, UK, 2017, pp. 326-329.

157. Majidi, S.H., and Beckermann, C., "Simulation of Air Entrainment during Mold Filling: Comparison with Water Modeling Experiments," in Proceedings of the 71st SFSA Technical and Operating Conference, Paper No. 3.2, Steel Founders' Society of America, Chicago, IL, 2017.

158. Archer, L., Hardin, R.A., and Beckermann, C., "Counter-Gravity Sand Casting of Steel with Pressurization During Solidification," in Proceedings of the 71st SFSA Technical and Operating Conference, Paper No. 3.7, Steel Founders' Society of America, Chicago, IL, 2017.

159. Majidi, S.H., Beckermann, C., Fainberg, J., Schaefer, W., and Bodenburg, M., "Modelling Approach and Challenges in Simulating Dross Formation in Ductile Iron Castings," Materials Science Forum, Vol. 925, 2018, pp. 419-426.

160. Hardin, R.A., and Beckermann, C., "Heat Transfer and Solidification Modeling of Continuous Steel Slab Casting," in Proceedings of the 2nd International Symposium on the Recent Developments in Plate Steels, Association for Iron & Steel Technology (AIST), Warrendale, PA, 2018, pp. 21-31.

161. Khalajzadeh, V., and Beckermann, C., "Advanced Modeling of Shrinkage Porosity and Application to Mn-Steel Castings," in Proceedings of the 72nd SFSA Technical and Operating Conference, Paper No. 5.7, Steel Founders' Society of America, Chicago, IL, 2018.

162. Galles, D., Lu, J., and Beckermann, C., "Determination of Pattern Allowances for a Distorted Steel Casting Using an Inverse Elastoplastic Analysis," in Proceedings of the 72nd SFSA Technical and Operating Conference, Paper No. 5.8, Steel Founders' Society of America, Chicago, IL, 2018.

163. Archer, L., Guerra, F.V., and Beckermann, C., "Measurement of Air Entrainment During Pouring of an Aluminum Alloy," in Shape Casting: 7th International Symposium Celebrating Prof. John Campbell’s 80th Birthday, eds. M. Tiryakioglu, W. Griffiths, and M. Jolly, TMS, Pittsburgh, PA, 2019, pp. 31-43.

164. Poweleit, D., David, D., Grozdanich, R., Hardin, R., Beckermann, C., Bartlett, L., Foley, R., Griffin, J., and Monroe, C., "Naturally Pressurized Gating Systems in Investment Castings," in Proceedings of the 73rd SFSA Technical and Operating Conference, Paper No. 3.6, Steel Founders' Society of America, Chicago, IL, 2019.

165. Ardis, A., Harper, P., Hardin, R., Beckermann, C., Griffin, J., Foley, R., Monroe, C., Poweleit, D., David, D., and Lynch, P., "Mechanical Properties of Test Bars and Castings Sections and an Analysis of the Cost of Equivalent Round Test Bars," in Proceedings of the 73rd SFSA Technical and Operating Conference, Paper No. 3.10, Steel Founders' Society of America, Chicago, IL, 2019.

166. Hardin, R., Beckermann, C., Monroe, R., David, D., and Allyn, B., "Measurements and Predictions of Lower Bound Mechanical Properties of Cast Steels," in Proceedings of the 73rd SFSA Technical and Operating Conference, Paper No. 4.3, Steel Founders' Society of America, Chicago, IL, 2019.

167. Esser, P., Schankies, C., Khalajzadeh, V., and Beckermann, C., "Advanced Modeling of Shrinkage Porosity in Castings," IOP Conf. Series: Materials Science and Engineering, Vol. 861, 2020, 012022 (8 pages).

168. Poweleit, D., Brown, H., David, D., Hardin, R., Beckermann, C., Foley, R., and Griffin, J., "Establishing Lower Bound Properties for Cast Parts," in Proceedings of the 74th SFSA Technical and Operating Conference, Steel Founders' Society of America, Chicago, IL, 2020.

170. Donahue, R., Hardin, R., and Beckermann, C., "Effect of Gating System and Pour Order on Steel Casting Cleanliness," in Proceedings of the 76th SFSA Technical and Operating Conference, Paper No. 3.4, Steel Founders' Society of America, Chicago, IL, 2022.

171. Hardin, R., and Beckermann, C., "Mechanical Properties of Commercial 8630 Q&T Steel Castings: Testing Results Compared to Simulations," in Proceedings of the 76th SFSA Technical and Operating Conference, Paper No. 4.1, Steel Founders' Society of America, Chicago, IL, 2022.