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Predictive Modeling

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Virtual Testing and Predictive Modeling
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Abstract

It is the goal of the aerospace industry to minimize the weight of structural parts without compromising the structural integrity and failure resistance of the systems they comprise. Over the past few years, more attention has been paid to composite materials as a possible solution to the challenges and tradeoffs inherent in aerospace design. In these complex composite materials, high-strength fibers provide reinforcement to polymers so that they become capable of carrying the high environmental and mechanical loads desired. Recently, reinforcing nanoparticles (nanofillers) have shown promise in the aerospace resin materials sector due to their superior mechanical and fatigue properties. In order to improve the interaction of these particles with the “host” matrix, there is a need to functionalize them for better interaction with and within the matrix. This functionalization can be guided and ultimately achieved through the use of multiscale modeling techniques and simulation, as part of a true four dimensional design space (width, height, length and material). These multiscale approaches and simulations necessitate significant computational capability. But, not only do they address the limits of conventional approaches on the number of atoms that can be simulated, but also they serve to address the time and length scales intrinsic in the atomistic approach and bring them more in line with those of the “meso-scopic regime” or real performance space. These hybrid approaches have recently shown success in solving these classes of systems. In the hybrid approach, multiple regions are defined within the configuration; some with direct atomistic interactions; some with detailed interactions defined by quantum mechanical density functional theory or semi-empirical or tight binding theory; still others defined by electrostatic or mechanical linkages; and yet others treated by a bulk or continuum representation. The objective of these methods is to predict material properties of the modified parent material when reinforced with nanoparticles using an aggregating approach, in which there are multiple connect domains of simulation. Algorithmic improvements to all of these approaches, coupled with the increasing speed of computational hardware, are making it possible to perform predictive modeling on ever larger systems. A number of methods are now available that are capable of modeling hundreds of thousands of atoms, and these results can have a significant impact on real-world engineering and failure analysis problems. This work reviews some of the modeling methods currently in use, provides illustrative examples on obtaining mechanical properties through fundamental laws, and discusses multidimensional material and device design. In this section, computational tools are illustrated that are able to bridge the gap between the characteristic time and spatial scales of the nanochemistry and the macro-scale engineering or physics of the aerospace system. Finally, discussions on the prospects for future modeling approaches will be included.

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References

  1. Naturalis Historia (Latin for "Natural History") is an Encyclopedia Written by Pliny the Elder. (circa AD 77), see http://www.unc.edu/awmc/pleiades/bibliography/plinynh.html

  2. R. French and F. Greenaway, Science in the Early Roman Empire: Pliny the Elder, his Sources and Influence, Croom Helm, London, 1986

    Google Scholar 

  3. G.H. Jóhannesson, T. Bligaard, A.V. Ruban, H.L. Skriver, K.W. Jacobsen, and J.K. Nørskov, “Combined Electronic Structure and Evolutionary Search Approach to Materials Design,” Phys. Rev. Lett., Vol. 88, 2002, p. 255506

    Article  Google Scholar 

  4. C.R.A. Catlow, S.A. French, A.A. Sokoland, and J.M. Thomas, “Computational Approaches to the Determination of Active Site Structures and Reaction Mechanisms in Heterogeneous Catalysts,” Phil. Trans. R. Soc. A, Vol. 363, 2005, pp. 913–936

    Article  Google Scholar 

  5. J.T. Wescott, Y. Qi, L. Subramanian, and T.W. Capehart, “Mesoscale Simulation of Morphology in Hydrated Perfluorosulfonic Acid Membranes,” J. Chem. Phys. Vol. 124, 2006, pp. 134702

    Article  Google Scholar 

  6. D.P. Woodruff, J. Robinson, “Some Structural Issues in Surface Alloys and Alloy Surfaces: Rumpling, Stacking Faults and Disorder,” Appl. Surf. Sci., Vol. 219, 2003, pp. 1–10

    Article  Google Scholar 

  7. L. Junqian, J. Guixiao, and Z. Yongfan, Chem. Eur. J., Vol. 13, No. 22, pp. 6430--6436,2007

    Google Scholar 

  8. J. Vanhellemont and E. Simeon, “Brother Silicon, Sister Germanium,” J. Electrochem. Soc., Vol. 154, 2007, pp. H572–H583,

    Article  Google Scholar 

  9. E. Schrödinger, “Die Gegenwärtige Situation in der Quantenmechanik,” Naturwissenschaften, Vol. 23, 1935, pp. 807–812, 823–828, 844–849

    Article  Google Scholar 

  10. L.A. Curtiss and K. Raghavachari, In: Computational Thermochemistry, K.K. Irikura and D.J. Frurip, Eds., ACS Symposium Series 677, American Chemical Society, Washington D.C., 1998, pp. 176–197

    Google Scholar 

  11. Frontiers in Chemical Engineering: Research Needs and Opportunities, By National Research Council, National Research Council (U.S.). Committee on Chemical Engineering Frontiers: Research Needs and Opportunities, Published by National Academies Press, 1988.

    Google Scholar 

  12. R.D. Cramer, “De Novo Design and Synthetic Accessibility,” J. Comput. Aided Mol. Des., Vol. 21, 2007, pp. 307–309, 309, 123

    Article  Google Scholar 

  13. M. Hassan, “Optimization and Visualization of Molecular Diversity of Combinatorial Libraries,” Mol. Divers., Vol. 2, 1996, pp. 1–2

    Article  MathSciNet  Google Scholar 

  14. Q. Yan, J. Wu, G. Zhou, W. Duan, and B.L. Gu, “Ab Initio Study of Transport Properties of Multiwalled Carbon Nanotubes,” Phys. Rev. B, Vol. 72, 2005, p. 155425

    Article  Google Scholar 

  15. DARPA-AIM (Accelerated Insertion of Materials) Initiative, (http://www.darpa.mil/dso/thrust/matdev/aim/index.html)

  16. E.O. Hall, “The Hall-Petch Relationship,” Proc. Phys. Soc. Ser. B, Vol. 64, 1951, pp. 747–753

    Article  Google Scholar 

  17. N.J. Petch, “Cleavage Strength of Polycrystals,” J. Iron. Phys., Vol. 12, 1948, pp. 186–232

    Google Scholar 

  18. A.A. Griffith, “Phenomena of Rupture and Flow in Solids,” Phil. Trans. Roy. Soc. Ser. A, Vol. 221, 1920, pp. 163–198

    Article  Google Scholar 

  19. L. Christodoulou (DARPA DSO), “Accelerated Insertion of Materials (AIM)”: Presentation at the Committee on Integrated Computational Materials Engineering, http://www7.nationalacademies.org/nmab/CICME_home_page.html

  20. L. Liu, K.W. Bai, H. Gong, and P. Wu, “Digital Materials Design: Computational Methodologies as a Discovery Tool,” Chem. Mater., Vol. 17, No.22, 2005, p. 5529

    Article  Google Scholar 

  21. H. Jin and P. Wu, “Decreasing the Hydrogen Desorption Temperature of LiNH2 Through Doping: A First-Principles Study,” Appl. Phys. Lett., Vol. 87, 2005, p. 81917

    Google Scholar 

  22. L. Liu, K. Bai, H. Gong, and P. Wu, “First-Principles Study of Sn and Ca Doping in CuInO2,” Phys. Rev. B., Vol. 72, 2005, p. 125204

    Article  Google Scholar 

  23. Feynman, “There’s Plenty of Room at the Bottom,” R.P. Eng. Sci., Vol. 23, 1960, p. 22

    Google Scholar 

  24. R. B. Thomson, V. Ginzburg, M.W. Matsen, and A.C. Balazs, “Predicting the Mesophases of Copolymer-Nanoparticle Composites,” Science, Vol. 292, 2001, p. 2469

    Article  Google Scholar 

  25. Y. Lin, A. Baker, J. He, K. Sill, H. Xiang, C. Abetz, X. Li, J. Wang, T. Emrick, S. Long, Q. Wang, A. Balazs, and T.P. Russell, “Self-Directed Self-Assembly of Nanoparticle/Copolymer Mixtures,” Nat. London, Vol. 434, No. 5, 2005, p. 55–59

    Article  Google Scholar 

  26. J. Lee, Z. Shou, and A. Balazs, “Modeling the Self-Assembly of Copolymer-Nanoparticle Mixtures Confined between Solid Surfaces,” Phys. Rev. Lett., Vol. 91, 2003, p. 136103.

    Article  Google Scholar 

  27. J. Wescott, P. Kung, and A. Maiti, “Conductivity of Carbon Nanotube Polymer Composites,” Appl. Phys. Lett., Vol. 90, 2007, p. 033116

    Article  Google Scholar 

  28. “Chemical Industry Vision2020 Technology Partnership Chemical Industry R&D Roadmap for Nanomaterials By Design: From Fundamentals to Function, 2003, http://www.chemicalvision2020.org/pdfs/nano_roadmap.pdf

  29. IMechE Experts Meeting on Nanotechnology, “NANOTECHNOLOGY The Science, Applications, Economic Impact, Way Forward,” Institution of Mechanical (IMechE): 2004, http://www.amgimanagement.com/pdf/IMechENanoBrochV92_Schedule.pdf

  30. J. Andzelm, A.E. Alvarado-Swaisgood, F.U. Axe, M.J. Doyle, G. Fitzgerald, C.M. Freeman, A.M. Gorman, J.-R. Hill, C.M. Kölmel, S.M. Levine, P.W. Saxe, K. Stark, L. Subramanian, M.A. van Daelen, E. Wimmer, and J.M. Newsam, “Heterogeneous Catalysis: Looking Forward with Molecular Simulation,” Catalysis Today, Vol. 50 No. 3–4, (12, May 1999), pp. 451–477

    Article  Google Scholar 

  31. R. Vaia and E.P. Giannelis, ``Polymer Nanocomposites: Status and Opportunities,’ pp. 394--401, MRS Bulletin Vol. 26, No. 5, May 2001

    Google Scholar 

  32. R. Shah, M.C. Payne, M. Lee, and J. Gale, “Understanding the Catalytic Behavior of Zeolites: A First-Principles Study of the Adsorption of Methanol,” Science, Vol. 271, No. 5254, 1996, pp. 1395–1397

    Article  Google Scholar 

  33. P.C. LeBaron, Z. Wang, and T.J. Pinnavaia, ``Polymer-layered Silicate Nanocomposites: An Overview’, Appl. Clay Sci., Vol. 15, No. 1--2, September 1999, pp.11--29

    Google Scholar 

  34. Q. Huo, D. Margolese, U. Ciesla, D.G. Demuth, P. Feng et al., “Organization of Organic-Molecules with Inorganic Molecular-Species into Nanocomposite Biphase ArrayS,” Chem. Mater., Vol. 6, 1994, p. 1176

    Article  Google Scholar 

  35. D.A. Drabold, S. Nakhmanson, and X. Zhang, “Electronic Structure of Amorphous Insulators and Photo Structural Effects in Chalco-genide Glasses,” Properties and Applications of Amorphous Materials, M. Thorpe and L. Tichy, Eds., NATO Science Series, II. Mathematics, Physics and Chemistry, Vol 9, 2001, pp. 221–250 Kluwer

    Chapter  Google Scholar 

  36. Kawasumi, Masaya et.al., US Patent 4810734 A

    Google Scholar 

  37. http://www.accelrys.com/reference/cases/studies/nanocomposites.html

  38. J.D. Gale and Z. Kristallogr, ``GULP: Capabilities and Prospects,’ Z. Kristallogr., Vol. 220, pp. 552--554, 2005.

    Google Scholar 

  39. A. Maiti, J. Wescott, and P. Kung, “Nanotube–Polymer Composites: Insights from Flory–Huggins Theory and Mesoscale Simulations,” Mol. Simul., Vol. 31, 2005, p. 143

    Article  Google Scholar 

  40. P. Haynes, C.-K. Skylaris, A. Mostofi, and M.C. Payne, “Elimination of Basis Set Superposition Error in Linear-Scaling Density-Functional Calculations with Local Orbitals Optimised in Situ,” Chem. Phys. Lett., Vol. 422, 2006, pp. 345–349

    Article  Google Scholar 

  41. http://www.accelrys.com/reference/cases/studies/nanocomposites2.html

  42. M. Lane, “Interface Fracture,” Annu. Rev. Mater. Res., Vol. 33, 2003, pp. 29–54

    Article  Google Scholar 

  43. M. Lane, R. Dauskardt, A. Vainchtein, and H. Gao, “Plasticity Contributions to Interface Adhesion in Thin-Film Inter-connect Structures,” J. Mater. Res., Vol. 15, 2000, pp. 2758–2769

    Article  Google Scholar 

  44. A. Chaka, J. Harris, and X.-P. Li, “Copper Corrosion Mechanisms of Polysulfides,” Mater. Res. Soc. Symp. Proc., Vol. 492, 1998, pp. 219–230

    Article  Google Scholar 

  45. T. Hong, J.R. Smith, and D.J. Srolovitz, “Metal-Ceramic Adhesion and the Harris Functional,” Phys. Rev., Vol. B47, 1993, p. 13615

    Google Scholar 

  46. L. Mishnaevsky, Damage and Failure of Materials: Concepts and Methods of Modeling, Wiley Interscience, 2007

    Google Scholar 

  47. D. Xu, C.Y. Hui, and E.J. Kramer, “The Role of Interfacial Interactions and Loss Function of the Adhesive in Polymer Adhesion by Us-ing Model Adhesives,” J. Appl. Phys., Vol. 72, No. 8, 3305, 1992, pp. 3294–3304

    Article  Google Scholar 

  48. F. Saulnier, T. Ondarcuhu, A. Aradian, and E. Raphael, “Adhesion Between a Viscoelastic Material and a Solid Surface,” Macromol., Vol. 37, 2004, pp. 1067–1075

    Article  Google Scholar 

  49. Q. Yao and J. Qu, "Interfacial Versus Cohesive Failure on Polymer-Metal Interface- Effects of Interface Roughness,” J. Elec-tron. Packaging, Vol. 124, 2002, pp. 127–134

    Google Scholar 

  50. A. Fedorov, R. van Tuijm, W. Vellinga, and J.Th.M. De Hosson, “Degradation and Recovery of Adhesion Properties of Deformed Metal–Polymer Interfaces Studied by Laser Induced Delamina-tion,” Prog. Org. Coat., Vol. 58, 2007, pp. 180–186

    Article  Google Scholar 

  51. R. van Tijum, W.P. Vellinga, and J.Th.M. De Hosson, “Effects of Self-Affine Surface Roughness on the Adhesion of Metal-Polymer Interfaces,” J. Mater. Sci., Vol. 42, 2007, pp. 3529–3536

    Google Scholar 

  52. M. van den Bosch, P. Schreurs, and M. Geers, “A Cohesive Zone Model with a Large Displacement Formulation Accounting for Interfa-cial Fibrillation,” Eur. J. Mech., Vol. 26, No. 1, 2007, pp. 1–19

    MATH  Google Scholar 

  53. R. van Tijum, W. Vellinga, and J.Th.M. De Hosson, “Adhesion Along Metal–Polymer Interfaces During Plastic Deformation,” J. Mater. Sci., Vol. 42, 2007, pp. 3529–3536

    Google Scholar 

  54. C.-K. Skylaris, O. Die´guez, P. Haynes, and M.C. Payne, “Comparison of Variational Real-Space Representations of the Ki-netic Energy Operator,” Phys. Rev. B, Vol. 66, 2002, p. 073103

    Article  Google Scholar 

  55. I. Daniel and O. Ishai, Engineering Mechanics of Composite Materi-als, Oxford University Press, New York, 1994

    Google Scholar 

  56. S.A. Michel, R. Kieselbach, and M.H. Jorg,. “Fatigue Strength of Carbon Fibre Composites up to the Gigacycle Regime (Gigacy-cle-Composites),” Int. J. Fatigue 2006, pp. 28261–28270

    Google Scholar 

  57. S. Pekker, J. Salvetat, E. Jakab, J. Bonard, and L. Forro, “Hydrogenation of Carbon Nanotubes and Graphite in Liquid Ammonia,” J. Phys. Chem. B, Vol. 105, 2001, p. 7938

    Article  Google Scholar 

  58. N. Chandra and H. Ghonem, “Interfacial Mechanics of Push-Out Tests: Theory and Experiments,” Compos. Part A Appl. Sci. Manuf., Vol. 32, No. 3–4, 2001, pp. 575–584

    Article  Google Scholar 

  59. A.B. Dalton, S. Collins, E. Muñoz, J.M. Razal, V.H. Ebron, J.P. Ferraris, J.N. Coleman, B.G. Kim, and R.H. Baughman, “Super-tough carbon-nanotube fibres,” Nature, Vol. 423, 2003, p. 703

    Google Scholar 

  60. J. Suhr, W. Zhang, P. Ajayan, and N. Koratkar, “Temperature-Activated Interfacial Friction Damping in Carbon Nanotube, Polymer Composites,” Nano Lett., Vol. 6, 2006, pp. 219–223

    Article  Google Scholar 

  61. D.R. Askeland, “The Science and Engineering of Materials,” 3rd edn., PWS Publishing, Boston, MA, 1994

    Google Scholar 

  62. J. Kong, N. Franklin, C. Zhou, M. Chapline, S. Peng, K. Cho, and H. Dai, “Nanotube Molecular Wires as Chemical Sensors,” Science, Vol. 287, 2000, p. 622

    Article  Google Scholar 

  63. G. Hansen, “The Roles of Nanostrands and Nickel Coated Fibers in Electrically Conductive Composite Design,” SAMPE J., Vol. 41, No. 2, 2005, p. 24

    Google Scholar 

  64. H. Koerner, W. Liu, M. Alexander, P. Mirau, H. Dowty, and R. Vaia, “Deformation-Morphology Correlations in Electrically Conductive Carbon Nanotube-Thermoplastic Polyurethane Nanocomposites,” Polymer, Vol. 46, No. 12, 2005, pp. 4405–4420

    Article  Google Scholar 

  65. The talk that Richard Feynman gave on December 29th 1959 at the annual meeting of the American Physical Society at the California Institute of Technology (Caltech) was first published in the February 1960 issue of Caltech’s Engineering and Science, which owns the copyright. It has been made available on the web at http://www.zyvex.com/nanotech/feynman.html with their kind permission, 1959

  66. R. Car and M. Parrinello, “Unified Approach for Molecular Dynamics and Density Functional Theory,” Phys. Rev. Lett. Vol. 55, 1985, pp. 2471–2474

    Article  Google Scholar 

  67. T.D. Kuhne, M. Krack, F. Mohamed, and M. Parrinello, “Efficient and Accurate Car-Parrinello-Like Approach to Born-Oppenheimer Molecular Dynamics,” Phys. Rev. Lett., Vol. 98, 2007, p. 066401

    Article  Google Scholar 

  68. J. Mackerle, “Coatings and Surface Modification Tech-nologies: A Finite Element Bibliography (1995–2005),” Modell. Simul. Mater. Sci. Eng., Vol. 13, 2005, p. 123

    Article  Google Scholar 

  69. Information and Communications Technologies Inter-Enterprise Computing: “The Materials Grid Project” http://www.technologyprogramme.org.uk/site/publicRpts/default.cfm?subcat=publicRpt3&ProjID=4E46

  70. Modelling and Informatics Explained : www.computenano.com

  71. W. Martin, J.R. Fuhr, D. Kelleher, A. Musgrove, J. Sugar, W.L. Wiese, P.J. Mohr, and K. Olsen, NIST Atomic Spectra Database (Version 2.0) (1999) and Version 3.0-Beta (October 2004)

    Google Scholar 

  72. M.D. Giles, TCAD Challenges in the Nanotechnology Era, Osaka University, Osaka, 2005

    Google Scholar 

  73. C.-K. Skylaris, P.D. Haynes, A.A. Mostofi, and M.C. Payne,``Introducing ONETEP: Linear-Scaling Density Functional Simulations on Parallel Computers’ J. Chem. Phys. 122, p. 084119, 2005

    Google Scholar 

  74. P. Sherwood, A.H. de Vries, M.F. Guest, G. Schreckenbach, C.R.A. Catlow, S.A. French, A.A. Sokol, S.T. Bromley, W. Thiel, A.J. Turner, S. Billeter, F. Terstegen, S. Thiel, J. Kendrick, S.C. Rogers, J. Casci, M. Wat-son, F. King, E. Karlsen, M. Sjovoll, A. Fahmi, A. Schaefer, and C.J. Lennartz, “QUASI: A General Purpose Implementation of the Qm/Mm Approach and its Application to Problems in Catalysis,” Theo-chem-J. Mol. Struct., Vol. 632, 2003, pp. 1–28

    Article  Google Scholar 

  75. J. Aboudi, “Mechanics of Composite Materials: A Unified Micromechanical Approach” Elsevier, Amsterdam, 1991

    Google Scholar 

  76. J.D. Eshelby, “The Determination of the Elastic Field of an Ellipsoidal Inclusion,” Proc. R. Soc. London A, Vol. 241, 1957, p. 376

    Article  MathSciNet  MATH  Google Scholar 

  77. Z. Hashin and B.W. Rosen, “The Elastic Moduli of Fiber-Reinforced Materials," J. Appl. Mech., Vol. 31, 1964, p. 223

    Article  Google Scholar 

  78. R.B. Pipes and P. Hubert II, “Helical Carbon Nanotube Arrays: Mechanical Properties,” Compos. Sci. Technol., Vol. 62, 2002, p. 419

    Article  Google Scholar 

  79. R.B. Pipes and P. Hubert II, “Comparison of Two Models of SWCN Polymer Composites,” Compos. Sci. Technol., Vol. 63, 2003, p. 1571

    Article  Google Scholar 

  80. G. Odegard, T. Gates, K. Wise, C. Park, and E.J. Siochi II, “Constitutive Modeling of Nanotube-Reinforced Polymer Composites,” Compos. Sci. Technol., Vol. 63, 2003, p. 1671

    Article  Google Scholar 

  81. E.T. Thostenson and T.W. Chou II, “On the Elastic Properties of Carbon Nanotube-Based Composites: Modeling and Characterization,” J. Phys. Appl. Phys., Vol. 36, 2003, p. 573

    Google Scholar 

  82. D. Lagoudas and G. Seidal, In: American Institute of Aeronautics and Astronautics Conference, Palm Springs, CA, 2004

    Google Scholar 

  83. http://www.nist.gov/srd/materials.htm

  84. http://www.matweb.com/

  85. http://pubs3.acs.org/journals/aamick/index.html

  86. http://www.grantadesign.com/

  87. D.F. Adams, “Inelastic Analysis of a Unidirectional Com-posite Subjected to Transverse Normal Loading”, J. Compos. Mater., Vol. 4, 1970, p. 310

    Article  Google Scholar 

  88. T.J.R Huges, Programming the Finite Element Method, Dover Pubs. 2002

    Google Scholar 

  89. X.L. Chen and Y.J. Liu, “Square Representative, Volume Elements for Evaluating the Effective Material Properties of Carbon Nano-tube-Based Composites,” Comput. Mater. Sci., Vol. 29, No. 1, 2004, pp. 1–11

    Google Scholar 

  90. C.Y. Li and T.W. Chou, “A Multiscale Modeling of the Interfacial Load Transfer in Carbon Nanotube/Polymer Composites,” J. Nanosci. Nanotechnol., Vol. 3, 2003, p. 423

    Article  Google Scholar 

  91. R. Bradshaw, F. Fisher, and L. Brinson, “Fiber Waviness in Nanotube-Reinforced Polymer Composites: II. Modelling Via Numerical Approximation of the Dilute Strain Concentration Tensor,” Compos. Sci. Technol., Vol. 63, No. 11, 2003, pp. 1705–1722

    Article  Google Scholar 

  92. F.T. Fisher, R.D. Bradshaw, and L.C. Brinson, “Effects of Nanotube Waviness on the Modulus of Nanotube-Reinforced Polymers,” Appl. Phys. Lett., Vol. 80, No. 24, 2002, pp. 4647–4649

    Article  Google Scholar 

  93. J. Fish and W. Chen, “RVE Based Multilevel Method for Periodic Heterogeneous Media with Strong Scale Mixing," J. Appl. Math., Vol. 46, 2003, pp. 87–106

    MathSciNet  MATH  Google Scholar 

  94. Y.J. Liu, N. Nishimura, Y. Otani, T. Takahashi, X.L. Chen, and H. Munakata, “A Fast Boundary Element Method for the Analysis of Fiber-Reinforced Composites Based on a Rigid-Inclusion Model,” ASME J. Appl. Mech., Vol. 72, No. 1, 2005, pp. 115–128

    Article  MATH  Google Scholar 

  95. S.A. Ospina, J. Restrepo, and B.L. Lopez, “Deformation of Polyethylene: Monte Carlo Simulation,” Mater. Res. Innovations, Vol. 7, 2003, p. 27

    Google Scholar 

  96. M.S. Ingber and T.D. Papathanasiou, "A Parallel-Supercomputing Investigation of the Stiffness of Aligned, Short-Fiber-Reinforced Composites using the Boundary Element Method," Int. J. Numer. Methods Eng., Vol. 30, 1997, pp. 3477–3491

    Article  Google Scholar 

  97. K.B. Lipkowitz and D.B. Boyd, “Preface on the Meaning and Scope of Computational Chemistry,” In: Reviews in Computational Chemistry, K.B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, Vol. 1, 1990, pp. vii–xii.

    Chapter  Google Scholar 

  98. J.P. Bowen and N.L. Allinger, “Molecular Mechanics: The Art and Science of Parameterization,” In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 2, 1991, pp. 81–97

    Chapter  Google Scholar 

  99. U. Dinur and A.T. Hagler, “New Approaches to Empirical Force Fields Reviews in Computational Chemistry,” In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 2, 1991, pp. 99–164

    Chapter  Google Scholar 

  100. R. Keunings,``Micro-Macro Methods for the Multiscale Simulation of Viscoelastic Flow Using Molecular Models of Kinetic Theory’, In: Rheology Reviews 2004, D.M. Binding and K. Walters, Eds., British Society of Rheology, pp. 67--98, 2004

    Google Scholar 

  101. D.B. Boyd, “Successes of Computer-Assisted Molecular Design,” In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 1, 1990, pp. 355–371

    Chapter  Google Scholar 

  102. Z. Slanina, S.-L. Lee, and C.-h. Yu, In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 8, 1996, pp. 1–62

    Google Scholar 

  103. D. Yang and A. Rauk, In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 7, 1995, pp. 261–301

    Google Scholar 

  104. Z. Slanina, S.-L. Lee, and C.-h. Yu, In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 8, 1996, pp. 1–62

    Google Scholar 

  105. M.V. Koudriachova, N.M. Harrison, and S.W. de Leeuw, “Density-Functional Simlations of Lithium Intercalation in Rutile,” Phys. Rev. B, Vol. 65, 2002, p. 235423

    Article  Google Scholar 

  106. R.A. Kendall, R.J. Harrison, R.J. Littlefield, and M.F. Guest, In: Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, Eds., VCH Publishers, New York, Vol. 6, 1995, pp. 209–316

    Google Scholar 

  107. J. Vrabec, M. Horsch, and H. Hasse, “Molecular Models of Hydrogen Bonding Fluids: Development and Validation Using Thermo-dynamic and NMR-Data,” Thermodynamics, 26, 28, 09, Rueil-Malmaison, France, 2007.

    Google Scholar 

  108. C.-K. Skylaris, P.D. Haynes, A.A. Mostofi, and M.C. Payne, “Using ONETEP for Accurate and Efficient O(N) Density Functional Calculations,” J. Phys. Condens. Matter., Vol. 17, 2005, pp. 5757–5769

    Article  Google Scholar 

  109. C.-K. Skylaris, P.D. Haynes, A.A. Mostofi, and M.C Payne, “Introducing ONETEP: Linear-Scaling Density Functional Simulations on Parallel Computers,” J. Chem. Phys., Vol. 122, 2005, p. 084119

    Article  Google Scholar 

  110. Y.S. Lee, S.A. Kucharski, R.J. Bartlett, “Coupled Cluster Approach with Triple Excitations,” J. Chem. Phys., Vol. 81, 1984, pp. 5906–5912

    Article  Google Scholar 

  111. Paul von Ragué Schleyer (Editor-in-Chief), Encyclopedia of Computational Chemistry. Wiley, 1998. ISBN 0-471-96588-X.

    Google Scholar 

  112. NIST Computational Chemistry Comparison and Benchmark Data Base – Contains a database of thousands of computational and experimental results for hundreds of systems.

    Google Scholar 

  113. “CSTB report Mathematical Research in Materials Sci-ence: Opportunities and Perspectives – CSTB Report,” http://books.nap.edu/openbook.php?record_id=2206&page=R1

  114. F. Starrost and E.A. Carter, "Modeling the Full Monty: Baring the Nature of Surfaces Across Time and Space," Surf. Sci. Millenium Issue, Vol. 500, 2002, p. 323

    Google Scholar 

  115. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clif-ford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Ko-maromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, and J.A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004

    Google Scholar 

  116. V. Milman and B. Winkler, “Ab Initio Modeling in Crys-tallography,” Int. J. Inorg. Mater., Vol. 10, 1999, pp. 273–279

    Article  Google Scholar 

  117. Y. Le Page, P.W. Saxe, J.R. Rodgers, “Symmetry-General Ab Initio Computation of Physical Properties Using Quantum Software Integrated with Crystal Structure Databases: Results and Perspectives,” Acta Cryst. B, Vol. 58, 2002, pp. 349–357

    Article  Google Scholar 

  118. G. Kresse and J. Furthmuller, “Efficiency of Ab-Initio To-tal Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set,” J. Comput. Mater. Sci., Vol. 6, 1996, p. 15

    Article  Google Scholar 

  119. M.C. Zerner, G.H. Loew, R.F. Kirchner, and U.T. Mueller-Westerhoff, “An Intermediate Neglect of Differential Overlap Technique for Spectroscopy of Transition-Metal Complexes. Ferro-cene,” J. Am. Chem. Soc., Vol. 102, 1980, pp. 589–599

    Article  Google Scholar 

  120. W.G. Schmidt, K. Seino, P.H. Hahn, F. Bechstedt, W. Lub, S. Wang, and J. Bernholc, “Calculation of Surface Optical Properties: From Qualitative Understanding to Quantitative Predictions,” Thin Solid Films, Vol. 455–456, 2004, pp. 764–771

    Article  Google Scholar 

  121. J.M. Thomas, “Computational Approaches to the Determination of Active Site Structures and Reaction Mechanisms in Heterogeneous Catalysts,” Phil. Trans. R. Soc. A, Vol. 363, 2005, pp. 913–936

    Article  Google Scholar 

  122. R.G. Parr and W. Yang, “Density Functional Theory of Atoms and Molecules,” Oxford University Press, New York, 1989

    Google Scholar 

  123. J.L. Fattebert and F. Gygi, “Theme Article – Realistic Modeling of Nanostructures Using Density Functional The-ory,” Computer Phys. Commun., Vol. 162, 2004, p. 24

    Article  Google Scholar 

  124. D. Alfe, “First-Principles Simulations of Direct Coexistence of Solid and Liquid Aluminum,” Phys. Rev. B, Vol. 68, 2003, p. 064423

    Article  Google Scholar 

  125. K. Mylvaganam and L.C. Zhang, “Ballistic Resistance Capacity of Carbon Nanotubes,” Nanotechnol., Vol. 18, 2007, p. 475701

    Article  Google Scholar 

  126. K. Mylvaganam and L.C. Zhang, “Deformation-Promoted Reactivity of Single-Walled Carbon Nanotubes”, Nanotechnol., Vol. 17, 2006, p. 410

    Article  Google Scholar 

  127. M.J.S. Dewar, E.G. Zoebisch. E.F. Healy, and J.J.P. Stewart, “AM1: A New General Purpose Quantum Mechanical Model,” J. Am. Chem. Soc., Vol. 107, 1985, pp. 3902–3909

    Article  Google Scholar 

  128. J.J.P. Stewart, “Calculation of the Geometry of a Small Protein Using Semiempirical Methods,” J. Mol. Struct. Theochem., Vol. 401, 1997, pp. 195–205

    Article  Google Scholar 

  129. Y.G. Yanovsky, “Multiscale Modeling of Polymer Com-posite Properties from Nano- to Macro,” J. Cent. S. Univ. Technol. Vol. 14(Supplement 1/February), 2007, pp. 38–42

    Article  Google Scholar 

  130. A.P. Horsfield and A.M. Bratkovsky, “Ab Initio Tight Binding,” J. Phys. Condens. Matter., Vol. 12, 2000, pp. R1–R24

    Article  Google Scholar 

  131. M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, Th. Frauenheim, S. Suhai, and G. Seifert, “Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Materials Properties,” Phys. Rev. B, Vol 58, 1998, pp. 7260–7268

    Article  Google Scholar 

  132. M. Elstner, T. Frauenheim, J. McKelvey, and G. Seifert, “Density Functional Tight Binding: Contributions from the American Chemical Society Symposium,” J. Phys. Chem. A, Vol. 111, 2007, pp. 5607–5608

    Article  Google Scholar 

  133. S. Mayo, B. Olafson, and W. Goddard III, “DREIDING: A Generic Force Field for Molecular Simulations,” J. Phys. Chem., Vol. 94, 1990, p. 8897

    Article  Google Scholar 

  134. H. Sun, “COMPASS: An ab Initio Forcefield Optimized for Condensed-Phase Applications – Overview with Details on Alkane and Benzene Compounds,” J. Phys. Chem. B, Vol. 102, 1998, pp. 7338–7364

    Article  Google Scholar 

  135. D.W. Brenner, “Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films,” Phys. Rev. B, Vol. 42, 1990, p. 9458

    Article  Google Scholar 

  136. O.A. Shenderova, V. Zhirnov, and D.W. Brenner, “Carbon Materials and Nanostructures,” Crit. Rev. Solid State Mater. Sci., Vol. 32, 2002, p. 347.

    Google Scholar 

  137. P.M. Axilrod and E. Teller, “Interaction of the Van Der Waals Type Between Three Atoms,” J. Chem. Phys., Vol. 11, 1943, pp. 299–300

    Article  Google Scholar 

  138. J.I. Siepmann, S. Karaborni, and B. Smit, “Simulating the Critical Behaviour of Complex Fluids,” Nature, Vol. 365, 1993, p. 330

    Article  Google Scholar 

  139. P. Dauber-Osguthorpe, V.A. Roberts, D.J. Osguthorpe, J. Wolff, M. Genest, and A.T. Hagler, “Structure and Energetics of Ligand Binding to Proteins: E. Coli Dihydrofolate Reductase-Trimethoprim, A Drug-Receptor System,” Proteins Struct. Funct. Genet., Vol. 4, 1988; pp. 31–47

    Article  Google Scholar 

  140. J.M. Thomas, “Computational Approaches to the Determination of Active Site Structures and Reaction Mechanisms in Heterogeneous Catalysts,” Phil. Trans. R. Soc. A, Vol. 363, 2005, pp. 913–936

    Article  Google Scholar 

  141. J.-R. Hill, C.M. Freeman, and L. Subramanian, “Use of Force Fields in Materials Modeling,” Rev. Comput. Chem., Vol. 16, 2000, pp. 141–216

    Article  Google Scholar 

  142. M.J. McQuaid, H. Sun, and D. Rigby, "Development and Validation of COMPASS Force Field Parameters for Molecules with Aliphatic Azide Chains,” J. Comp. Chem., Vol. 25, 2003, pp. 61–71.

    Article  Google Scholar 

  143. D. Rigby, H. Sun, and B.E. Eichinger, "Computer Simulations of Poly(Ethylene Oxide): Force Field, PVT Diagram and Cyclization Behaviour,” Polym. Int., Vol. 44, 1997, pp. 311–330

    Google Scholar 

  144. J.M. Briggs, T.B. Nguyen, and W.L. Jorgensen, “Monte Carlo Simulations of Liquid Acetic Acid and Methyl Acetate with the OPLS Potential Functions,” J. Phys. Chem., Vol. 95, 1991, p. 315

    Article  Google Scholar 

  145. S.Y. Jiang et al., “Structures, Vibrations, and Force Fields of Dithiophosphate Wear Inhibitors from Ab Initio Quantum Chemistry,” J. Phys. Chem., Vol. 100, 1996, pp. 15760–15769

    Article  Google Scholar 

  146. A.D.MacKerell Jr., B. Brooks, C.L. Brooks III, L. Nilsson, B. Roux, Y. Won, and M. Karplus, “CHARMM: The Energy Function and Its Parameterization with an Overview of the Program,” In: P. v. R. Schleyer (ed.) The Encyclopedia of Computational Chemistry, Wiley, New York, 1998, pp. 271–277

    Google Scholar 

  147. W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz Jr., D.M. Ferguson, D.C. Spellmeyer, T. Fox, J.W. Caldwell, and P.A. Kollman, "A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules,” J. Am. Chem. Soc., Vol. 117, 1995, pp. 5179–5197

    Article  Google Scholar 

  148. J. Gale and A.L. Rohl, “The General Utility Lattice Program,” Mol. Simul., Vol. 29, 2003, pp. 291–341

    Article  MATH  Google Scholar 

  149. P. Ewald, “Die Berechnung Optischer Und Elektrostatischer Gitterpotentiale,” Ann. Phys., Vol. 64, 1921, pp. 253–287

    Article  MATH  Google Scholar 

  150. W.A. Goddard et al., “Simulation and Design of Materials – Applications to Polymers, Ceramics, Semiconductors, and Catalysis,” Abstracts of Papers of the American Chemical Society 208, 391-PHYS, 1994

    Google Scholar 

  151. J. Tersoff, “Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon,” Phys. Rev. Lett., Vol. 61, 1988, p. 2879

    Article  Google Scholar 

  152. F. de Brito Mota, J.F. Justo, and A. Fazzio, “Hydrogen Role on the Properties of Amorphous Silicon Nitride,” J. Appl. Phys., Vol. 86, 1999, p. 1843

    Article  Google Scholar 

  153. D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. Stuart, B. Ni, and S.B Sinnott,., “Second Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression for Hydrocarbons,” J. Phys. Condens. Matter., Vol. 14, 2002, pp. 783–802

    Article  Google Scholar 

  154. A.C.T. van Duin, S. Dasgupta, F. Lorant, and W.A. Goddard III., “ReaxFF: A Reactive Force Field for Hydrocarbons,” J. Phys. Chem. A, Vol. 105, 2001, pp. 9396–9409

    Article  Google Scholar 

  155. M.J. Cheng, K. Chenoweth, J. Oxgaard, A.C.T. van Duin, and W.A. Goddard, "The Single-Site Vanadyl Activation, Functionalization, and Re-oxidation Reaction Mechanism for Propane Oxidative Dehydrogenation on the Cubic V4O10 Cluster," J. Phys. Chem. B., Vol. 111, 2007, pp. 14440–14440

    Article  Google Scholar 

  156. A.K. Rappe and C.J. Casewit, “Molecular Mechanics Across Chemistry,” University Science Books, California, 1997

    Google Scholar 

  157. D.M. Root, C.R. Landis, and T. Cleveland, “Valence Bond Concepts Applied to the Molecular Mechanics Description of Molecular Shapes. 1. Application to Nonhypervalent Molecules of the P-Block,” J. Am. Chem. Soc., Vol. 115, 1993, pp. 4201–4209

    Article  Google Scholar 

  158. J.L. Suter, P.V. Coveney, H.C. Greenwell, and M. Thyveetil, “Large-Scale Molecular Dynamics Study of Montmorillonite Clay: Emergence of Undulatory Fluctuations and Determination of Material Properties,” J. Phys. Chem. C, Vol. 111, 2007, pp. 8248–8259

    Article  Google Scholar 

  159. C. Moon, P.C. Taylor, and P.M. Rodger, “Molecular Dynamics Study of Gas Hydrate formation,” J. Am. Chem. Soc., Vol. 125, 2003, pp. 4706–4707

    Article  Google Scholar 

  160. J. Ma, Y. Liu, H. Lu, and R. Komanduri, “Multiscale Simulation of Nanoindentation Using the Generalized Interpolation Material Point (GIMP) Method, Dislocation Dynamics (DD) and Molecular Dynamics (MD),” CMES, Vol. 16, 2006, pp. 41–56

    Google Scholar 

  161. A.F. Voter, “Introduction to the Kinetic Monte Carlo Method,” In Radiation Effects in Solids, edited by K.E. Sickafus and E.A. Kotomin, Springer, NATO Publishing Unit, Dordrecht, The Netherlands, 2005

    Google Scholar 

  162. A. Chatterjee and D.G. Vlachos, “An Overview of Spatial Microscopic and Accelerated Kinetic Monte Carlo Methods,” J. Computer-Aided Mater. Des., Vol. 14, 2007, p. 253

    Article  Google Scholar 

  163. C. Chui and M.C. Boyce, "Monte Carlo Modelling of Amorphous Polymer Deformation: Evolution of Stress with Strain," Macromol., Vol. 32, 1999, p. 3795

    Article  Google Scholar 

  164. P. Hoogerbrugge and J. Koelman, “Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics,” Europhys. Lett., Vol. 19, 1992, pp. 155–160

    Article  Google Scholar 

  165. R. Groot and P. Warren, "Dissipative Particle Dynamics: Bridging the Gap Between Atomistic and Mesoscopic Simulation," J. Chem. Phys., Vol. 107, No. 11, 1997, pp. 4423–4435

    Article  Google Scholar 

  166. D. Broseta and G.H. Fredrickson, “Phase Equilibria in Copolymer/Homopolymer Ternary Blends: Molecular Weight Effects,” J. Chem. Phys., Vol. 93, 1990, p. 2927

    Article  Google Scholar 

  167. G. Fredrisckson, “The Equilibrium Theory of Inhomoge-neous Polymers,” Oxford University Press, ISBN-13: 978-0-19-856729-5, 2005

    Google Scholar 

  168. A. Knoll, K. Lyakhova, A. Horvat, G. Krausch, G. Sevink, A. Zvelindovsky, and R. Magerle, “Direct Imaging and Mesoscale Modelling of Phase Transitions in a Nanostructured Fluid,” Nature Mater., Vol. 3, 2004, pp. 886–890

    Article  Google Scholar 

  169. G.M. Odegard, T.S. Gates, K.E. Wise, C. Park, and E.J. Siochi, “Constitutive Modeling of Nanotube-Reinforced Polymer Composites,” Compos. Sci. Tech-nol. Elsevier, Vol. 63, 2003, pp. 1671–1687

    Google Scholar 

  170. W.K. Liu, E.G. Karpov, S. Zhang, and H.S. Park,``An Introduction to Computational Nano Mechanics and Materials, Computer Methods in Applied Mechanics for Nanoscale Mechanics and Materials), 2004

    Google Scholar 

  171. Z. Peng, H. Yonggang, P.H. Geubelle, and H Kehchih, ``On the Continuum Modeling of Carbon Nano-tubes,’ Vol. 18, No. 5, Acta Mechanica Sinica, Elsevier, 2002

    Google Scholar 

  172. C. Sun, B. Kim, and J. Bogdanoff, ``On the Derivation of Equivalent Simple Models for Beam and Plate-Like Structures in Dynamic Analysis’, AIAA/ASME/ASCE/AHS 22nd Structures, Structural Dynamics & Materials Conference, AIAA, pp. 523--532, 1981

    Google Scholar 

  173. P. Valavala and G. Odegard, “Modeling Techniques for Determination of Mechanical Properties of Polymer Nanocomposites," Rev. Adv. Mater. Sci., Vol. 9, 2005, pp. 34–44

    Google Scholar 

  174. S. Frankland and V. Harik , “The Stress–Strain Behavior of Polymer–Nanotube Composites from Molecular Dynamics Simulation,” Compos. Sci. Technol., Vol. 63, 2003, p. 1655

    Article  Google Scholar 

  175. Y. Hu and S. Sinnott II, “Molecular Dynamics Simulations of Polyatomic-Ion Beam Deposition Induced Chemical Modification of Carbon Nanotube/Polymer Composites,” J. Mater. Chem., Vol. 14, 2004, p. 719

    Google Scholar 

  176. D. Srivastava and K. Cho, “Thermal Expansion and Diffusion Coefficients of Carbon Nanotube-Polymer Composites,” Nano Lett., Vol. 2, No. 6, 2002, pp. 647–650

    Google Scholar 

  177. V. Lordiand and N. Yao, “Molecular Mechanics of Binding in Carbon-Nanotube-Polymer Composites,” J. Mater. Res., Vol. 15, 2000, p. 2770

    Article  Google Scholar 

  178. Z. Lianga, J. Goua, C. Zhang, B. Wanga, and L. Kramer, “Investigation of Molecular Interactions Between (10, 10) Single-Walled Nanotube and Epon 862 Resin/DETDA Curing Agent Molecules,” Mater. Sci. Eng. A, Vol. 365, 2004, p. 228

    Article  Google Scholar 

  179. S. Frankland and V. Harik, “Analysis of Carbon Nano-tube Pull-Out from a Polymer Matrix,” Surf. Sci., Vol. 525, No. 1, 2003, pp. L103–L108

    Google Scholar 

  180. A. Maiti, J. Wescott, and G. Goldbeck-Wood, “Mesoscale Modelling: Recent Developments and Applications to Nanocomposites, Drug Delivery and Precipitation Membranes,” Int. J. Nanotechnol., Vol. 2, 2005, pp. 198–214

    Article  Google Scholar 

  181. A.T. Sears, “Carbon Nanotube Mechanics: Continuum Model Development from Molecular Mechanics Virtual Experiments,” Dissertation Submitted to the Faculty of the Virginia Polytechnic Institute and State University for the Degree of Doctor of Philosophy In Department of Engineering Mechanics, 2008.

    Google Scholar 

  182. A. Rahman, “Correlations in the Motion of Atoms in Liquid Argon,” Phys. Rev., Vol. 136, 1964, p. 405

    Article  Google Scholar 

  183. G.E. Moore, “Cramming More Components onto Integrated Circuits," Electronics Magazine, Vol. 38, 1965, pp. 114–117

    Google Scholar 

  184. Zhe Fan, Feng Qiu, Arie Kaufman, Suzanne Yoakum-Stover, “GPU Cluster for High Performance Computing,” ACM / IEEE Supercomputing Conference, Pittsburgh, PA, 2004

    Google Scholar 

  185. “Materials Grid Project” http://www.materialsgrid.org/people.html, 2008

  186. “Pipeline Pilot Enterprise Server”, http://accelrys.com/products/scitegic/platform.html, 2009

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Doyle, M. (2009). Predictive Modeling. In: Farahmand, B. (eds) Virtual Testing and Predictive Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-95924-5_9

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