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References

Published online by Cambridge University Press:  05 June 2012

Ellad B. Tadmor
Affiliation:
University of Minnesota
Ronald E. Miller
Affiliation:
Carleton University, Ottawa
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Chapter
Information
Modeling Materials
Continuum, Atomistic and Multiscale Techniques
, pp. 702 - 745
Publisher: Cambridge University Press
Print publication year: 2011

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References

[AB96] J. E., Angelo and M. I., Baskes. Interfacial studies using the EAM and MEAM. Interface Sci., 4(1–2):47–63, 1996.Google Scholar
[AB02] M., Arroyo and T., Belytschko. An atomistic-based finite deformation membrane for single layer crystalline films. J. Mech. Phys. Solids, 50:1941–1977, 2002.Google Scholar
[AB04] M., Arroyo and T., Belytschko. Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy–Born rule. Phys. Rev. B, 69:115415, 2004.Google Scholar
[ABB96] N. L., Allan, T. H. K., Barron, and J. A. O., Bruno. The zero static internal stress approximation in lattice dynamics, and the calculation of isotope effects on molar volumes. J. Chem. Phys., 105:8300–8303, 1996.Google Scholar
[ABBH00] F. F., Abraham, N., Bernstein, J. Q., Broughton, and D., Hess. Dynamic fracture of silicon: Concurrent simulation of quantum electrons, classical atoms, and the continuum solid. MRS Bull., 25(5):27–32, 2000.Google Scholar
[ABBK98] F. F., Abraham, J.Q., Broughton, N., Bernstein, and E., Kaxiras. Spanning the length scales in dynamic simulation. Comput. Phys., 12:538, 1998.Google Scholar
[ABI09] ABINIT. Abinit website. http://www.abinit.org, 2009.
[ABRT65] N., Aslund, R. F., Barrow, W. G., Richards, and D. N., Travis. Rotational analysis of bands of b-x system of Cu2 and of a-x system of Bi2. Ark. Fys., 30(2):171, 1965.Google Scholar
[AD74] S. A., Adelman and J. D., Doll. Generalized Langevin equation approach for alom/solid-surface scattering – collinear atom/harmonic chain model. J. Chem. Phys., 61(10):4242–4245, 1974.Google Scholar
[AD76] S. A., Adelman and J. D., Doll. Generalized Langevin equation approach for atom–solid-surface scattering – general formulation for classical scattering off harmonic solids. J. Chem. Phys., 64(6):2375–2388, 1976.Google Scholar
[Adk83] C. J., Adkins. Equilibrium Thermodynamics. Cambridge: Cambridge University Press, third edition, 1983.Google Scholar
[AGM+90] S. F., Altschul, W., Gish, W., Miller, E. W., Myers, and D. J., Lipman. Basic local alignment search tool. J. Mol. Biol., 215:403–410, 1990.Google Scholar
[AJ05] M. F., Ashby and D. R. H., Jones. Engineering Materials 1. Oxford: Butterworth-Heinemann, third edition, 2005.Google Scholar
[AK07] M., Aoki and T., Kurokawa. A simple environment-dependent overlap potential and cauchy violation in solid argon. J. Phys. Condens. Matter, 19:236228, 2007.Google Scholar
[AL08] M., Arndt and M., Luskin. Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel–Kontorova model. Multiscale Model. Simul., 7(1):147–170, 2008.Google Scholar
[Alb00] D. Z., Albert. Time and Chance. Cambridge: Harvard University Press, 2000.Google Scholar
[AM76] N. W., Ashcroft and N. D., Mermin. Solid State Physics. Philadelphia: Saunders College, 1976.Google Scholar
[AMB95] J. E., Angelo, N. R., Moody, and M. I., Baskes. Trapping of hydrogen to lattice-defects in nickel. Modell. Simul. Mater. Sci. Eng., 3(3):289–307, 1995.Google Scholar
[And80] H. C., Andersen. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys., 72(4):2384–2393, 1980.Google Scholar
[And94] G., Andrews. Number Theory. New York: Dover Publications, 1994.Google Scholar
[ANMPV07] M., Aoki, D., Nguyen-Manh, D. G., Pettifor, and V., Vitek. Atom-based bond-order potentials for modelling mechanical properties of metals. Prog. Mater. Sci., 52(2–3):154–195, 2007.Google Scholar
[Apo69] T. M., Apostol. Calculus, Volume II. Multi-variable Calculus and Linear Algebra with Applications. New York: Wiley, second edition, 1969.Google Scholar
[AR03] G. J., Ackland and S. K., Reed. Two-band second moment model and an interatomic potential for caesium. Phys. Rev. B, 67(17):174108, 2003.Google Scholar
[ARK+94] J. B., Adams, A., Rockett, J., Kieffer, et al. Atomic-level computer simulation. J. Nucl. Mater., 216:265–74, 1994.Google Scholar
[Arn63] V. I., Arnold. Proof of a theorem by A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Russ. Math. Surv., 18:9–36, 1963.Google Scholar
[Arn89] V. I., Arnold. Mathematical Methods of Classical Mechanics. New York: Springer-Verlag, second edition, 1989.Google Scholar
[Asa83] R. J., Asaro. Crystal plasticity. J. Appl. Mech., 50(4b):921–934, 1983.Google Scholar
[Ash66] N. W., Ashcroft. Electron-ion pseudopotentials in metals. Phys. Lett., 23:48–50, 1966.Google Scholar
[AST09] M., Arndt, V., Sorkin, and E. B., Tadmor. Efficient algorithms for discrete lattice calculations. J. Comput. Phys., 228:4858–4880, 2009.Google Scholar
[AT87] M. P., Allen and D. J., Tildesley. Computer Simulation of Liquids. Oxford: Clarendon Press, 1987.Google Scholar
[AT10] N. C., Admal and E. B., Tadmor. A unified interpretation of stress in molecular systems. J. Elast., 100:63–143, 2010.Google Scholar
[AT11] N. C., Admal and E. B., Tadmor. Stress and heat flux for arbitrary multi-body potentials: A unified framework. J. Chem. Phys, 134:184106, 2011.Google Scholar
[AW57] B. J., Alder and T. E., Wainright. Phase transitions for a hard sphere system. J. Chem. Phys., 27:1208–1209, 1957.Google Scholar
[AW59] B. J., Alder and T. E., Wainright. Studies in molecular dynamics: I. General method. J. Chem. Phys., 31:459–466, 1959.Google Scholar
[AW95] G. B., Arfken and H. J., Weber. Mathematical Methods of Physicists. San Diego: Academic Press, fourth edition, 1995.Google Scholar
[BABK99] J. Q., Broughton, F. F., Abraham, N., Bernstein, and E., Kaxiras. Concurrent coupling of length scales: Methodology and application. Phys. Rev. B, 60(4):2391–2403, 1999.Google Scholar
[Bak39] C. M., Bakewell. Source Book in Ancient Philosophy. New York: Charles Scribner's Sons, revised edition, 1939.Google Scholar
[Bal02] J. M., Ball. Some open problems in elasticity. In P., Holmes, P., Newton and A., Weinstein, editors, Geometry, Mechanics, and Dynamics, Chapter 1, pages 3–59. New York: Springer-Verlag, 2002.Google Scholar
[Bas92] M. I., Baskes. Modified embedded-atom potentials for cubic materials and impurities. Phys. Rev. B, 46(5):2727–2742, 1992.Google Scholar
[Bas94] J. L., Bassani. Plastic-flow of crystals. Adv. Appl. Mech., 30:191–258, 1994.Google Scholar
[BAT10] B., Bar On, E., Altus, and E. B., Tadmor. Surface effects in non-uniform nanobeams: continuum and atomistic modeling. Int. J. Solids Struct., 47:1243–1252, 2010.Google Scholar
[Baž78] Z. P., Bažant. Spurious reflection of elastic waves in nonuniform finite element grids. Comput. Meth. Appl. Mech. Eng., 16:91–100, 1978.Google Scholar
[BBL02] X., Blanc, C., Le Bris, and P.-L., Lions. From molecular models to continuum mechanics. Arch. Ration. Mech. Anal., 164:341–381, 2002.Google Scholar
[BBL+07] S., Badia, P., Bochev, R., Lehoucq, et al. A force-based blending model for atomistic-to-continuum coupling. Int. J. Multiscale Comput. Eng., 5(5):387–406, 2007.Google Scholar
[BBLP10] X., Blanc, C., Le Bris, F., Legoll, and C., Patz. Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches. J. Nonlinear Sci., 20(2):241–275, 2010.Google Scholar
[BBO+83] B. R., Brooks, R. E., Bruccoleri, B. D., Olafson, et al. CHARMM – a program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem., 4(2):187–217, 1983.Google Scholar
[BC06] V. V., Bulatov and W., Cai. Computer Simulations of Dislocations. Oxford Series on Materials Modelling. Oxford: Oxford University Press, 2006.Google Scholar
[BCF86] F., Bavaud, Ph., Choquard, and J.-R., Fontaine. Statistical mechanics of elastic moduli. J. Stat. Phys., 42:621–646, 1986.Google Scholar
[BDE+08] P. T., Bauman, H. B., Dhia, N., Elkhodja, J. T., Oden, and S., Prudhomme. On the application of the Arlequin method to the coupling of particle and continuum models. Comput. Mech., 42(4):511–530, 2008.Google Scholar
[Ber04] S., Berryman. Democritus, . In E. N., Zalta, editor, The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/fall2004/entries/democrites/, 2004.Google Scholar
[BF94] G. E., Beltz and L. B., Freund. Analysis of the strained-layer critical thickness concept based on a Peierls–Nabarro model of a threading dislocation. Philos. Mag. A, 69:183–202, 1994.Google Scholar
[BFS91] G., Bozzolo, J., Ferrante, and J. R., Smith. Universal behaviour in ideal slip. Scr. Metall. Mater., 25:1927–1931, 1991.Google Scholar
[BG90] G., Burns and A. M., Glazer. Space Groups for Solid State Scientists. San Diego: Academic Press, second edition, 1990.Google Scholar
[BGCB94] T. S., Bush, J. D., Gale, C. R. A., Catlow, and P. D., Battle. Self-consistent interatomic potentials for the simulation of binary and ternary oxides. J. Mater. Chem., 4(6):831–837, 1994.Google Scholar
[BGM71] T. H. K., Barron, T. G., Gibbons, and R. W., Munn. Thermodynamics of internal strain in perfect crystals. J. Phys. C: Solid State Phys., 4:2805–2821, 1971.Google Scholar
[BH54] M., Born and K., Huang. Dynamical Theory of Crystal Lattices. Oxford: Clarendon, 1954.Google Scholar
[BH82] O., Brulin and R. K. T., Hsieh, editors. Mechanics of Micropolar Media. Singapore: World Scientific, 1982.Google Scholar
[BH86] R., Biswas and D. R., Hamann. Simulated annealing of silicon atom clusters in Langevin molecular-dynamics. Phys. Rev. B, 34(2):895–901, 1986.Google Scholar
[BH01] M. I., Baskes and R. G., Hoagland. Dislocation core structures and mobilities in MoSi2. Acta Mater., 49(13):2357–2364, 2001.Google Scholar
[BH03] S. G., Brush and N. S., Hall. The Kinetic Theory of Gasses: An Anthology of Classic Papers with Historical Commentary. London: Imperial College Press, 2003.Google Scholar
[BHT92] H., Ballamane, T., Halicioglu, and W. A., Tiller. Comparative study of silicon empirical interatomic potentials. Phys. Rev. B, 46(4):2250–2279, 1992.Google Scholar
[Bir31] G. D., Birkhoff. Proof of the ergodic theorem. Proc. Nat. Acad. Sci. USA, 17:656–660, 1931.Google Scholar
[BK97] V., Bulatov and E., Kaxiras. Semidiscrete variational Peierls framework for dislocation core properties. Phys. Rev. Lett., 78(22):4221–4224, 1997.Google Scholar
[BKC09] N., Bernstein, J. R., Kermode, and G., Csanyi. Hybrid atomistic simulation methods for materials systems. Rep. Prog. Phys., 72(2), 2009.Google Scholar
[BKG+06] E., Bitzek, P., Koskinen, F., Gähler, M., Moseler and P., Gumbsch. Structural relaxation made simple. Phys. Rev. Lett., 97(17):170201, 2006.Google Scholar
[BKJ97] M. Z., Bazant, E., Kaxiras and J. F., Justo. Environment-dependent interatomic potential for bulk silicon. Phys. Rev. B, 56:8542–8552, 1997.Google Scholar
[BKO+96] T., Belytschko, Y., Krongauz, D., Organ, M., Fleming and P., Krysl. Meshless methods: An overview and recent developments. Comput. Meth. Appl. Mech. Eng., 139:3–47, 1996.Google Scholar
[BL05] C., Le Bris and P.-L., Lions. From atoms to crystals: a mathematical journey. Bull. Am. Math. Soc., 42:291–363, 2005.Google Scholar
[BLL99] S. D., Bond, B. J., Leimkuhler, and B. B., Laird. The Nosé–Poincaré method for constant temperature molecular dynamics. J. Comput. Phys., 151:114–134, 1999.Google Scholar
[Blu70] L. M., Blumenthal. Theory and Applications of Distance Geometry. New York: Chelsea, second edition, 1970.Google Scholar
[BM32] M., Born and J. E., Mayer. Zur gittertheorie der ionenkristalle. Z. Phys., 75:1–18, 1932.Google Scholar
[BM58] G. E. P., Box and M. E., Muller. A note on the generation of random normal deviates. Ann. Math. Stat., 29(2):610–611, 1958.Google Scholar
[BM96] G. T., Barkema and N., Mousseau. Event-based relaxation of continuous disordered systems. Phys. Rev. Lett., 77(21):4358–4361, 1996.Google Scholar
[BMW03] C. M., Bender, P. N., Meisinger and Q., Wang. All Hermitian hamiltonians have parity. J. Phys. A: Math. Gen., 36:1029–1031, 2003.Google Scholar
[BN47] L., Bragg and J. F., Nye. A dynamical model of a crystal structure. Proc. R. Soc. London, Ser. A, 190(1023):474–481, 1947.Google Scholar
[BNW89] M. I., Baskes, J. S., Nelson, and A. F., Wright. Semiempirical modified embedded-atom potentials for silicon and germanium. Phys. Rev. B, 40(9):6085–6100, 1989.Google Scholar
[Bor23] M., Born. Atomtheorie des Festen Zustandes. Leipzig: B. G. Teubner, second edition, 1923.Google Scholar
[BPB+08] S., Badia, M., Parks, P., Bochev, M., Gunzburger and R., Lehoucq. On atomistic-to-continuum coupling by blending. Multiscale Model. Simul., 7(1):381–406, 2008.Google Scholar
[BPV+84] H. J. C., Berendsen, J. P. M., Postma, W. F., Vangunsteren, A., Dinola, and J. R., Haak. Molecular-dynamics with coupling to an external bath. J. Chem. Phys., 81(8):3684–3690, 1984.Google Scholar
[Bra87] W., Braun. Distance geometry and related methods for protein structure determination from NMR data. Q. Rev. Biophys., 19(3/4):115–157, 1987.Google Scholar
[Bra05] A., Brandt. Multiscale solvers and systematic upscaling in computational physics. Comput. Phys. Commun., 169(1–3):438–441, 2005. Europhysics Conference on Computational Physics, Genova, Italy, Sep 01–04, 2004.Google Scholar
[Bre90] D. W., Brenner. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B, 42(15):9458–9471. 1990.Google Scholar
[Bre92] D. W., Brenner. Erratum: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B, 46(3):1948, 1992.Google Scholar
[Bre00] D. W., Brenner. The art and science of an analytic potential. Phys. Stat. Sol. B, 217:23–40, 2000.Google Scholar
[Bri95] J., Bricmont. Science of chaos or chaos in science?Ann. NY Acad. Sci., 775:131–175, 1995.Google Scholar
[Bro04] H. W., Broer. KAM theory: The legacy of Kolmogorov's 1954 paper. Bull. Am. Math. Soc., 41:507–521, 2004.Google Scholar
[BS88] A., Banerjea and J. R., Smith. Origins of the universal binding-energy relation. Phys. Rev. B, 37(12):6632–6645, 1988.Google Scholar
[BSH+02] D. W., Brenner, O. A., Shenderova, J. A., Harrison, et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter, 14(4):783–802, 2002.Google Scholar
[BvdSvD95] H. J. C., Berendsen, D., van der Spoel, and R., van Drunen. GROMACS: A message-passing parallel molecular dynamics implementation. Comput. Phys. Commun., 91(1–3):43–56, 1995.Google Scholar
[BvK12] M., Born and T., von Karman. On fluctuations in spatial grids. Phys. Z., 13:297–309, 1912.Google Scholar
[CA80] D. M., Ceperley and B. J., Alder. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett., 45(7):566–569, 1980.Google Scholar
[Cah99] R.W., Cahn. Slaying the crystal homunculus. Nature, 400(6745):625, 1999.Google Scholar
[Cal85] H. B., Callen. Thermodynamics and an Introduction to Thermostatics. New York: John Wiley and Sons, second edition, 1985.Google Scholar
[Cal01] C., Callender. Taking thermodynamics too seriously. Stud. Hist. Phil. Mod. Phys., 32(4):539–553, 2001.Google Scholar
[Cam94] R. C., Cammarata. Surface and interface stress effects in thin films. Prog. Surf. Sci., 46(1):1–38, 1994.Google Scholar
[Car90] A. E., Carlsson. Beyond pair potentials in elemental transition metals and semiconductors. In H., Ehrenreich and D., Turnbull, editors, Solid State Physics, Volume 43, pages 1–91. Academic Press Inc., 1990.Google Scholar
[CAS10] CASTEP. CASTEP website, http://www.castep.org, 2010.
[Cau50] A., Cauchy. Mémoire sur les syst`emes isotropes de points matériels. Mém. Acad. Sci. Paris, 22:615–654, 1850.Google Scholar
[Cau28a] A., Cauchy. Exercises du Mathématique, Volume 3, chapter Sur l'équilibre et le mouvement d'un système du points matériels sollicités par des forces d'attraction ou de répulsion mutuelle, pages 227–252. Paris: Chez de Bure Frères, 1828.Google Scholar
[Cau28b] A., Cauchy. Exercises de Mathématique, Volume 3, Chapter: De la pression ou tension dans un système de points matériels, pages 253–277. Paris: Chez de Bure Frères, 1828.Google Scholar
[CBA03] M., Cafiero, S., Bubin, and L., Adamowicz. Non-Born–Oppenheimer calculations of atoms and molecules. Phys. Chem. Chem. Phys., 5(8):1491–1501, 2003.Google Scholar
[CBC+03] W., Cai, V.V., Bulatov, J., Chang, J., Li, and S., Yip. Periodic image effects in dislocation modelling. Philos. Mag., 83(5):539–567, 2003.Google Scholar
[CBM99] G. H., Campbell, J., Belak and J. A., Moriarty. Atomic structure of the sigma 5 (310)/[001] symmetric tilt grain boundary in molybdenum. Acta Mater., 47(15–16):3977–3985, 1999.Google Scholar
[CBS03] F. J., Cherne, M. I., Baskes and R. B., Schwarz. Atomistic simulations of the phase stability and elastic properties of nickel-zirconium alloys. J. Non- Cryst. Solids, 317(1–2):45–51, 2003.Google Scholar
[CC93] S. J., Cook and P., Clancey. Comparison of semi-empirical potential functions for silicon and germanium. Phys. Rev. B, 47:7686–7699, 1993.Google Scholar
[CD94] D. S., Corti and P. G., Debenedetti. A computational study of metastability in vapor–liquid equilibrium. Chem. Eng. Sci., 49(17):2717–2734, 1994.Google Scholar
[CD97] C., Creemers and P., Deurinck. Platinum segregation to the (111) surface of ordered Pt80Fe20: LEIS results and model simulations. Surf. Interface Anal., 25(3):177–190, 1997.Google Scholar
[CD98] D. S., Corti and P. G., Debenedetti. Statistical mechanics of fluids under internal constraints: Rigorous results for the one-dimensional hard rod fluid. Phys. Rev. E, 57(4):4211–4226, 1998.Google Scholar
[CDC+08] D. A., Case, T.A., Darden, T. E., Cheatham, III et al. AMBER 10. http://www.ambermd.org, 2008.
[CDGK04] L., Chen, P. G., Debenedetti, C.W., Gear, and I. G., Kevrekidis. From molecular dynamics to coarse self-similar solutions: a simple example using equationfree computation. J. Non-Newtonian Fluid Mech., 120(1–3):215–223, 2004. 3rd International Workshop on Nonequilibrium Thermodynamics and Complex Fluids, Princeton, NJ, Aug 14–17, 2003.Google Scholar
[CdKBY00] W., Cai, M., de Koning, V.V., Bulatov, and S., Yip. Minimizing boundary reflections in coupled-domain simulations. Phys. Rev. Lett., 85(15):3213–3216. 2000.Google Scholar
[CDKM06] S., Conti, G., Doltzmann, B., Kirchheim, and S., Müller. Sufficient conditions for the validity of the Cauchy–Born rule close to so(n). J. Eur. Math. Soc., 8:515–530, 2006.Google Scholar
[CvdV99] G., Ceder and A., Van der Ven. Phase diagrams of lithium transition metal oxides: investigations from first principles. Electrochim. Acta, 45(1–2):131–150, 1999.Google Scholar
[CDvDG05] S., Cheung, W.Q., Deng, A. C. T., van Duin and W. A., Goddard, III. ReaxFF(MgH) reactive force field for magnesium hydride systems. J. Phys. Chem. A, 109(5):851–859, 2005.Google Scholar
[CG01] P., Cermelli and M. E., Gurtin. On the characterization of geometrically necessary dislocations in finite plasticity. J. Mech. Phys. Solids, 49:1539–1568. 2001.Google Scholar
[CGE80] A. E., Carlsson, C.D., Gelatt, and H., Ehrenreich. Ab-initio pair potential applied to metals. Philos. Mag. A, 41(2):241–250, 1980.Google Scholar
[CGL+07] C., Cui, Z., Guo, Y., Liu, et al. Characteristics of cobalt-based alloy coating on tool steel prepared by powder feeding laser cladding. Opt. Laser Technol., 39(8):1544–1550, 2007.Google Scholar
[CGLK04] J., Cisternas, C.W., Gear, S., Levin, and I. G., Kevrekidis. Equation-free modelling of evolving diseases: Coarse-grained computations with individualbased models. Proc. R. Soc. London, Ser. A, 460(2050):2761–2779, 2004.Google Scholar
[CH88] G. M., Crippen and T. F., Havel. Distance Geometry and Molecular Conformation. New York: Wiley, 1988.Google Scholar
[CH09] A. J., Chorin and O. H., Hald. Stochastic Tools in Mathematics and Science. New York: Springer, second edition, 2009.Google Scholar
[Cha43] S., Chandrasekhar. Stochastic problems in physics and astronomy. Rev. Mod. Phys., 15(1):1–89, 1943.Google Scholar
[Cha99] P., Chadwick. Continuum Mechanics: Concise Theory and Problems. Mineola: Dover, second edition, 1999.Google Scholar
[Che05] G., Chen. Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons. New York: Oxford University Press, 2005.Google Scholar
[CL68] F., Cyrot-Lackmann. Calculation of cohesion and surface tension of transition metals by a tight binding method. J. Phys. Chem. Solids, 29(7):1235–&, 1968.Google Scholar
[Cla70] R., Clausius. On a mechanical theorem applicable to heat. Philos. Mag., 40:122–127, 1870.Google Scholar
[CM03] W. A., Curtin and R. E., Miller. Atomistic/continuum coupling methods in multi-scale materials modeling. Modell. Simul. Mater. Sci. Eng., 11(3):R33–R68, 2003.Google Scholar
[CN63] B.D., Coleman and W., Noll. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal., 13:167–178, 1963.Google Scholar
[CO77] M., Cassandro and E., Olivieri. A rigorous study of metastability in a continuous model. J. Stat. Phys., 17(4):229–244, 1977.Google Scholar
[Col05] L., Colombo. Tight-binding molecular dynamics: A primer. Riv. Nuovo Cimento, 28(10):1–59, 2005.Google Scholar
[Cop10] Copper Development Association. Low temperature properties of copper. http://www.copper.org/resources/properties/, 2010.
[Cot08] R., Cotterill. The Material World. Cambridge: Cambridge University Press, second edition, 2008.Google Scholar
[Cou78a] C. S. G., Cousins. Inner elasticity. J. Phys. C: Solid State Phys., 11:4867–4879. 1978.Google Scholar
[Cou78b] C. S. G., Cousins. Symmetry of the inner elastic constants. J. Phys. C: Solid State Phys., 11:4881–4900, 1978.Google Scholar
[CP74] R.D., Crowninshield and M. H., Pope. Response of compact bone in tension at various strain rates. Ann. Biomed. Eng., 2(2):217–225, 1974.Google Scholar
[CP85] R., Car and M., Parrinello. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett., 55(22):2471–2474, 1985.Google Scholar
[Cri77] G. M., Crippen. A novel approach to calculation of conformation: distance geometry. J. Comput. Phys., 24:96–107, 1977.Google Scholar
[Cri05] T., Crilly. Arthur Cayley: Mathematician Laureate of the Victorian Age. Baltimore: The Johns Hopkins University Press, 2005.Google Scholar
[Cur86] W. A., Curtin. Theories of inhomogeneous media: far-infrared absorption in composites and a density functional theory of freezing. PhD thesis, Cornell University, 1986.
[CvDDG09] K., Chenoweth, A. C. T., van Duin, S., Dasgupta and W. A., Goddard, III. Initiation mechanisms and kinetics of pyrolysis and combustion of JP-10 hydrocarbon jet fuel. J. Phys. Chem. A, 113(9):1740–1746, 2009.Google Scholar
[CWA83] D., Chandler, J.D., Weeks and H. C., Andersen. Van der Waals picture of liquids, solids, and phase transformations. Science, 220(4599):787–794, 1983.Google Scholar
[CY91] K. S., Cheung and S., Yip. Atomic-level stress in an inhomogeneous system. J. Appl. Phys., 70(10):5688–5690, 1991.Google Scholar
[Dav94] P. J., Davis. Circulant Matrices. New York: Chelsea Publishing, second edition, 1994.Google Scholar
[Daw89] M. S., Daw. Model of metallic cohesion – the embedded-atom method. Phys. Rev. B, 39(11):7441–7452, 1989.Google Scholar
[DB83] M. S., Daw and M. I., Baskes. Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys. Rev. Lett., 50(17):1285–1288. 1983.Google Scholar
[DB84] M. S., Daw and M. I., Baskes. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B, 29:6443–6453, 1984.Google Scholar
[DBBW86] M. S., Daw, M. I., Baskes, C. L., Bisson and W. G., Wolfer. Application of the embedded atom method to fracture, dislocation dynamics and hydrogen embrittlement. In R.H., Jones and W.W., Gerberich, editors, Modeling Environmental Effects on Crack Growth Processes, pages 99–124. Warrendale: The Materials Society, 1986.Google Scholar
[DCL70] F., DuCastel and F., Cyrot-Lackmann. Moments developments and their application to electronic charge distribution of d-bands. J. Phys. Chem. Solids, 31(6):1295–1306, 1970.Google Scholar
[DCL71] F., DuCastel and F., Cyrot-Lackmann. Moments developments. 2. Application to crystalline structures and stacking fault energies of transition metals. J. Phys. Chem. Solids, 32(1):285–301, 1971.Google Scholar
[DELT07] M., Dobson, R. S., Elliott, M., Luskin and E. B., Tadmor. A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics. J. Comput.-Aided Mater. Des., 14:219–237, 2007.Google Scholar
[Deu04] P., Deuflhard. Newton Methods for Nonlinear Problems. Berlin: Springer-Verlag, 2004.Google Scholar
[DF04] D. S., Dummit and R. M., Foote. Abstract Algebra. Hoboken: John Wiley and Sons, third edition, 2004.Google Scholar
[DFB93] M. S., Daw, S. M., Foiles and M. I., Baskes. The embedded-atom method – a review of theory and applications. Mater. Sci. Rep., 9(7–8):251–310, 1993.Google Scholar
[DFS04] R., Drautz, M., Fahnle and J. M., Sanchez. General relations between manybody potentials and cluster expansions in multicomponent systems. J. Phys. Condens. Matter, 16(23):3843–3852, 2004.Google Scholar
[dGM62] S. R., de Groot and P., Mazur. Non-Equilibrium Thermodynamics. Amsterdam: North-Holland Publishing Company, 1962.Google Scholar
[DJ07] T., Dumitrica and R. D., James. Objective molecular dynamics. J. Mech. Phys. Solids, 55(10):2206–2236, 2007.Google Scholar
[DL08a] M., Dobson and M., Luskin. Analysis of a force-based quasicontinuum approximation. Math. Modell. Numer. Anal. (ESAIM:M2AN), 42(1):113–119, 2008.Google Scholar
[DL08b] M., Dobson and M., Luskin. An analysis of the effect of ghost force oscillation on the quasicontinuum error. Math. Modell. Numer. Anal. (ESAIM:M2AN), 43(3):591–604, 2008.Google Scholar
[DLO10a] M., Dobson, M., Luskin and C., Ortner. Sharp stability estimates for the forcebased quasicontinuum approximation of homogeneous tensile deformation. Multiscale Model. Simul., 8(3):782–802, 2010.Google Scholar
[DLO10b] M., Dobson, M., Luskin and C., Ortner. Stability, instability, and error of the force-based quasicontinuum approximation. Arch. Ration. Mech. Anal., 197(1):179–202, 2010.Google Scholar
[DMA75] J. D., Doll, L. E., Myers and S. A., Adelman. Generalized Langevin equation approach for atom-solid-surface scattering – inelastic studies. J. Chem. Phys., 63(11):4908–4914, 1975.Google Scholar
[Dov93] M. T., Dove. Introduction to Lattice Dynamics. Cambridge: Cambridge University Press, 1993.Google Scholar
[DPS04] D. K., Datta, R. C., Picu and M. S., Shephard. Composite grid atomistic continuum method: An adaptive approach to bridge continuum with atomistic analysis. Int. J. Multiscale Comput. Eng., 2(3):71–90, 2004.Google Scholar
[DTLMK11] L. M., Dupuy, E. B., Tadmor, F., Legoll, R. E., Miller and W. K., Kim. Finite temperature quasicontinuum. 2011. In preparation.
[DTMP05] L. M., Dupuy, E. B., Tadmor, R. E., Miller and R., Phillips. Finite temperature quasicontinuum: Molecular dynamics without all the atoms. Phys. Rev. Lett., 95:060202, 2005.Google Scholar
[DZ99] D. X., Du and Q.-S., Zheng. A note on Cauchy–Voigt dispute of independent constants in anisotropic elastic Hooke's law. Mech. Res. Commun., 26:295–300, 1999.Google Scholar
[DZM+07] R., Drautz, Z. W., Zhou, D. A., Murdick, B., Gillespie, H. N. G., Wadley and D. G., Pettifor. Analytic bond-order potentials for modelling the growth of semiconductor thin films. Prog. Mater. Sci., 52(2–3):196–229, 2007.Google Scholar
[EA94] F., Ercolessi and J. B., Adams. Interatomic potentials from first-principles calculations – the force-matching method. Europhys. Lett., 26:583, 1994.Google Scholar
[EE11] P., Ehrenfest and T., Ehrenfest. Encyklopädie der mathematische Wissenschaften, Volume 4 part 32, chapter Begriffliche Grundagen der statistischen Auffassung in der Mechanik. 1911. English translation by M. J. Moravcsik, The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca: Cornell University Press, 1959.Google Scholar
[EEL+07] W., E, B., Engquist, X., Li, W., Ren and E., Vanden-Eijnden. Heterogeneous multiscale methods: A review. Commun. Comput. Phys., 2(3):367–450, 2007.Google Scholar
[EH01] W., E and Z., Huang. Matching conditions in atomistic-continuum modeling of materials. Phys. Rev. Lett., 87(13):135501, 2001.Google Scholar
[EH02] W., E and Z. Y., Huang. A dynamic atomistic-continuum method for the simulation of crystalline materials. J. Comput. Phys., 182(1):234–261, 2002.Google Scholar
[Ein16] A., Einstein. Die grundlage der allgemeinen relativitätstheorie. Ann. der Phys., 49:769–822, 1916.Google Scholar
[EK87] R., Elber and M., Karplus. A method for determining reaction paths in large molecules: Application to myoglobin. Chem. Phys. Lett., 139(5):375–380, 1987.Google Scholar
[EKAE06] R., Erban, I. G., Kevrekidis, D., Adalsteinsson, and T. C., Elston. Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation. J. Chem. Phys., 124(8):084106, 2006.Google Scholar
[EKO06] R., Erban, I. G., Kevrekidis and H. G., Othmer. An equation-free computational approach for extracting population-level behavior from individualbased models of biological dispersal. Physica D, 215(1):1–24, 2006.Google Scholar
[ELY06] W. E, J., Lu, and J. Z., Yang. Uniform accuracy of the quasicontinuum method. Phys. Rev. B, 74(21):214115/1–12, 2006.Google Scholar
[EM90] D. J., Evans and G. P., Morriss. Statistical Mechanics of Nonequilibrium Liquids. London: Academic Press, 1990.Google Scholar
[EM07] W. E, and P., Ming. Cauchy–Born rule and the stability of crystalline solids: Static problems. Arch. Ration. Mech. Anal., 183:241–297, 2007.Google Scholar
[EMM+08] K., Endo, C., Masumoto, D., Matsumoto, T., Ida, M., Mizuno and N., Kato. Fragment distribution of thermal decomposition for PS and PET with QMD calculations by considering the excited and charged model molecules. Appl. Surf. Sci., 255(4):856–859, 2008.Google Scholar
[Erc08a] F., Ercolessi. Lecture notes on tight-binding molecular dynamics, and tight-binding justification of classical potentials. http://www.fisica.uniud.it∼ercolessi/SA/tb.pdf, 2008.
[Erc08b] F., Ercolessi. AMolecular Dynamics Primer, http://fisica.uniud.it/∼ercolessi/md/md, 2008.
[ERH85] Z., Elkoshi, H., Reiss, and D., Hammerich. One-dimensional rigorous hole theory for fluids: internally constrained ensembles. J. Stat. Phys., 41(3/4):685–708, 1985.Google Scholar
[Eri70] J. L., Ericksen. Nonlinear elasticity of diatomic crystals. Int. J. Solids Struct., 6(7):951–957, 1970.Google Scholar
[Eri84] J. L., Ericksen, The Cauchy and Born hypothesis for crystals. In M., Gurtin editor, Phase Transformations and Material Instabilities in Solids, pages 61–77. New York, Academic Press, 1984.Google Scholar
[Eri97] J. L., Ericksen. Equilibrium theory for X-ray observations of crystals. Arch. Ration. Mech. Anal., 139:181–200, 1997.Google Scholar
[Eri02] A. C., Eringen. Nonlocal Continuum Field Theories. New York: Springer, 2002.Google Scholar
[Eri08] J. L., Ericksen. On the Cauchy–Born rule. Math. Mech. Solids, 13:199–220, 2008.Google Scholar
[ERVE02] W., E, W., Ren and E., Vanden-Eijnden. String method for the study of rare events. Phys. Rev. B, 66(5):052301, 2002.Google Scholar
[ERVE09] W., E, W., Ren and E., Vanden-Eijnden. A general strategy for designing seamless multiscale methods. J. Comput. Phys., 228(15):5437–5453, 2009.Google Scholar
[ES79] D. M., Esterling and A., Swaroop. Inter-atomic potentials from experimental phonon-spectra. 1. prototypes. Phys. Status Solidi B, 96(1):401–411, 1979.Google Scholar
[ES09] B., Eidel and A., Stukowski. A variational formulation of the quasicontinuum method based on energy sampling of clusters. J. Mech. Phys. Solids, 57(1):87–108, 2009.Google Scholar
[ETP86] F., Ercolessi, E., Tosatti and M., Parrinello. Au (100) surface reconstruction. Phys. Rev. Lett., 57(6):719–722, 1986.Google Scholar
[ETS06a] R. S., Elliott, N., Triantafyllidis and J. A., Shaw. Stability of crystalline solids–I: Continuum and atomic lattice considerations. J. Mech. Phys. Solids, 54:161–192, 2006.Google Scholar
[ETS06b] R. S., Elliott, J. A., Shaw and N., Triantafyllidis. Stability of crystalline solids – II: Application to temperature-induced martensitic phase transformations in a bi-atomic crystal. J. Mech. Phys. Solids, 54(1):193–232, 2006.Google Scholar
[Eva83] D. J., Evans. Computer “experiment” for nonlinear thermodynamics of Couette flow. J. Chem. Phys., 78(6):3297–3302, 1983.Google Scholar
[Eva98] L. C., Evans. Partial Differential Equations, Volume 19 of Graduate Studies in Mathematics. Providence: American Mathematical Society, 1998.Google Scholar
[EW77] J. J., Erpenbeck and W.W., Wood. Molecular dynamics techniques for hardcore systems. In J., Berne, editor, Statistical Mechanics, Part B: Time-dependent processes, Volume 6 of Modern Theoretical Chemistry, Chapter 1, pages 1–40. New York: Plenum Press, 1977.Google Scholar
[Ezr06] G. S., Ezra. Reversible measure-preserving integrators for non-Hamiltonian systems. J. Chem. Phys., 125(3):034104, 2006.Google Scholar
[FAF91] M. W., Finnis, P., Agnew and A. J. E., Foreman. Thermal excitation of electrons in energetic displacement cascades. Phys. Rev. B, 44(2):567–574, 1991.Google Scholar
[Far94] D., Farkas. Interatomic potentials for Ti–Al with and without angular forces. Modell. Simul. Mater. Sci. Eng., 2(5):975–984, 1994.Google Scholar
[FBD86] S. M., Foiles, M. I., Baskes, and M. S., Daw. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B, 33(12):7983–7991, 1986.Google Scholar
[FC99] M. C., Fivel and G. R., Canova. Developing rigorous boundary conditions to simulations of discrete dislocation dynamics. Modell. Simul. Mater. Sci. Eng., 7(5):753–768, 1999.Google Scholar
[Fey85] R. P., Feynman. QED: The Strange Theory of Light and Matter. Princeton: Princeton University Press, 1985.Google Scholar
[FF77] R., Fletcher and T. L., Freeman. A modified Newton method forminimization. J. Optimiz. Theory App., 23:357–372, 1977.Google Scholar
[FG05] R. A., Friesner and V., Guallar. Ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis. Annu. Rev. Phys. Chem., 56:389–427, 2005.Google Scholar
[FGC96] M. C., Fivel, T. J., Gosling and G. R., Canova. Implementing image stresses in a 3D dislocation simulation. Modell. Simul. Mater. Sci. Eng., 4(6):581–596, 1996.Google Scholar
[FGU96] C., Filippi, X., Gonze and C. J., Umrigar. Generalized gradient approximations to density functional theory. In J. M., Seminario, editor, Recent Developments and Applications of Modern Density Functional Theory, Volume 4 of Theoretical and Computational Chemistry. Amsterdam: Elsevier, 1996.Google Scholar
[FH65] R. P., Feynman and A. R., Hibbs. Quantum Mechanics and Path Integrals. New York: McGraw-Hill, 1965.Google Scholar
[FHCO04] M., Fago, R. L., Hayes, E. A., Carter and M., Ortiz. Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation. Phys. Rev. B, 70(10):100102, 2004.Google Scholar
[Fin03] M., Finnis. Interatomic Forces in Condensed Matter. Oxford: Oxford University Press, 2003.Google Scholar
[Fis64] M. E., Fisher. The free energy of a macroscopic system. Arch. Ration. Mech. Anal., 17:377–410, 1964.Google Scholar
[FJ00] G., Friesecke and R. D., James. A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods. J. Mech. Phys. Solids, 48(6–7):1519–1540. 2000.Google Scholar
[FL70] M. E., Fisher and J. L., Lebowitz. Asymptotic free energy of a system with periodic boundary conditions. Commun. Math. Phys., 19:251–272, 1970.Google Scholar
[FLS06] R. P., Feynman, R. B., Leighton and M., Sands. The Feynman Lectures on Physics, The Definitive and Extended Edition. Boston: Addison-Wesley, second edition, 2006.Google Scholar
[FMAH94] N. A., Fleck, G. M., Muller, M. F., Ashby and J. W., Hutchinson. Strain gradient plasticity: Theory and experiment. Acta Metall. Mater., 42:475–487, 1994.Google Scholar
[FNS+07] J., Fish, M. A., Nuggehally, M. S., Shephard, et al.Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force. Comput. Meth. Appl. Mech. Eng., 196(45–48):4548–4560, 2007.Google Scholar
[FOH08] S. M., Foiles, D. L., Olmsted, and E. A., Holm. Using atomistic simulations to inform mesoscale simulations of microstructural evolution. In A., El-Azab, editor, Proc. 4th International Conference of MultiscaleMaterials Modeling (MMM), pages 362–368, Tallahassee: Florida State University, 2008.Google Scholar
[Foi85] S. M., Foiles. Calculation of the surface segregation of Ni–Cu alloys with the use of the embedded-atom method. Phys. Rev. B, 32(12):7685–7693, 1985.Google Scholar
[Foi94] S. M., Foiles. Evaluation of harmonic methods for calculating the free energy of defects in solids. Phys. Rev. B, 49:14930–14938, 1994.Google Scholar
[Fos09] R. L., Fosdick, 2009. Private communications.
[Fow36] R. H., Fowler. Statistical Mechanics: The Theory of the Properties of Matter in Equilibrium. Cambridge: Cambridge University Press, second edition, 1936.Google Scholar
[FPA+95] C., Fiolhais, J. P., Perdew, S. Q., Armster, J. M., MacLaren and M., Brajczewska. Dominant density parameters and local pseudopotentials for simple metals. Phys. Rev. B, 51:14001–14011, 1995.Google Scholar
[Fre26] J., Frenkel. Zur theorie der elastizitätsgrenze und der festigkeit kristallinischer körper. Z. Phys., 37(7/8):572–609, 1926.Google Scholar
[FS84] M. W., Finnis and J. E., Sinclair. A simple empirical n-body potential for transition-metals. Philos. Mag. A, 50(1):45–55, 1984.Google Scholar
[FS02] D., Frenkel and B., Smit. Understanding Molecular Simulation: From Algorithms to Applications. San Diego: Academic Press, second edition, 2002.Google Scholar
[FSR83] J., Ferrante, J. R., Smith and J. H., Rose. Diatomic molecules and metallic adhesion, cohesion, and chemisorption: A single binding-energy relation. Phys. Rev. Lett., 50(18):1385–1386, 1983.Google Scholar
[FT02] G., Friesecke and F., Theil. Validity and failure of the Cauchy–Born hypothesis in a two dimensional mass-spring lattice. J. Nonlinear Sci., 12:445–478, 2002.Google Scholar
[FW99] J. H., Frederick and C., Woywod. General formulation of the vibrational kinetic energy operator in internal bond-angle coordinates. J. Chem. Phys., 111(16):7255–7271, 1999.Google Scholar
[Gau10] Gaussian, . Gaussian website. http://www.gaussian.com, 2010.
[GB95] P., Gumbsch and G. E., Beltz. On the continuum versus atomistic descriptions of dislocation nucleation and cleavage in nickel. Modell. Simul. Mater. Sci. Eng., 3(5):597–613, 1995.Google Scholar
[GBKH03] N. M., Ghoniem, E. P., Busso, N., Kioussis and H. C., Huang. Multiscale modelling of nanomechanics and micromechanics: an overview. Philos. Mag., 83(31–34, Sp. Iss. SI):3475–3528, 2003. 1st International Conference on Multiscale Materials Modelling (MMM), London, England, June 17–22, 2002.Google Scholar
[GCL73] J. P., Gaspard and F., Cyrot-Lackmann. Density of states from moments–application to impurity band. J. Phys. C: Solid State Phys., 6(21):3077–3096. 1973.Google Scholar
[GE10] V. S., Guthikonda and R. S., Elliott. Modeling martensitic phase transformation in shape memory alloys with the self-consistent lattice dynamics approach. J. Mech. Phys. Solids, 2010. submitted.Google Scholar
[Gea71] C. W., Gear. Numerical Initial Value Problems in Ordinary Differential Equations. Englewood Cliffs: Prentice-Hall, 1971.Google Scholar
[GF00] I. M., Gelfand and S. V., Fomin. Calculus of Variations. Mineola: Dover, 2000. Translated by Richard A. Silverman.Google Scholar
[GFA10] M. E., Gurtin, E., Fried and L., Anand. The Mechanics and Thermodynamics of Continua. Cambridge: Cambridge University Press, 2010.Google Scholar
[GFS89] J.J., Gracio, J. V., Fernandes and J. H., Schmitt. Effect of grain-size on substructural evolution and plastic behavior of copper. Mater. Sci. Eng. A, 118:97–105, 1989.Google Scholar
[GGMV60] J.B., Gibson, A.N., Goland, M., Milgram and G. H., Vineyard. Dynamics of radiation damage. Phys. Rev., 120(4):1229–1253, 1960.Google Scholar
[GHBF08] P. M., Gullett, M. F., Horstemeyer, M. I., Baskes and H., Fang. A deformation gradient tensor and strain tensors for atomistic simulations. Modell. Simul. Mater. Sci. Eng., 16:015001, 2008.Google Scholar
[Gib02] J.W., Gibbs. Elementary Principles in Statistical Mechanics. New York: C. Scribner and Sons, 1902.Google Scholar
[GIKI98] M., Giesen, G. S., Icking-Konert and H., Ibach. Fast decay of adatom islands and mounds on Cu(111): A new effective channel for interlayer mass transport. Phys. Rev. Lett., 80(3):552–555, 1998.Google Scholar
[Gil10] S. P. A., Gill. Nonequilibrium molecular dynamics and multiscale modeling of heat conduction in solids. In T., Dumitrica, editor, Trends in Computational Nanomechanics, Volume 9, Chapter 4, pages 83–132. Dordrecht: Springer Science and Business Media, 2010.Google Scholar
[GK98] H., Gao and P., Klein. Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J. Mech. Phys. Solids, 46:187–218, 1998.Google Scholar
[GK08] T. C., Germann and K., Kadau. Trillion-atom molecular dynamics becomes a reality. Int. J. Mod. Phys. C, 19:1315–1319, 2008.Google Scholar
[GLW08] V., Gravemeier, S., Lenz and W. A., Wall. Towards a taxonomy for multiscale methods in computational mechanics: Building blocks of existing methods. Comput. Mech., 41(2):279–291, 2008.Google Scholar
[GM75] M. E., Gurtin and A. I., Murdoch. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal., 57(4):291–323, 1975.Google Scholar
[Gol80] H., Goldstein. Classical Mechanics. Reading: Addison-Wesley, second edition, 1980.Google Scholar
[Gor76] J. E., Gordon. The New Science of Strong Materials or Why You Don't Fall Through the Floor. Princeton: Princeton University Press, second edition, 1976.Google Scholar
[GR87] L., Greengard and V., Rokhlin. A fast algorithm for particle simulations. J. Comput. Phys., 73(2):325–348, 1987.Google Scholar
[Gra87] W. T., Grandy Jr. Foundations of Statistical Mechanics. Volume I: Equilibrium Theory. Dordrecht: D. Reidel Publishing, 1987.Google Scholar
[Gra00] W.W., Grabowski. Cloud microphysics and the tropical climate: Cloudresolving model perspective. J. Clim., 13(13):2306–2322, 2000.Google Scholar
[Gra04] W.W., Grabowski. An improved framework for superparameterization. J. Atmos. Sci., 61(15):1940–1952, 2004.Google Scholar
[Gra08] H., MorrisonW.W., Grabowski. Modeling supersaturation and subgridscale mixing with two-moment bulk warm microphysics. J. Atmos. Sci., 65(3):792–812, 2008.Google Scholar
[Gri21] A. A., Griffith. The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. London, Ser. A, 221:163–198, 1921.Google Scholar
[Gri05] D. J., Grifffiths. Introduction to Quantum Mechanics. Upper Saddle River: Pearson Prentice-Hall, second edition, 2005.Google Scholar
[GS99] W.W., Grabowski and P. K., Smolarkiewicz. CRCP: A cloud resolving convection parameterization for modeling the tropical convecting atmosphere. Physica D, 133(1–4):171–178, 1999. 18th Annual International Conference of the Center-for-Nonlinear-Studies, Los Alamos, New Mexico, May 11–15, 1998.Google Scholar
[GS02] W.W., Grabowski and P. K., Smolarkiewicz. A multiscale anelastic model for meteorological research. Mon. Weather Rev., 130(4):939–956, 2002.Google Scholar
[GStVB98] C. F., Guerra, J.G., Snijders, G., te Velde and E. J., Baerends. Towards an order-N DFT method. Theor. Chem. Acc., 99(6):391–403, 1998.Google Scholar
[Gui02] B., Guillot. A reappraisal of what we have learnt during three decades of computer simulations on water. J. Mol. Liq., 101:219–260, 2002.Google Scholar
[Gur65] M. E., Gurtin. Thermodynamics and the possibility of spatial interaction in elastic materials. Arch. Ration. Mech. Anal., 19:339–352, 1965.Google Scholar
[Gur95] M. E., Gurtin. The nature of configurational forces. Arch. Ration. Mech. Anal., 131:67–100, 1995.Google Scholar
[Gur00] M. E., Gurtin. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids, 48(5):989–1036, 2000.Google Scholar
[GW66] M. E., Gurtin and W.O., Williams. On the Clausius–Duhem inequality. J. Appl. Math. Phys. (ZAMP), 17:626–633, 1966.Google Scholar
[GWZ06] X., Guo, J.B., Wang and H.W., Zhang. Mechanical properties of single-walled carbon nanotubes based on higher order Cauchy–Born rule. Int. J. Solids Struct., 43:1276–1290, 2006.Google Scholar
[HA87] J.D., Honeycutt and H. C., Andersen. Molecular-dyanmics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem., 91:4950–4963, 1987.Google Scholar
[Haf87] J., Hafner. From Hamiltonians to Phase Diagrams. Berlin: Springer-Verlag, 1987.Google Scholar
[Hal05] T. C., Hales. A proof of the Kepler conjecture. Ann. Math., 162(3):1065–1185, 2005.Google Scholar
[Har66] W. A., Harrison. Pseudopotentials in the Theory of Metals. New York: PWA Benjamin, Inc., 1966.Google Scholar
[Har82] R. J., Hardy. Formulas for determining local properties in moleculardynamics simulations: Shock waves. J. Chem. Phys., 76:622–628, 1982.Google Scholar
[Har00] W. A., Harrison. AppliedQuantum Mechanics. River Edge: World Scientific, 2000.Google Scholar
[HB01] D., Hull and D., Bacon. Introduction to Dislocations. Oxford: Oxford University Press, fourth edition, 2001.Google Scholar
[HBF+96] A. P., Horsfield, A. M., Bratkovsky, M., Fearn, D. G., Pettifor and M., Aoki. Bond-order potentials: Theory and implementation. Phys. Rev. B, 53:12694–1271, 1996.Google Scholar
[HCCK02] J. R., Hu, S.C., Chang, F. R., Chen and J. J., Kai. HRTEM investigation of the multiplicity of sigma =9 [011]/(122) symmetric tilt grain boundary in Cu. Mater. Chem. Phys., 74(3):313–319, 2002.Google Scholar
[HH70] F. J., Humphreys and P. B., Hirsch. The deformation of single crystals of copper and copper-zinc alloys containing alumina particles. II. Microstructure and dislocation-particle interactions. Proc. R. Soc. London, Ser. A, 318(1532):73–92, 1970.Google Scholar
[HH99] Y., Huang and F. J., Humphreys. Measurements of grain boundary mobility during recrystallization of a single-phase aluminium alloy. Acta Mater., 47(7):2259–2268, 1999.Google Scholar
[HH03] D., Heggie and P., Hut. The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics. Cambridge: Cambridge University Press, 2003.Google Scholar
[HHL09] W. G., Hoover, C.G., Hoover and J. F., Lutsko. Microscopic and macroscopic stress with gravitation and rotational forces. Phys. Rev. E, 79:036709, 2009.Google Scholar
[HI02] F.W., Hehl and Y., Itin. The Cauchy relations in linear elasticity theory. J. Elast., 66:185–192, 2002.Google Scholar
[Hil56] T. L., Hill. Statistical Mechanics: Principles and Selected Applications. New York: McGraw-Hill, 1956.Google Scholar
[HJ99] G., Henkelman and H., Jónsson. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys., 111(15):7010–7022, 1999.Google Scholar
[HJ00] G., Henkelman and H., Jónsson. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys., 113(22):9978–9985, 2000.Google Scholar
[HJ01] G., Henkelman and H., Jónsson. Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J. Chem. Phys., 115(21):9657–9666, 2001.Google Scholar
[HJJ98] G., MillsH., Jónsson and K.W., Jacobsen. Nudged elastic band method for finding minimum energy paths of transitions. In B. J., Berne, G., Ciccoti, and D. F., Coker, editors, Classical and Quantum Dynamics in Condensed Phase Simulations, Chapter 16, pages 385–404. Singapore: World Scientific, 1998.Google Scholar
[HJJ00] G., Henkelman, G., Jóhannesson and H., Jónsson. Progress on Theoretical Chemistry and Physic, chapter Methods for Finding Saddle Points and Minimum Energy Paths, pages 269–300. Dordrecht: Kluwer Academic Publishers, 2000.
[HK64] P., Hohenberg and W., Kohn. Inhomogeneous electron gas. Phys. Rev., 136(3B):B864–B871, 1964.Google Scholar
[HKC83] T. F., Havel, I.D., Kuntz, and G. M., Crippen. The theory and practice of distance geometry. Bull. Math. Biol., 45:665–720, 1983.Google Scholar
[HL63] G. K., Horton and J.W., Leech. On the statistical mechanics of the ideal inert gas solids. Proc. Phys. Soc., 82:816–854, 1963.Google Scholar
[HL92] J. P., Hirth and J., Lothe. Theory of Dislocations. Malabar: Krieger, 1992.Google Scholar
[HL00] E., Hairer and C., Lubich. Energy conservation by Stormer-type numerical integrators. In D. F., Griffiths and G. A., Watson editors, Numerical Analysis 1999, volume 420, pages 169–189, 2000. 18th Dundee Biennial Conference on Numerical Analysis, Dundee, Scotland, Jun 29–Jul 02, CRC Press, 1999.Google Scholar
[HLM82] W. G., Hoover, A.J.C., Ladd and B., Moran. High-strain-rate plasticflow studied via non-equilibrium molecular-dynamics. Phys. Rev. Lett., 48(26):1818–1820, 1982.Google Scholar
[HLW06] E., Hairer, C., Lubich, and G., Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Volume 31 of Computational Mathematics. Berlin: Springer, second edition, 2006.Google Scholar
[HM86] J. P., Hansen and I. R., McDonald. Theory of Simple Liquids. London: Academic Press, second edition, 1986.
[HM99] D., Holland and M., Marder. Cracks and atoms. Adv. Mater., 11:793–806, 1999.Google Scholar
[HMP91] J., Huang, M., Meyer and V., Pontikis. Core structure of a dissociated edge dislocation and pipe diffusion in copper investigated by molecular-dynamics. J. de Phys. III, 1(6):867–883, 1991.Google Scholar
[Hol00] G. A., Holzapfel. Nonlinear Solid Mechanics. Chichester: Wiley, 2000.Google Scholar
[Hoo85] W. G., Hoover. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A, 31(3):1695–1697, 1985.Google Scholar
[Hoo86] W. G., Hoover. Molecular Dynamics, Volume 258 of Lecture Notes in Physics. Berlin: Springer, 1986. Available at www.williamhoover.info/MD.pdf.
[Hoo87] R., Hooke. Micrographia [A facsimile edition]. Lincolnwood: Science Heritage Ltd., 1987.
[Hoo99] W. G., Hoover. Time Reversibility, Computer Simulation, and Chaos. Singapore: World Scientific, 1999.Google Scholar
[HPM99] C., Herzig, T., Przeorski and Y., Mishin. Self-diffusion in gamma-TiAl: An experimental study and atomistic calculations. Intermetallics, 7(3–4):389–404, 1999.Google Scholar
[HR95] B. L., Holian and R., Ravelo. Fracture simulations using large-scalemolecular dynamics. Phys. Rev. B, 51(17):11275–11288, 1995.Google Scholar
[HSMP06] P.D., Haynes, C.-K., Skylaris, A.A., Mostofi and M. C., Payne. ONETEP: linear-scaling density-functional theory with local orbitals and plane waves. Phys. Stat. Sol. B, 243(11):2489–2499, 2006.Google Scholar
[HTC98] S. C., Harvey, R.K.Z., Tan and T. E., Cheatham. The flying ice cube: Velocity rescaling in molecular dynamics leads to violation of energy equipartition. J. Comput. Chem., 19(7):726–740, 1998.Google Scholar
[Hua63] K., Huang. Statistical Mechanics. New York: Wiley, 1963.Google Scholar
[Hun05] P., Hunenberger. Thermostat algorithms formolecular dynamics simulations. In Advanced Computer Simulation Approaches for Soft Matter Sciences I, volume 173 of Advances in Polymer Science, pages 105–147. Berlin: Springer-Verlag, 2005.Google Scholar
[HWF+98] H., Haas, C. Z., Wang, M., Fahnle, C., Elsasser and K. M., Ho. Environmentdependent tight-binding model for molybdenum. Phys. Rev. B, 57(3):1461–1470. 1998.Google Scholar
[HXS+00] W.Y., Hu, H.D., Xu, X. L., Shu, et al. Calculation of thermodynamic properties of Mg-RE alloys by an analytic modified embedded atom method. J. Phys. D: Appl. Phys., 33(6):711–718, 2000.Google Scholar
[HXW+09] K., Han, Y., Xin, R., Walsh, S., Downey, II and P.N., Kalu. The effects of grain boundary precipitates on cryogenic properties of aged 316-type stainless steels. Mater. Sci. Eng. A, 516(1–2):169–179, 2009.Google Scholar
[IBA00] S., Ismail-Beigi and T. A., Arias. Ab initio study of screw dislocations in Mo and Ta: A new picture of plasticity in bcc transition metals. Phys. Rev. Lett., 63:1499–1502, 2000.Google Scholar
[IK50] J. H., Irving and J. G., Kirkwood. The statistical mechanical theory of transport processes. IV. the equations of hydrodynamics. J. Chem. Phys., 18:817–829, 1950.Google Scholar
[Irv08] Irving, . Jack Howard Irving [obituary]. Los Angeles Times, 2008.Google Scholar
[Jac88] K.W., Jacobsen. Bonding in metallic systems: An effective medium approach. Comments Condens. Matter Phys., 14:129–161, 1988.Google Scholar
[Jam06] R.D., James. Objective structures. J. Mech. Phys. Solids, 54:2354–2390, 2006.Google Scholar
[Jau67] W., Jaunzemis. Continuum Mechanics. New York: Macmillan, 1967.Google Scholar
[JBA02] A.N., Jackson, A.D., Bruce and G. J., Ackland. Lattice-switch monte carlo method: application to soft potentials. Phys. Rev. E, 65:036710, 2002.Google Scholar
[JD97] B., Joós and M. S., Duesbery. The Peierls stress of dislocations: An analytic formula. Phys. Rev. Lett., 78(2):266–269, 1997.Google Scholar
[Jen06] F., Jensen. Introduction to Computational Chemistry. Chichester: John Wiley & Sons, 2006.Google Scholar
[JG89] R.O., Jones and O., Gunnarsson. The density functional formalism, its applications and prospects. Rev. Mod. Phys., 61(3):689–746, 1989.Google Scholar
[JGP09] D., Jarecka, W.W., Grabowski and H., Pawlowska. Modeling of subgrid-scale mixing in large-eddy simulation of shallow convection. J. Atmos. Sci., 66(7):2125–2133, 2009.Google Scholar
[JHK+07] B., Jelinek, J., Houze, S., Kim, M. F., Horstemeyer, M. I., Baskes and S.-G., Kim. Modified embedded-atom method interatomic potentials for the Mg–Al alloy system. Phys. Rev. B, 75(5):054106, 2007.Google Scholar
[JL89] J., Jellinek and D. H., Li. Separation of the energy of overall rotation in any n-body system. Phys. Rev. Lett., 62(3):241–244, 1989.Google Scholar
[JNP87] K.W., Jacobsen, J. K., Norskov and M. J., Puska. Interatomic interactions in the effective-medium theory. Phys. Rev. B, 35(14):7423–7442, 1987.Google Scholar
[Joh64] R. A., Johnson. Interstitials and vacancies in α iron. Phys. Rev., 134(5A):A1329–A1336, 1964.Google Scholar
[Joh72] R. A., Johnson. Relationship between two-body interatomic potentials in a lattice model and elastic constants. Phys. Rev. B, 6(6):2094–2100, 1972.Google Scholar
[Joh88] R. A., Johnson. Analytic nearest-neighbor model for fcc metals. Phys. Rev. B, 37(8):3924–3931, 1988.Google Scholar
[Jon24a] J. E., Jones. On the determination of molecular fields. I. From the variation of the viscosity of a gas with temperature. Proc. R. Soc. London, Ser. A, 106(738):441–462, 1924.Google Scholar
[Jon24b] J. E., Jones. On the determination of molecular fields. II. From the equation of state of a gas. Proc. R. Soc. London, Ser. A, 106(738):463–477, 1924.Google Scholar
[JRD94] B., Joos, Q., Ren, and M. S., Duesbery. Peierls–Nabarro model of dislocations in silicon with generalized stacking fault restoring forces. Phys. Rev. B, 50:5890–5898, 1994.Google Scholar
[JvDGD09] D., Jiang, A. C. T., van Duin, W. A., Goddard, III and S., Dai. Simulating the initial stage of phenolic resin carbonization via the ReaxFF reactive force field. J. Phys. Chem. A, 113(25):6891–6894, 2009.Google Scholar
[JZL+03] H., Jiang, P., Zhang, B., Liu, et al. The effect of nanotube radius on the constitutive model for carbon nanotubes. Comput. Mater. Sci., 28(3–4):429–442, 2003.Google Scholar
[Kah10] A., Kahn. Surface and interface science laboratory website. http://www.princeton.edu/∼kahnlab/, 2010.
[Kan95a] L.N., Kantorovich. Thermoelastic properties of perfect crystals with nonprimitive lattices. I. General theory. Phys. Rev. B, 51(6):3520–3534, 1995.Google Scholar
[Kan95b] L.N., Kantorovich. Thermoelastic properties of perfect crystals with nonprimitive lattices. II. Application to KCl and NaCl. Phys. Rev. B, 51(6):3535–3548, 1995.Google Scholar
[Kax03] E., Kaxiras. Atomic and Electronic Structure of Solids. Cambridge: Cambridge University Press, 2003.Google Scholar
[KC92] L. P., Kubin and G., Canova. The modelling of dislocation patterns. Scr. Metall., 27:957–962, 1992.Google Scholar
[KCDM02] T., Kruml, D., Caillard, C., Dupas and J. L., Martin. A transmission electron microscopy in situ study of dislocation mobility in Ge. J. Phys. Condens. Matter, 14(48):12897–12902, 2002. Conference on Extended Defects in Semiconductors (EDS 2002), Bologna, Italy, Jun 01–06, 2002.Google Scholar
[KCF+05] W. E., King, G. H., Campbell, A., Frank, et al. Ultrafast electron microscopy in materials science, biology and chemistry. J. Appl. Phys., 97:111101, 2005.Google Scholar
[KD80] M. H., Klapper and D., DeBrota. Use of Caley–Menger determinants in the calculation of molecular structures. J. Comput. Phys., 37:56–69, 1980.Google Scholar
[Kea66] P.N., Keating. Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev., 145(2):637–645, 1966.Google Scholar
[Kep66] J., Kepler. On the Six-cornered Snowflake [edited and translated from the Latin by Colin Hardie, with essays by L. L., Whyte and B. F. J., Mason]. Oxford: Clarendon Press, 1966.
[KF96a] G., Kresse and J., Furthmuller. Efficiency of ab-initio total energy calculations formetals and semiconductors using a plane-wave basis set. Comput. Mater. Sci., 6(1):15–50, 1996.Google Scholar
[KF96b] G., Kresse and J., Furthmuller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 54(16):11169–11186, 1996.Google Scholar
[KG98] P., Klein and H., Gao. Crack nucleation and growth as strain localization in a virtual-bond continuum. Eng. Fract. Mech., 61:21–48, 1998.Google Scholar
[KGF91] S., Kohlhoff, P., Gumbsch and H. F., Fischmeister. Crack propagation in bcc crystals studied with a combined finite-element and atomistic model. Philos. Mag. A, 64(4):851–878, 1991.Google Scholar
[KGH04] I. G., Kevrekidis, C. W., Gear, and G., Hummer. Equation-free: The computeraided analysis of complex multiscale systems. AIChE J., 50(7):1346–1355, 2004.Google Scholar
[KGK00] A., Kelly, G. W., Groves and P., Kidd. Crystallography and Crystal Defects. Chichester: Wiley, revised edition, 2000.Google Scholar
[Khi49] A. I., Khinchin. Mathematical Foundations of Statistical Mechanics. New York: Dover Publications, 1949.Google Scholar
[Kir35] J. G., Kirkwood. Statistical mechanics of fluid mixtures. J. Chem. Phys., 3(5):300–313, 1935.Google Scholar
[Kir46] J. G., Kirkwood. The statistical mechanical theory of transport processes. I. General theory. J. Chem. Phys., 14:180–201, 1946.Google Scholar
[Kit96] C., Kittel. Introduction to Solid State Physics. Hoboken: Wiley, seventh edition, 1996.Google Scholar
[KO01] J., Knap and M., Ortiz. An analysis of the quasicontinuum method. J. Mech. Phys. Solids, 49(9):1899–1923, 2001.Google Scholar
[Koi65a] W. T., Koiter. The energy criterion of stability for continuous elastic bodies. – I. Proc. of the Koninklijke Nederlandse Akademie Van Wetenschappen, Ser. B, 68(4):178–189, 1965.Google Scholar
[Koi65b] W. T., Koiter. The energy criterion of stability for continuous elastic bodies. — II. Proc. of the Koninklijke Nederlandse Akademie Van Wetenschappen, Ser. B, 68(4):190–202, 1965.Google Scholar
[Koi65c] W. T., Koiter. On the instability of equilibrium in the absence of a minimum of the potential energy. Proc. of the Koninklijke Nederlandse Akademie Van Wetenschappen, Ser. B, 68(3):107–113, 1965.Google Scholar
[Kol54] A. N., Kolmogorov. On the conservation of conditionally periodic motions for a small change in Hamilton's functions [in Russian]. Dokl. Akad. Nauk SSSR, 98:525–530, 1954. English translation in LNP, 93:51–56, 1979.Google Scholar
[KPH98] C. L., Kelchner, S. J., Plimpton and J. C., Hamilton. Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B, 58(17):11085–11088, 1998.Google Scholar
[Kra08] H., Kragh. Max Planck and quantum theory: The reluctant revolutionary. Sci. Culture Rev., 5(6):23–31, 2008.Google Scholar
[Kro94] Herbert, Kroemer. Quantum Mechanics: For Engineering, Materials Science, and Applied Physics. Englewood Cliffs: Prentice Hall, 1994.Google Scholar
[KS65] W., Kohn and L. J., Sham. Self-consistent equations including exchange and correlation effects. Phys. Rev., 140(4A):A1133–A1138, 1965.Google Scholar
[KSB+99] L., Kalé, R., Skeel, M., Bhandarkar, et al. NAMD2: Greater scalability for parallel molecular dynamics. J. Comput. Phys., 151(1):283–312, 1999.Google Scholar
[Kuh78] T. S., Kuhn. Black Body Theory and theQuantum Discontinuity: 1894–1912. Oxford: Oxford University Press, 1978.Google Scholar
[KV95] J. D., Kress and A. F., Voter. Low-order moment expansions to tight binding for interatomic potentials: Successes and failures. Phys. Rev. B, 52:8766–8775. 1995.Google Scholar
[KZ06] P. A., Klein and J. A., Zimmerman. Coupled atomistic-continuum simulations using arbitrary overlapping domains. J. Comput. Phys., 213(1):86–116, 2006.Google Scholar
[Lal06] J. N., Lalena. From quartz to quasicrystals: probing nature's geometric patterns in crystalline substances. Crystallogr. Rev., 12(2):125–180, 2006.Google Scholar
[Lan70] C., Lanczos. The Variational Principles of Mechanics. Mineola: Dover, fourth edition, 1970.Google Scholar
[Lan73] O. E., Lanford. Entropy and equilbrium states in classical statistical mechanics. In A., Lenard, editor, Statistical Mechanics and Mathematical Problems, pages 1–113. Berlin: Springer-Verlag, 1973.Google Scholar
[Law93] B., Lawn. Fracture of Brittle Solids. Cambridge: Cambridge University Press, 1993.Google Scholar
[LB06] M. J., Louwerse and E. J., Baerends. Calculation of pressure in case of periodic boundary conditions. Chem. Phys. Lett., 421:138–141, 2006.Google Scholar
[LBK02] G., Lu, V. V., Bulatov, and N., Kioussis. Dislocation constriction and crossslip: An ab initio study. Phys. Rev. B, 66(14):144103, 2002.Google Scholar
[LC85] G. V., Lewis and C. R. A., Catlow. Potential models for ionic oxides. J. Phys. C: Solid State Phys., 18(6):1149–1161, 1985.Google Scholar
[LCN03] M. J., Leamy, P. W., Chung and R., Namburu. On an exact mapping and a higher order Born rule for use in analyzing graphene carbon nanotubes. Technical Report ARL-TR-3117, US Army Research Laboratory, Aberdeen Proving Ground, MD, 2003.
[Leb93] J. L., Lebowitz. Boltzmann's entropy and time's arrow. Phys. Today, 46(9):32–38, 1993.Google Scholar
[Leb99] J. L., Lebowitz. Statistical mechanics: A selective review of two central issues. Rev. Mod. Phys., 71:S346–S357, 1999.Google Scholar
[LHM+07] B. Q., Luan, S., Hyun, J. F., Molinari, N., Bernstein and M. O., Robbins. Multiscale modeling of two-dimensional contacts. Phys. Rev. E, 74:046710, 2007.Google Scholar
[Li10] J., Li. AtomEye website. http://mt.seas.upenn.edu/Archive/Graphics/A/, 2010.
[Lib05] K. G., Libbrecht. The physics of snow crystals. Rep. Prog. Phys., 68(4):855–895, 2005.Google Scholar
[Lio38] J., Liouville. Sur la théorie de la variation des constantes arbitraires. Journal de Mathémathiques Pures et Appliquées, 3:342–349, 1838.Google Scholar
[LJ25] J. E., Lennard-Jones. On the forces between atoms and ions. Proc. R. Soc. London, Ser. A, 109(752):584–597, 1925.Google Scholar
[LJ07] B.-J., Lee and J.-W., Jang. A modified embedded-atom method interatomic potential for the Fe–H system. Acta Mater., 55(20):6779–6788, 2007.Google Scholar
[LJCV08] G., Lebon, D., Jou and J., Casas-Vázquez. Understanding Non-equilitrium Thermodynamics: Foundations, Applications, Frontiers. Berlin: Springer-Verlag, 2008.Google Scholar
[LK05] G., Lu and E., Kaxiras. Overview of multiscale simulations of materials. In M., Rieth and W., Schommers, editors, Handbook of Theoretical and Computational Nanotechnology, Volume 4, Chapter 22. Stevenson Ranch: American Scientific Publishers, 2005.Google Scholar
[LKBK00a] G., Lu, N., Kioussis, V. V., Bulatov and E., Kaxiras. Generalized-stackingfault energy surface and dislocation properties of aluminum. Phys. Rev. B, 62(5):3099–3108, 2000.Google Scholar
[LKBK00b] G., Lu, N., Kioussis, V. V., Bulatov, and E., Kaxiras. The Peierls–Nabarro model revisited. Philos. Mag. Lett., 80(10):675–682, 2000.Google Scholar
[LKZP04] W. K., Liu, E. G., Karpov, S., Zhang and H. S., Park. An introduction to computational nano mechanics and materials. Comput. Meth. Appl. Mech. Eng., 193:1529–1578, 2004.Google Scholar
[LL61] G., Leibfried and W., Ludwig. Theory of anharmonic effects in crystals. In F., Seitz and D., Turnbull, editors, Solid State Physics: Advances in Research and Applications, Volume 12, pages 275–459. New York: Academic Press, 1961.Google Scholar
[LL80] L. D., Landau and E. M., Lifshitz. Statistical Physics, Part I. Oxford: Pergamon, third edition, 1980.Google Scholar
[LM02] F., Legoll and R., Monneau. Designing reversible measure invariant algorithms with applications to molecular dynamics. J. Chem. Phys., 117(23):10452–10464, 2002.Google Scholar
[LNS89] R., LeSar, R., Najafabadi, and D. J., Srolovitz. Finite-temperature defect properties from free-energy minimization. Phys. Rev. Lett., 63:624–627, 1989.Google Scholar
[LO09] M., Luskin and C., Ortner. An analysis of node-based cluster summation rules in the quasticontinuum method. SIAM J. Numer. Anal., 47(4):3070–3086, 2009.Google Scholar
[Lov27] A. E. H., Love. A Treatise on the Mathematical Theory of Elasticity. Cambridge: Cambridge University Press, 1927.Google Scholar
[LP79] J. L., Lebowitz and O., Penrose. Towards a rigorous molecular theory of metastability. In E. W., Montroll and J. L., Lebowitz, editors, Fluctuation Phenomena, pages 293–340. New York: North-Holland, 1979.Google Scholar
[LR95] R. G., Littlejohn and M., Reinsch. Internal or shape coordinates in the n-body problem. Phys. Rev. A, 52(3):2035–2051, 1995.Google Scholar
[LR97] R. G., Littlejohn and M., Reinsch. Gauge fields in the separation of rotations and internal motions in the n-body problem. Rev. Mod. Phys., 69(1):213–275, 1997.Google Scholar
[LRS96] B., Leimkuhler, S., Reich and R. D., Skeel. Integration Methods for Molecular Dynamics, Volume 82 of IMA Volumes in Mathematics and its Applications, pages 161–186. New York: Springer-Verlag, 1996.Google Scholar
[LS97] V. F., Lotrich and K., Szalewicz. Three-body contribution to binding energy of solid argon and analysis of crystal structure. Phys. Rev. Lett., 79(7):1301–1304. 1997.Google Scholar
[LS08] R. B., Lehoucq and S. A., Silling. Force flux and the peridynamic stress tensor. J. Mech. Phys. Solids, 56:1566–1577, 2008.Google Scholar
[LSAL03] Y., Li, D. J., Siegel, J. B., Adams and X.-Y., Liu. Embedded-atom-method tantalum potential developed by the force-matching method. Phys. Rev. B, 67(12):125101, 2003.Google Scholar
[LSB03] B. J., Lee, J. H., Shim and M. I., Baskes. Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method. Phys. Rev. B, 68(14), 2003.Google Scholar
[LTK06] G., Lu, E. B., Tadmor, and E., Kaxiras. From electrons to finite elements: A concurrent multiscale approach for metals. Phys. Rev. B, 73(2):024108, 2006.Google Scholar
[Lut89] J. F., Lutsko. Generalized expressions for the calculation of elastic constants by computer simulation. J. Appl. Phys., 65:2991–2997, 1989.Google Scholar
[Mac04] A. D., MacKerell. Empirical force fields for biological macromolecules: Overview and issues. J. Comput. Chem., 25:1584–1604, 2004.Google Scholar
[Mal69] L. E., Malvern. Introduction to the Mechanics of a Continuous Medium. Englewood Cliffs: Prentice-Hall, 1969.Google Scholar
[Mar75a] J. W., Martin. Many-body forces in metals and the Brugger elastic constants. J. Phys. C: Solid State Phys., 8:2837–2857, 1975.Google Scholar
[Mar75b] J. W., Martin. Many-body forces in solids and the Brugger elastic constants: II. Inner elastic constants. J. Phys. C: Solid State Phys., 8:2858–2868, 1975.Google Scholar
[Mar75c] J. W., Martin. Many-body forces in solids: Elastic constants of diamond-type crystals. J. Phys. C: Solid State Phys., 8:2869–2888, 1975.Google Scholar
[Mar90] E., Marquit. A plea for a correct translation of Newton's law of inertia. Am. J. Phys., 58:867–870, 1990.Google Scholar
[Mar04] R. M., Martin. Electronic Structure: Basic Theory and Practical Methods. Cambridge: Cambridge University Press, 2004.Google Scholar
[Max70] J. C., Maxwell. On reciprocal figures, frames, and diagrams of forces. Trans. R. Soc. Edin., xxvi:1–43, 1870.Google Scholar
[Maz00] G. F., Mazenko. Equilibrium Statistical Mechanics. New York: John Wiley and Sons, 2000.Google Scholar
[MB82] R., Mullen and T., Belytschko. Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation. Int. J. Numer. Methods Eng., 18:11–29, 1982.Google Scholar
[MB93] A. I., Murdoch and D., Bedeaux. On the physical interpretation of fields in continuum mechanics. Int. J. Eng. Sci., 31(10):1345–1373, 1993.Google Scholar
[MB94] A. I., Murdoch and D., Bedeaux. Continuum equations of balance via weighted averages of microscopic quantities. Proc. Math. Phys. Sci., 445(1923):157–179, 1994.Google Scholar
[MBG+06] J. A., Moriarty, L. X., Benedict, J. N., Glosli, et al. Robust quantum-based interatomic potentials for multiscale modeling in transition metals. J. Mater. Res., 21(3):563–573, 2006.Google Scholar
[MBR+02] J. A., Moriarty, J. F., Belak, R. E., Rudd, P., Soderlind, F. H., Streitz and L. H., Yang. Quantum-based atomistic simulation of materials properties in transition metals. J. Phys. Condens. Matter, 14(11):2825–2857, 2002.Google Scholar
[MDF94] M. J., Mills, M. S., Daw and S. M., Foiles. High-resolution transmission electron-microscopy studies of dislocation cores in metals and intermetallic compounds. Ultramicroscopy, 56:79–93, 1994.Google Scholar
[Men00] K., Menger. What is the calculus of variations and what are its applications? In J., Newman, editor, The World of Mathematics, Volume 2, Part V, Chapter 8, pages 886–890. Mineola: Dover, 2000.
[Met87] N., Metropolis. The beginning of the Monte Carlo method. Los Alamos Science, 15:125–130, 1987.Google Scholar
[Mey85] H.-D., Meyer. Theory of the Liapunov exponents of Hamiltonian systems and a numerical study on the transition from regular to irregular classical motion. J. Chem. Phys., 84(8):3147–3161, 1985.Google Scholar
[MH36] W. E., Morrell and J. H., Hildebrand. The distribution of molecules in amodel liquid. J. Chem. Phys., 4(3):224–227, 1936.Google Scholar
[MH94] J. E., Marsden and T. J. R., Hughes. Mathematical Foundations of Elasticity. New York: Dover, 1994.Google Scholar
[MH00] D., Marx and J., Hutter. Ab initio molecular dynamics: Theory and implementation. In J., Grotendorst, editor, Modern Methods and Algorithms of Quantum Chemistry, Volume 1, pages 301–449. Jülich: John von Neumann Institute for Computing, 2000.Google Scholar
[Mis04] Y., Mishin. Atomistic modeling of the γ and γ′-phases of the Ni–Al system. Acta Mater., 52(6):1451–1467, 2004.Google Scholar
[MJ94] G., Mills and H., Jónsson. Quantum and thermal effects in H2 dissociative adsorption – evaluation of free-energy barriers in multidimensional quantum-systems. Phys. Rev. Lett., 72(7):1124–1127, 1994.Google Scholar
[MJS95] G., Mills, H., Jónsson, and G. K., Schenter. Reversible work transition-state theory – application to dissociative adsorption of hydrogen. Surf. Sci., 324(2–3):305–337, 1995.Google Scholar
[MKT92] G. J., Martyna, M. L., Klein and M., Tuckerman. Nosé–Hoover chains – the canonical ensemble via continuous dynamics. J. Chem. Phys., 97(4):2635–2643. 1992.Google Scholar
[MM77] J. E., Mayer and M. G., Mayer. Statistical Mechanics. New York: Wiley, second edition, 1977.Google Scholar
[MM81] R. A., MacDonald and W. M., MacDonald. Thermodynamic properties of fcc metals at high temperatures. Phys. Rev. B, 24:1715–1724, 1981.Google Scholar
[MM00] R., Malek and N., Mousseau. Dynamics of Lennard-Jones clusters: A characterization of the activation–relaxation technique. Phys. Rev. E, 62(6, Part A):7723–7728, 2000.Google Scholar
[MMEG07] M., Mrovec, M., Moseler, C., Elsaesser and P., Gumbsch. Atomistic modeling of hydrocarbon systems using analytic bond-order potentials. Prog. Mater. Sci., 52(2–3):230–254, 2007.Google Scholar
[MMP+01] Y., Mishin, M. J., Mehl, D. A., Papaconstantopoulos, A. F., Voter and J. D., Kress. Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Phys. Rev. B, 63(22):224106, 2001.Google Scholar
[MMP02] Y., Mishin, M. J., Mehl and D. A., Papaconstantopoulos. Embedded-atom potential for B2 – NiAl. Phys. Rev. B, 65(22), 2002.Google Scholar
[Moo90] D. M., Moody. Unsteady expansion of an ideal gas into a vacuum. J. Fluid Mech., 214:455–468, 1990.Google Scholar
[Mor29] P. M., Morse. Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev., 34(1):57–64, 1929.Google Scholar
[Mor88] J. A., Moriarty. Density-functional formulation of the generalized pseudopotential theory: Transition-metal interatomic potentials. Phys. Rev. B, 38(5):3199–3231, 1988.Google Scholar
[Mor90] J. A., Moriarty. Analytic representation of multiion interatomic potentials in transition-metals. Phys. Rev. B, 42(3):1609–1628, 1990.Google Scholar
[Mor94] J. A., Moriarty. Angular forces and melting in bcc transition metals: A case study of molybdenum. Phys. Rev. B, 49(18):12431–12445, 1994.Google Scholar
[Mos62] J. K., Moser. On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II., 1:1–20, 1962.Google Scholar
[MP76] H. J., Monkhorst and J.D., Pack. Special points for Brillouin-zone integrations. Phys. Rev. B, 13(12):5188–5192, 1976.Google Scholar
[MP96] R., Miller and R., Phillips. Critical analysis of local constitutive models for slip and decohesion. Philos. Mag. A, 73(4):803, 1996.Google Scholar
[MPBO96] R., Miller, R., Phillips, G., Beltz and M., Ortiz. A non-local formulation of the Peierls dislocation model. J. Mech. Phys. Solids, 46(10):1845–68, 1996.Google Scholar
[MPDJ98] M. C., Michelini, R., Pis Diez, and A. H., Jubert. A density functional study of small nickel clusters. Int. J. Quantum Chem., 70(4–5):693–701, 1998.Google Scholar
[MPT83] P. S., Marcus, W.H., Press and S. A., Teukolsky. Multiscale modelequations for turbulent convection and convective overshoot. Astrophys. J., 267(2):795–821, 1983.Google Scholar
[MQ06] R. I., McLachlan and G. R. W., Quispel. Geometric integrators for ODEs. J. Phys. A: Math. Gen., 39(19):5251–5285, 2006.Google Scholar
[MRR+53] N., Metropolis, A.W., Rosenbluth, M.N., Rosenbluth, A.H., Teller and E., Teller. Equation of state calculations by fast computing machines. J. Chem. Phys., 21:1087–1092, 1953.Google Scholar
[MRT06] S., Morante, G. C., Rossi and M., Testa. The stress tensor of a molecular system: An exercise in statistical mechanics. J. Chem. Phys., 125:034101, 2006.Google Scholar
[MS00] R. E., Miller and V.B., Shenoy. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11:139–147, 2000.Google Scholar
[MS06] G., Martin and F., Soisson. Kinetic Monte Carlo method to model diffusion controlled phase transformations in the solid state. In S., Yip, editor, Handbook of Materials Modeling, Part A, Methods, Chapter 7.9, pages 2223–2248. New York: Springer Science and Business Media, 2006.Google Scholar
[MS07] R., Maranganti and P., Sharma. Length scales at which classical elasticity breaks down for various materials. Phys. Rev. Lett., 98(19), 2007.Google Scholar
[MSV01] F., Montalenti, M. R., Sorensen and A. R., Voter. Closing the gap between experiment and theory: Crystal growth by temperature accelerated dynamics. Phys. Rev. Lett., 87(12), 2001.Google Scholar
[MT02] R. E., Miller and E.B., Tadmor. The quasicontinuum method: Overview, applications and current directions. J. Comput.-Aided Mater. Des., 9:203–239, 2002.Google Scholar
[MT07] R. E., Miller and E. B., Tadmor. Hybrid continuum mechanics and atomistic methods for simulating materials deformation and failure. MRS Bull., 32:920–926, 2007.Google Scholar
[MT09a] R. E., Miller and E. B., Tadmor. Multiscale benchmark code, multibench, 2009. Available at www.qcmethod.org.
[MT09b] R. E., Miller and E. B., Tadmor. A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Modell. Simul. Mater. Sci. Eng., 17:053001, 2009.Google Scholar
[MTP02] K. L., Merkle, L. J., Thompson and F., Phillipp. Collective effects in grain boundary migration. Phys. Rev. Lett., 88(22), 2002.Google Scholar
[MU49] N., Metropolis and S., Ulam. The Monte Carlo method. J. Am. Stat. Assoc., 44:335–341, 1949.Google Scholar
[Mur83] A. I., Murdoch. The motivation of continuum concepts and relations from discrete considerations. Q. J. Mech. Appl. Math., 36:163–187, 1983.Google Scholar
[Mur85] A. I., Murdoch. A corpuscular approach to continuum-mechanics: Basic considerations. Arch. Ration. Mech. Anal., 88:291–321, 1985.Google Scholar
[Mur03] A. I., Murdoch. On the microscopic interpretation of stress and couple stress. J. Elast., 71:105–131, 2003.Google Scholar
[Mur07] A. I., Murdoch. A critique of atomistic definitions of the stress tensor. J. Elast., 88:113–140, 2007.Google Scholar
[MV01] F., Montalenti and A. F., Voter. Applying accelerated molecular dynamics to crystal growth. Phys. Stat. Sol. B, 226(1):21–27, 2001. 2nd Motorola Workshop on Computational Materials and Electronics, Tempe, AZ, Nov. 09–10, 2000.Google Scholar
[MV02] F., Montalenti and A. F., Voter. Exploiting past visits or minimum-barrier knowledge to gain further boost in the temperature-accelerated dynamics method. J. Chem. Phys., 116(12):4819–4828, 2002.Google Scholar
[MVH+10] J., Marian, G., Venturini, B. L., Hansen, et al. Finite-temperature extension of the quasicontinuum method using Langevin dynamics: Entropy losses and analysis of errors. Modell. Simul. Mater. Sci. Eng., 18(1), 2010.Google Scholar
[MW97] J. A., Moriarty and M., Widom. First-principles interatomic potentials for transition-metal aluminides: Theory and trends across the 3d series. Phys. Rev. B, 56(13):7905–7917, 1997.Google Scholar
[MW99] L. J., Munro and D. J., Wales. Defect migration in crystalline silicon. Phys. Rev. B, 59(6):3969–3980, 1999.Google Scholar
[NA95] F.R.N., Nabarro and A. S., Argon. Egon Orowan. 2 August 1902–3 August 1989. Biographical Memoirs of Fellows of the Royal Society, 41:317–340, 1995.Google Scholar
[Nab47] F.R.N., Nabarro. Dislocations in a simple cubic lattice. Proc. Phys. Soc. London, 59:256, 1947.Google Scholar
[Nab87] F.R.N., Nabarro. Theory of Crystal Dislocations. New York: Dover Books on Physics and Chemistry, 1987.Google Scholar
[New30] I., Newton. Opticks: or a Treatise on the Reflexions, Refractions, Inflexions and Colours of Light. London, fourth english edition. William Inngs, 1730.Google Scholar
[NKN+07] A., Nakano, R. K., Kalia, K., Nomura, et al. A divide-and-conquer/cellulardecomposition framework for million-to-billion atom simulations of chemical reactions. Comput. Mater. Sci., 38(4):642–652, 2007.Google Scholar
[NL80] J. K., Norskøv and N.D., Lang. Effective-medium theory of chemical binding: Application to chemisorption. Phys. Rev. B, 21(6):2131–2136, 1980.Google Scholar
[NM83] O. H., Nielsen and R. M., Martin. 1st-principles calculation of stress. Phys. Rev. Lett., 50(9):697–700, 1983.Google Scholar
[NM85] O. H., Nielsen and R. M., Martin. Quantum-mechanical theory of stress and force. Phys. Rev. B, 32(6):3780–3791, 1985.Google Scholar
[NM02] R. J., Needs and A., Mujica. Theoretical description of high-pressure phases of semiconductors. High Pressure Res., 22(2, Sp. Iss. SI):421–427, 2002.Google Scholar
[NMVH07] D., Nguyen-Manh, V., Vitek, and A. P., Horsfield. Environmental dependence of bonding: A challenge for modelling of intermetallics and fusion materials. Prog. Mater. Sci., 52(2–3):255–298, 2007.Google Scholar
[Nol55] W., Noll. Die herleitung der grundgleichungen der thermomechanik der kontinua aus der statischen mechanik. J. Ration. Mech. Anal., 4:627–646, 1955.Google Scholar
[Nos84] S., Nosé. A molecular-dynamics method for simulations in the canonical ensemble. Mol. Phys., 52(2):255–268, 1984.Google Scholar
[NPM90] R. M., Nieminen, M. J., Puska, and M. J., Manninen, editors. Many-Atom Interactions in Solids, Volume 48 of Proceedings in Physics. Berlin: Springer-Verlag, 1990.Google Scholar
[NRL09] NRL. Crystal lattice structures website. http://cst-www.nrl.navy.mil/lattice/index.html, 2009.
[NW99] J., Nocedal and S. J., Wright. Numerical Optimization. New York: Springer Verlag, 1999.Google Scholar
[Ogd84] R.W., Ogden. Non-linear Elastic Deformations. Chichester: Ellis Horwood, 1984.Google Scholar
[Omn99] R., Omn`es. Understanding Quantum Mechanics. Princeton: Princeton University Press, 1999.Google Scholar
[O'Ro98] J., O'Rourke. Computational Geometry in C. Cambridge: Cambridge University Press, second edition, 1998.Google Scholar
[Oro34a] E., Orowan. Zur kristallplastizität. I Tieftemperaturplastizitt und beckersche formel. Z. Phys., 89(9–10):605–613, 1934.Google Scholar
[Oro34b] E., Orowan. Zur kristallplastizität. II Die dynamische auffassung der kristallplastizität. Z. Phys., 89(9–10):614–633, 1934.Google Scholar
[Oro34c] E., Orowan. Zur kristallplastizität. III Über den mechanismus des gleitvorganges. Z. Phys., 89(9–10):634–659, 1934.Google Scholar
[Oro44] E., Orowan. Discussion of the significance of tensile and other mechanical test properties of metals. In Proceedings of the Institute of Mechanical Engineers, Volume 151, pages 131–146, London: Institute of Mechanical Engineers, 1944.Google Scholar
[OSC04] W. K., Olson, D., Swigon, and B.D., Coleman. Implications of the dependence of the elastic properties of DNA on nucleotide sequence. Philos. Trans. R. Soc. London, Ser. A, 362(1820):1403–1422, 2004.Google Scholar
[Par76] G. P., Parry. On the elasticity of monatomic crystals. Math. Proc. Camb. Phil. Soc., 80:189–211, 1976.Google Scholar
[Par04] G. P., Parry. On essential and non-essential descriptions of multilattices. Math. Mech. Solids, 9:411–418, 2004.Google Scholar
[PB05] C.W., Padgett and D.W., Brenner. A continuum-atomistic method for incorporating Joule heating into classical molecular dynamics simulations. Mol. Simul., 31(11):749–757, 2005.Google Scholar
[PBL08] M. L., Parks, P.B., Bochev and R. B., Lehoucq. Connecting atomistic-tocontinuum coupling and domain decomposition. Multiscale Model. Simul., 7(1):362–380, 2008.Google Scholar
[PBO06] S., Prudhomme, P. T., Bauman and J. T., Oden. Error control for molecular statics problems. Int. J. Multiscale Comput. Eng., 4(5–6):647–662, 2006.Google Scholar
[PBS66] O. G., Peterson, D.N., Batchelder and R.O., Simmons. Measurements of x-ray lattice constant, thermal expansivity, and isothermal compressibility of argon crystals. Phys. Rev., 150(2):703–711, 1966.Google Scholar
[PC03] J.W., Ponder and D. A., Case. Force fields for protein simulations. In Protein Simulations, volume 66 of Advances in protein chemistry, pages 27–85. San Diego: Academic Press Inc 2003.Google Scholar
[PDSK07] M., Praprotnik, L., Delle Site and K., Kremer. A macromolecule in a solvent: Adaptive resolution molecular dynamics simulation. J. Chem. Phys., 126(13), 2007.Google Scholar
[PDSK08] M., Praprotnik, L., Delle Site and K., Kremer. Multiscale simulation of soft matter: From scale bridging to adaptive resolution. Annu. Rev. Phys. Chem., 59:545–571, 2008.Google Scholar
[Pei40] R. E., Peierls. The size of a dislocation. Proc. Phys. Soc. London, 52:34, 1940.Google Scholar
[Pei64] R. E., Peierls. Quantum Theory of Solids. Oxford: Oxford University Press, second edition, 1964.Google Scholar
[Pen79] O., Penrose. Foundations of statistical mechanics. Rep. Prog. Phys., 42:1937–2006, 1979.Google Scholar
[Pen99] R., Penrose. The Emperor's New Mind. Oxford: Oxford University Press, 1999.Google Scholar
[Pen02] O., Penrose. Statistical mechanics of nonlinear elasticity. Markov Processes and Related Fields, 8:351–364, 2002. Available online at www.ma.hw.ac.uk/∼oliver/.Google Scholar
[Pen05] O., Penrose. Foundations of Statistical Mechanics: A Deductive Treatment. Mineola: Dover Publications, 2005.Google Scholar
[Pen06] O., Penrose. Correction to ‘statistical mechanics of nonlinear elasticity’. Markov Processes and Related Fields, 12:169, 2006. Available online at www.ma.hw.ac.uk/∼oliver/.Google Scholar
[Pet89] D. G., Pettifor. New many-body potential for the bond order. Phys. Rev. Lett., 63(22):2480–2483, 1989.Google Scholar
[Pet95] D. G., Pettifor. Bonding and Structure of Molecules and Solids. Oxford: Oxford University Press, 1995.Google Scholar
[Phi01] R., Phillips. Crystals, Defects and Microstructures. Cambridge: Cambridge University Press, 2001.Google Scholar
[Pit85] M., Pitteri. On ν + 1-lattices. J. Elast., 15:3–25, 1985.Google Scholar
[Pit86] M., Pitteri. Continuum equuations of balance in classical statistical mechanics. Arch. Ration. Mech. Anal., 94:291–305, 1986.Google Scholar
[Pit90] M., Pitteri. On a statistical-kinetic model for generalized continua. Arch. Ration. Mech. Anal., 111:99–120, 1990.Google Scholar
[Pit98] M., Pitteri. Geometry and symmetry of multilattices. Int. J. Plast., 14:139–157, 1998.Google Scholar
[PK07] H. S., Park and P. A., Klein. Surface Cauchy–Born analysis of surface stress effects on metallic nanowires. Phys. Rev. B, 75(8), 085408, 2007.Google Scholar
[PK08] H. S., Park and P. A., Klein. Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress. J. Mech. Phys. Solids, 56(11):3144–3166. 2008.Google Scholar
[PKW06] H. S., Park, P.A., Klein and G. J., Wagner. A surface Cauchy–Born model for nanoscale materials. Int. J. Numer. Methods Eng., 68(10):1072–1095, 2006.Google Scholar
[PL71] O., Penrose and J. L., Lebowitz. Rigorous treatment of metastable states in the van der Waals–Maxwell theory. J. Stat. Phys., 3(2):211–236, 1971.Google Scholar
[PL04] H. S., Park and W. K., Liu. An introduction and tutorial on multiple-scale analysis in solids. Comput. Meth. Appl. Mech. Eng., 193:1733–1772, 2004.Google Scholar
[Pla01] M., Planck. Ueber das Gesetz der Energieverteilung im Normalspectrum. Ann. der Phys., 309:553–563, 1901.Google Scholar
[Pla13] M., Plancherel. Beweis der Unmöglichkeit ergödischer mechanischer Systeme. Ann. der Phys., 42:1061–1163, 1913.Google Scholar
[Pla20] M., Planck. The genesis and present state of development of the quantum theory (Nobel lecture). http://nobelprize.org/nobel_prizes/physics/laureates/1918.planck-lecture.html, June 2, 1920.
[PLBK01] R., Plass, J. A., Last, N. C., Bartelt and G. L., Kellogg. Nanostructures – self-assembled domain patterns. Nature, 412(6850):875, 2001.Google Scholar
[Pli95] S. J., Plimpton. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys., 117:1–19, 1995.Google Scholar
[Pli09] S. J., Plimpton. LAMMPS website. http://lammps.sandia.gov, 2009.
[PMC+95] R.O., Piltz, J.R., Maclean, S. J., Clark, et al. Structure and properties of silicon XII: A complex tetrahedrally bonded phase. Phys. Rev. B, 52(6):4072–4085, 1995.Google Scholar
[PMKW78] P., Pierański, J., Malecki, W., Kuczyński and K., Wojciechowski. A hard-disc system, an experimental model. Philos. Mag. A, 37:107–115, 1978.Google Scholar
[PMP01] D. N., Pawaskar, R., Miller, and R., Phillips. Structure and energetics of longperiod tilt grain boundaries using an effective hamiltonian. Phys. Rev. B, 63:214105–214118, 2001.Google Scholar
[PMRC90] B., Pouligny, R., Malzbender, P., Ryan and N. A., Clark. Analog simulation of melting in two dimensions. Phys. Rev. B, 42(1):988–991, 1990.Google Scholar
[PNN10] PNNL. NWChem website. http://www.emsl.pnl.gov/capabilities/computing/nwchem, 2010.
[PO04] D. G., Pettifor and I. I., Oleynik. Interatomic bond-order potentials and structural prediction. Prog. Mater. Sci., 49(3–4):285–312, 2004.Google Scholar
[Pol34] M., Polanyi. Über eine Art Gitterstörung, die einen Kristall plastisch machen könnte. Z. Phys., 89(9–10):660–664, 1934.Google Scholar
[Pol71] E., Polak. Computational Methods in Optimization: A Unified Approach, volume 77 of Mathematics in Science and Engineering. Academic Press, New York, 1971.Google Scholar
[PR81] M., Parrinello and A., Rahman. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys., 52(12):7182–7190, 1981.Google Scholar
[PR82] M., Parrinello and A., Rahman. Strain fluctuations and elastic-constants. J. Chem. Phys., 76(5):2662–2666, 1982.Google Scholar
[PRTT05] J. M., Porta, L., Ros, F., Thomas and C., Torras. A branch-and-prune solver for distance constraints. IEEE Trans. Rob., 21(2):176–187, 2005.Google Scholar
[PTA+92] M. C., Payne, M. P., Teter, D. C., Allan, T. A., Arias and J. D., Joannopoulos. Iterative minimization techniques for ab initio total energy calculations: Molecular dyanmics and conjugate gradients. Rev. Mod. Phys., 64:1045–1097. 1992.Google Scholar
[PTVF92] W. H., Press, S. A., Teukolsky, W. T., Vetterling and B. P., Flannery. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge: Cambridge University Press, second edition, 1992.Google Scholar
[PTVF08] W. H., Press, S. A., Teukolsky, W. T., Vetterling and B. P., Flannery. Numerical recipes: The art of scientific computing. http://www.nr.com, 2008.
[PW92] J. P., Perdew and Y., Wang. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B, 45(23):13244–13249, 1992.Google Scholar
[PZ81] J. P., Perdew and A., Zunger. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B, 23(10):5048–5079. 1981.Google Scholar
[PZ00] M., Pitteri and G., Zanzotto. Continuum Models for Phase Transitions and Twinning in Crystals. London: CRC/Chapman and Hall, 2000.Google Scholar
[QSCM05] S., Qu, V., Shastry, W. A., Curtin and R. E., Miller. A finite temperature, dynamic, coupled atomistic/discrete dislocation method. Modell. Simul. Mater. Sci. Eng., 13(7):1101–1118, 2005.Google Scholar
[QWL04] D., Qian, G. J., Wagner and W. K., Liu. A multiscale projection method for the analysis of carbon nanotubes. Comput. Meth. Appl. Mech. Eng., 193:1603–32, 2004.Google Scholar
[Rad87] C., Radin. Low temperature and the origin of crystalline symmetry. Int. J. Mod. Phys. B, 1(5 & 6):1157–1191, 1987.Google Scholar
[Rah64] A., Rahman. Correlations in the motion of atoms in liquid argon. Phys. Rev., 136(2A):A405–A411, 1964.Google Scholar
[Rap95] D. C., Rapaport. The Art of Molecular Dynamics Simulation. New York: Cambridge University Press, 1995.Google Scholar
[Ray82] J. R., Ray. Fluctuations and thermodynamics properties of anisotropic solids. J. Appl. Phys., 53(9):6441–6443, 1982.Google Scholar
[Ray83] J. R., Ray. Molecular-dynamics equations of motion for systems varying in shape and size. J. Chem. Phys., 79(10):5128–5130, 1983.Google Scholar
[RB94] J. R., Rice and G. E., Beltz. The activation energy for dislocation nucleation at a crack. J. Mech. Phys. Solids, 42:333–360, 1994.Google Scholar
[RB98] R. E., Rudd and J. Q., Broughton. Coarse-grained molecular dynamics and the atomic limit of finite elements. Phys. Rev. B, 58(10):R5893–R5896, 1998.Google Scholar
[RB99] R. E., Rudd and J. Q., Broughton. Atomistic simulation of MEMS resonators through the coupling of length scales. J. Model. Simul. Microsys., 1(1):29–38, 1999.Google Scholar
[RB00] R. E., Rudd and J. Q., Broughton. Concurrent coupling of length scales in solid state systems. Phys. Stat. Sol. B, 217:251–291, 2000.Google Scholar
[RB05] R. E., Rudd and J. Q., Broughton. Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature. Phys. Rev. B, 72(14):144104, 2005.Google Scholar
[RD91] T. J., Raeker and A. E., DePristo. Theory of chemical bonding based on the atom-homogeneous electron-gas system. Int. Rev. Phys. Chem., 10(1):1–54, 1991.Google Scholar
[Ref00] K., Refson. MOLDY: a portable molecular dynamics simulation program for serial and parallel computers. Comput. Phys. Commun., 126(3):310–329, 2000.Google Scholar
[Rei64] M., Reiner. The Deborah number. Phys. Today, 17:62, 1964.Google Scholar
[Rei85] F., Reif. Fundamentals of Statistical and Thermal Physics. Singapore: McGraw-Hill, international edition, 1985.Google Scholar
[RFA02] M., Ruda, D., Farkas and J., Abriata. Interatomic potentials for carbon interstitials in metals and intermetallics. Sci. Mater., 46(5):349–355, 2002.Google Scholar
[RFG09] M., Ruda, D., Farkas and G., Garcia. Atomistic simulations in the Fe–C system. Comput. Mater. Sci., 45(2):550–560, 2009.Google Scholar
[RFS81] J. H., Rose, J., Ferrante and J. R., Smith. Universal binding energy curves for metals and bimetallic interfaces. Phys. Rev. Lett., 47:675–678, 1981.Google Scholar
[RG81] J. R., Ray and H. W., Graben. Direct calculation of fluctuation formulae in the microcanonical ensemble. Mol. Phys., 43(6):1293–1297, 1981.Google Scholar
[RGH81] J. R., Ray, H. W., Graben, and J. M., Haile. A new adiabatic ensemble with particle fluctuations. J. Chem. Phys., 75(8):4077–4079, 1981.Google Scholar
[Ric92] J. R., Rice. Dislocation nucleation from a crack tip: An analysis based on the Peierls concept. J. Mech. Phys. Solids, 40:239, 1992.Google Scholar
[RL02] J. M., Rickman and R., LeSar. Free-energy calculations in materials research. Annu. Rev. Mater. Res., 32:195–217, 2002.Google Scholar
[Ros13] A., Rosenthal. Beweis der unmöglichkeit ergödischer gasssystemse. Ann. der Phys., 42:796–806, 1913.Google Scholar
[RPFS00] K., Rościszewski, B., Paulus, P., Fulde, and H., Stoll. Ab initio coupled-cluster calculations for the fcc and hcp structures of rare-gas solids. Phys. Rev. B, 62(9):5482–5488, 2000.Google Scholar
[RPW+91] J. M., Rickman, S. R., Phillpot, D., Wolf, D. L., Woodraska and S., Yip. On the mechanism of grain-boundary migration in metals – a molecular-dynamics study. J. Mater. Res., 6(11):2291–2304, 1991.Google Scholar
[RR84] J. R., Ray and A., Rahman. Statistical ensembles and molecular-dynamics studies of anisotropic solids. J. Chem. Phys., 80(9):4423–4428, 1984.Google Scholar
[RS96] J. D., Rittner and D. N., Seidman. < 110 > symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies. Phys. Rev. B, 54(10):6999–7015, 1996.Google Scholar
[RSF70] R. A., Rege, E. S., Szekeres and W. D., Forgeng. 3-dimensional view of alumina clusters in aluminum-killed low-carbon steel. Metall. Trans., 1(9):2652–&, 1970.Google Scholar
[RSGF84] J. H., Rose, J. R., Smith, F., Guinea and J., Ferrante. Universal features of the equation of state of metals. Phys. Rev. B, 29(6):2963–2969, 1984.Google Scholar
[Rub00] M. B., Rubin. Cosserat Theories: Shells, Rods and Points, Volume 79 of Solid Mechanics and its Applications. Dordrecht: Kluwer, 2000.Google Scholar
[Rud01] R. E., Rudd. Concurrent multiscale modeling of embedded nanomechanics. In V., Bulatov, F., Cleri, L., Colombo, L., Lewis, and N., Mousseau, editors, Advances in Materials Theory and Modeling – Bridging Over Multiple-Length and Time Scales, Mater. Res. Soc. Symp. Proc., Vol. 677, pages AA1.6.1–AA1.6.12. Warrendale: Materials Research Society, 2001.Google Scholar
[Rue63] D., Ruelle. Classical statistical mechanics of a system of particles. Helv. Phys. Acta, 36:183–197, 1963.Google Scholar
[Rue69] D., Ruelle. Statistical Mechanics: Rigorous Results. Reading: Benjamin, 1969.Google Scholar
[Rue99] D., Ruelle. Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J. Stat. Phys., 95:393–468, 1999.Google Scholar
[Rus06] A., Ruszczyński. Nonlinear Optimization. Princeton: Princeton University Press, 2006.Google Scholar
[SABW82] W. C., Swope, H. C., Andersen, P. H., Berens and K. R., Wilson. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters. J. Chem. Phys., 76:637–649, 1982.Google Scholar
[SAG+02] J. M., Soler, E., Artacho, J. D., Gale, et al. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter, 14(11):2745–2779, 2002.Google Scholar
[Sak94] J. J., Sakurai. Modern Quantum Mechanics. Reading: Addison-Wesley, revised edition, 1994.Google Scholar
[Sal01] J., Salençon. Handbook of Continuum Mechanics: General Concepts, Thermoelasticity. Berlin: Springer, 2001.Google Scholar
[San93] D. E., Sands. Introdcution to Crystallography. Mineola: Dover, 1993.Google Scholar
[SB06] A. P., Sutton and R. W., Balluffi. Interfaces in Crystalline Materials. Oxford: Oxford University Press, 2006.Google Scholar
[SBR93] Y., Sun, G. E., Beltz and J. R., Rice. Estimates from atomic models of tensionshear coupling in dislocation nucleation from a crack tip. Mater. Sci. Eng. A, 170:67–85, 1993.Google Scholar
[Sch26] E., Schrödinger. An undulatory theory of the mechanics of atoms and molecules. Phys. Rev., 28(6):1049–1070, 1926.Google Scholar
[Sch44] E., Schrödinger. What is Life. The Physical Aspect of the Living Cell. Cambridge: Cambridge University Press, 1944.Google Scholar
[Sch76] L. A., Schwalbe. Equilibrium vacancy concentration measurements in solid argon. Phys. Rev. B, 14(4):1722–1732, 1976.Google Scholar
[Sch83a] R., Schiestel. Multiple scale concept in turbulence modeling. 1. Multiplescale model for turbulence kinetic-energy and mean-square of passive scalar fluctuations. J. Mec. Theor. Appl., 2(3):417–449, 1983.Google Scholar
[Sch83b] E., Schrödinger. My View of the World. Woodbridge: Ox Bow Press, 1983.Google Scholar
[SDG84] J. M., Sanchez, F., Ducastelle and D., Gratias. Generalized cluster description of multicomponent systems. Physica A, 128(1–2):334–350, 1984.Google Scholar
[SDKF08] R., Stote, A., Dejaegere, D., Kuznetsov and L., Falquet. CHARMM molecular dynamics simulation tutorial. http://www.ch.embnet.org/MD-tutorial, 2008.
[SdVG+03] P., Sherwood, A. H., de Vries, M. F., Guest, et al. QUASI: A general purpose implementation of the QM/MM approach and its application to problems in catalysis. J. Mol. Struct., 632(Sp. Iss. SI):1–28, 2003.Google Scholar
[Seq09] SeqQuest. SeqQuest website. http://dft.sandia.gov/Quest, 2009.
[SES07] P., Steinmann, A., Elizondo and R., Sunyk. Studies of validity of the Cauchy Born rule by direct comparison of continuum and atomistic modelling. Modell. Simul. Mater. Sci. Eng., 15:5271–5281, 2007.Google Scholar
[Set06] J. P., Sethna. Statistical Mechanics: Entropy, Order Parameters, and Complexity. Oxford: Oxford University Press, 2006.Google Scholar
[SET11] V., Sorkin, R. S., Elliott, and E. B., Tadmor. A local quasicontinuum for 3D multilattice crystalline materials: Application to shape-memory alloys. Phys. Rev. B, 2011. submitted.
[Sew80] G. L., Sewell. Stability, equilibrium and metastability in statistical mechanics. Phys. Rep., 57(5):307–342, 1980.Google Scholar
[SGK+06] P., Schwerdtfeger, N., Gaston, R. P., Krawczyk, R., Tonner and G. E., Moyano. Extension of the Lennard–Jones potential: Theoretical investigations into rare-gas clusters and crystal lattices of He, Ne, Ar, and Kr using many-body interaction expansions. Phys. Rev. B, 73(6):064112, 2006.Google Scholar
[SH82] P., Schofield and J. R., Henderson. Statistical mechanics of inhomogeneous fluids. Proc. R. Soc. London, Ser. A, 379(1776):231–246, 1982.Google Scholar
[SH86] A. M., Stoneham and J. H., Harding. Interatomic potentials in solid state chemistry. Annu. Rev. Phys. Chem., 37:52–80, 1986.Google Scholar
[Sha03] T., Shardlow. Splitting for dissipative particle dynamics. SIAM J. Sci. Comput., 24(4):1267–1282, 2003.Google Scholar
[She94] J. R., Shewchuk. An introduction to the conjugate gradient method without the agonizing pain. www.cs.cmu.edu/∼quake-papers/painless-conjugategradient.pdf, 1994.
[SHH69] D. R., Squire, A. C., Holt and W. G., Hoover. Isothermal elastic constants for argon. Theory and Monte Carlo calculations. Physica, 42:388–397, 1969.Google Scholar
[Shi96] T. W., Shield. An experimental study of the plastic strain fields near a notch tip in a copper single crystal during loading. Acta Mater., 44(4):1547–1561, 1996.Google Scholar
[Sho48] W., Shockley. Minutes of the meeting at Chicago, Illinois December 29–31, 1947. Phys. Rev., 73(10):1217–1236, 1948. (“Half Dislocations”, page 1232).Google Scholar
[SIE10] SIESTA. SIESTA website. http://www.icmab.es/siesta, 2010.
[Sil02] S. A., Silling. The reformulation of elasiticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids, 48:175–209, 2002.Google Scholar
[Sin63] Ya. G., Sinai. On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics. Dokl. Akad. Nauk SSSR, 153:1261–1264, 1963. English translation in Sov. Math.-Dokl, 4:1818–1822, 1964.Google Scholar
[SK54] J. C., Slater and G. F., Koster. Simplified LCAO method for the periodic potential problem. Phys. Rev., 94(6):1498–1524, 1954.Google Scholar
[SK08] E., Salomon and A., Kahn. One-dimensional organic nanostructures: A novel approach based on the selective adsorption of organic molecules on silicon nanowires. Surf. Sci., 602(13):L79–L83, 2008.Google Scholar
[Skl93] L., Sklar. Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge: Cambridge University Press, 1993.Google Scholar
[SL08] S., Suresh and J., Li. Materials science: deformation of the ultra-strong. Nature, 456:716–717, 2008.Google Scholar
[SM66] A. J. F., Siegert and E., Meeron. Generalizations of the virial and Wall theorems in classical statistical mechanics. J. Math. Phys, 7:741–750, 1966.Google Scholar
[SM03] A., Suzuki and Y., Mishin. Interaction of point defects with grain boundaries in fcc metals. Interface Sci., 11(4):425–437, 2003.Google Scholar
[SM05] F., Sansoz and J. F., Molinari. Mechanical behavior of sigma tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study. Acta Mater., 53:1931–1944, 2005.Google Scholar
[SMC02] L. E., Shilkrot, R. E., Miller, and W. A., Curtin. Coupled atomistic and discrete dislocation plasticity. Phys. Rev. Lett., 89(2):025501, 2002.Google Scholar
[SMC04] L. E., Shilkrot, R. E., Miller, and W. A., Curtin. Multiscale plasticity modeling: Coupled atomistic and discrete dislocation mechanics. J. Mech. Phys. Solids, 52(4):755–787, 2004.Google Scholar
[SMC05] B., Shiari, R. E., Miller, and W. A., Curtin. Coupled atomistic/discrete dislocation simulations of nanoindentation at finite temperature. J. Eng. Mater. Technol., Trans. ASME, 127(4):358–368, 2005.Google Scholar
[SMK07] B., Shiari, R. E., Miller and D.D., Klug. Multiscale simulation of material removal processes at the nanoscale. J. Mech. Phys. Solids, 55(11):2384–2405, 2007.Google Scholar
[SMSJ04] T., Shimokawa, J. J., Mortensen, J., Schiøtz and K.W., Jacobsen. Matching conditions in the quasicontinuum method: Removal of the error introduced at the interface between the coarse-grained and fully atomistic region. Phys. Rev. B, 69:214104/1–10, 2004.Google Scholar
[SMT+98] V.B., Shenoy, R., Miller, E. B., Tadmor, R., Phillips and M., Ortiz. Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett., 80(4):742–745, 1998.Google Scholar
[SMT+99] V.B., Shenoy, R., Miller, E. B., Tadmor, D., Rodney, R., Phillips and M., Ortiz. An adaptive methodology for atomic scale mechanics: The quasicontinuum method. J. Mech. Phys. Solids, 47:611–642, 1999.Google Scholar
[SMV00] M. R., Sorensen, Y., Mishin and A. F., Voter. Diffusion mechanisms in Cu grain boundaries. Phys. Rev. B, 62(6):3658–3673, 2000.Google Scholar
[SOL07] F., Shimizu, S., Ogata and J., Li. Theory of shear banding in metallic glasses and molecular dynamics calculations. Mater. Trans., 48:2923–2927, 2007.Google Scholar
[SPT00] V.B., Shenoy, R., Phillips, and E. B., Tadmor. Nucleation of dislocations beneath a plane strain indenter. J. Mech. Phys. Solids, 48:649–673, 2000.Google Scholar
[SR74] F. H., Stillinger and A., Rahman. Improved simulation of liquid water by molecular dynamics. J. Chem. Phys., 60(4):1545–1557, 1974.Google Scholar
[SS86] M. J., Sippl and H. A., Scheraga. Cayley–Menger coordinates. Proc. Nat. Acad. Sci. USA, 83:2283–2287, 1986.Google Scholar
[SS92] J. R., Smith and D. J., Srolovitz. Developing potentials for atomistic simulations. Modell. Simul. Mater. Sci. Eng., 1:101–109, 1992.Google Scholar
[SS03] R., Sunyk and P., Steinmann. On higher gradients in continuum-atomistic modelling. Int. J. Solids Struct., 40:6877–96, 2003.Google Scholar
[SSH+03] E. J., Shin, B. S., Seong, Y. S., Han, K. P., Hong, C. H., Lee and H. J., Kang. Effect of precipitate size and dispersion on recrystallization behavior in Tiadded ultra low carbon steels. J. Appl. Crystallogr., 36(3 Part 1):624–628, 2003.Google Scholar
[SSP99] V., Shenoy, V., Shenoy and R., Phillips. Finite temperature quasicontinuum methods. In T., Diaz de la Rubia, E., Kaxiras, V., Bulatov, N. M., Ghoniem and R., Phillips, editors, Multiscale Modelling of Materials, Mater. Res. Soc. Symp. Proc., Vol. 538, pages 465–471. Warrendale: Materials Research Society, 1999.Google Scholar
[ST07] H. M., Senn and W., Thiel. QM/MM methods for biological systems. In Atomistic Approaches in Modern Biology: from Quantum Chemistry to Molecular Simulations, Volume 268 of Topics in Current Chemistry, pages 173–290. Berlin: Springer, 2007.Google Scholar
[Sta50] I., Stackgold. The Cauchy relations in molecular theory of elasticity. Q. Appl. Math., 8:169–186, 1950.Google Scholar
[STBK01] G. S., Smith, E.B., Tadmor, N., Bernstein and E., Kaxiras. Multiscale simulations of silicon nanoindentation. Acta Mater., 49(19):4089–4101, 2001.Google Scholar
[Sti95] F. H., Stillinger. Statistical mechanics of metastable matter: superheated and stretched liquids. Phys. Rev. E, 52(5):4685–4690, 1995.Google Scholar
[STK00] G. S., Smith, E. B., Tadmor, and E., Kaxiras. Multiscale simulation of loading and electrical resistance in silicon nanoindentation. Phys. Rev. Lett., 84(6):1260–1263, 2000.Google Scholar
[Sut91a] W., Sutherland. A kinetic theory of solids, with an experimental introduction. Philos. Mag., 32(194):31–43, 1891.Google Scholar
[Sut91b] W., Sutherland. A kinetic theory of solids, with an experimental introduction. Philos. Mag., 32(195):215–225, 1891.Google Scholar
[Sut91c] W., Sutherland. A kinetic theory of solids, with an experimental introduction. Philos. Mag., 32(199):524–553, 1891.Google Scholar
[Sut92] A. P., Sutton. Irrational interfaces. Prog. Mater. Sci., 36:167–202, 1992.Google Scholar
[SV00] M. R., Sørensen and A. F., Voter. Temperature-accelerated dynamics for simulation of infrequent events. J. Chem. Phys., 112:9599–9606, 2000.Google Scholar
[SvDL+09] E., Salmon, A. C. T., van Duin, F., Lorant, P.-M., Marquaire and W. A., Goddard, III. Thermal decomposition process in algaenan of Botryococcus braunii race 1. part 2: Molecular dynamics simulations using the ReaxFF reactive force field. Org. Geochem., 40(3):416–427, 2009.Google Scholar
[SW82] F. H., Stillinger and T. A., Weber. Hidden structure in liquids. Phys. Rev. A, 25(2):978–989, 1982.Google Scholar
[SW83] F. H., Stillinger and T. A., Weber. Dynamics of structural transitions in liquids. Phys. Rev. A, 28(4):2408–2416, 1983.Google Scholar
[SW84] F. H., Stillinger and T. A., Weber. Packing structures and transitions in liquids and solids. Science, 225(4666):983–989, 1984.Google Scholar
[SW85] F. H., Stillinger and T. A., Weber. Computer-simulation of local order in condensed phases of silicon. Phys. Rev. B, 31(8):5262–5271, 1985.Google Scholar
[SW03] A., Shurki and A., Warshel. Structure/function correlations of proteins using MM, QM/MM, and related approaches: Methods, concepts, pitfalls, and current progress. In Protein Simulations, Volume 66 of Advances in Protein Chemistry, pages 249–313. San Diego: Elsevier, 2003.Google Scholar
[SWPF97] B., Schonfelder, D., Wolf, S. R., Phillpot and M., Furtkamp. Molecular-dynamics method for the simulation of grain-boundary migration. Interface Sci., 5(4):245–262, 1997.Google Scholar
[SWSW06] Z. H., Sun, X. X., Wang, A. K., Soh and H. A., Wu. On stress calculations in atomistic simulations. Modell. Simul. Mater. Sci. Eng., 14:423–431, 2006.Google Scholar
[SZ03] D., Shilo and E., Zolotoyabko. Stroboscopic x-ray imaging of vibrating dislocations excited by 0.58 GHz phonons. Phys. Rev. Lett., 91(11), 2003.Google Scholar
[Sza93] D., Szasz. Ergodicity of classical billiard balls. Physica A, 194:86–92, 1993.Google Scholar
[TA86] N., Triantafyllidis and E. C., Aifantis. A gradient approach to localization of deformation. 1. Hyperelastic materials. J. Elast., 16:225–237, 1986.Google Scholar
[Tad96] E. B., Tadmor. The quasicontinuum method. PhD thesis, Brown University, 1996.Google Scholar
[Tay34a] G. I., Taylor. The mechanism of plastic deformation of crystals. Part I. Theoretical. Proc. R. Soc. London, Ser. A, 145(855):362–387, 1934.Google Scholar
[Tay34b] G. I., Taylor. The mechanism of plastic deformation of crystals. part II. comparison with observations. Proc. R. Soc. London, Ser. A, 145(855):388–404, 1934.Google Scholar
[Tay99] C.C.W., Taylor. The Atomists: Leucippus and Democritus: Fragments, a Text and Translation with a Commentary. Toronto: University of Toronto Press, 1999.
[TC60] D., Turnbull and R. L., Cormia. A dynamic hard sphere model. J. Appl. Phys., 31(4):674–678, 1960.Google Scholar
[Ter86] J., Tersoff. New empirical model for the structural properties of silicon. Phys. Rev. Lett., 56(6):632–635, 1986.Google Scholar
[Ter88a] J., Tersoff. Empirical interatomic potential for silicon with improved elastic properties. Phys. Rev. B, 38(14):9902–9905, 1988.Google Scholar
[Ter88b] J., Tersoff. New empirical approach for the structure and energy of covalent systems. Phys. Rev. B, 37(12):6991–7000, 1988.Google Scholar
[Ter89] J., Tersoff. Modeling solid-state chemistry: Interatomic potentials for multicomponent systems. Phys. Rev. B, 39(8):5566–5568, 1989.Google Scholar
[TESM09] E. B, Tadmor, R. S., Elliott, J. P., Sethna and R. E., Miller. Knowledgebase of interatomic models (KIM). http://openkim.org, 2009.
[TF00] K., Tillmann and A., Forster. Critical dimensions for the formation of interfacial misfit dislocations of In0.6Ga0.4As islands on GaAs(001). Thin Solid Films, 368(1):93–104, 2000.Google Scholar
[TG51] S. P., Timoshenko and J.N., Goodier. Theory of Elasticity. New York: McGraw-Hill, 1951.Google Scholar
[TH03] E. B., Tadmor and S., Hai. A Peierls criterion for the onset of deformation twinning at a crack tip. J. Mech. Phys. Solids, 51(5):765–793, 2003.
[TIP+05] S., Tejima, M., Iizuka, N., Park, S., Berber, H., Nakamura and D., Tomanek. Large scale nanocarbon simulations. In Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show, Volume 2, pages 181–184. Danville: Nano Science and Technology Institute, 2005.Google Scholar
[TKH91] M., Toda, R., Kubo and N., Hashitsume. Statistical Physics II: Nonequilibrium Statistical Mechanics, Volume 31 of Springer Series in Solid-State Sciences. Berlin: Springer-Verlag, second edition, 1991. Third corrected printing 1998.
[TKS92] M., Toda, R., Kubo and N., Saitô. Statistical Physics I: Equilibrium Statistical Mechanics, Volume 30 of Springer Series in Solid-State Sciences. Berlin: Springer-Verlag, second edition, 1992. Third corrected printing 1998.
[TM77] W. R., Tyson and W. A., Miller. Surface free energies of solid metals: Estimation from liquid surface tension measurements. Surf. Sci., 62(1):267–276, 1977.Google Scholar
[TM04] P. A., Tipler and G., Mosca. Physics for Scientists and Engineers, Volume 2. New York: W. H. Freeman, fifth edition, 2004.Google Scholar
[TM09] E. B., Tadmor and R. E., Miller. Quasicontinuum method website. http://www.qcmethod.org, 2009.
[TME12] E. B., Tadmor, R. E., Miller, and R. S., Elliott. Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations. Cambridge: Cambridge University Press, 2012.Google Scholar
[TN65] C., Truesdell and W., Noll. The non-linear field theories of mechanics. In S., Flügge, editor, Handbuch der Physik, Volume III/3, pages 1–603. Berlin: Springer, 1965.Google Scholar
[TN04] C., Truesdell and W., Noll. In S. S., Antman, editor, The Non-Linear Field Theories of Mechanics. Berlin: Springer-Verlag, third edition, 2004.Google Scholar
[TOP96] E. B., Tadmor, M., Ortiz and R., Phillips. Quasicontinuum analysis of defects in solids. Philos. Mag. A, 73(6):1529–1563, 1996.Google Scholar
[Tor72] I., McC. Torrens. Interatomic Potentials. New York: Academic Press, 1972.
[Tou64] R. A., Toupin. Theories of elasticity with couple-stress. Arch. Ration. Mech. Anal., 17:85–112, 1964.Google Scholar
[TPO96] E. B., Tadmor, R., Phillips, and M., Ortiz. Mixed atomistic and continuum models of deformation in solids. Langmuir, 12(19):4529–4534, 1996.Google Scholar
[TPO00] E. B., Tadmor, R., Phillips, and M., Ortiz. Hierarchical modeling in the mechanics of materials. Int. J. Solids Struct., 37:379–389, 2000.Google Scholar
[TPT93] C., Tserbak, H. M., Polatoglou, and G., Theodorou. Unified approach to the electronic structure of strained Si/Ge superlattices. Phys. Rev. B, 47(12):7104–7124, 1993.Google Scholar
[Tru68] C., Truesdell. Essays in the History of Mechanics. New York: Springer-Verlag, 1968.Google Scholar
[Tru77] C., Truesdell. A First Course in Rational Continuum Mechanics. New York: Academic Press, 1977.Google Scholar
[Tsa79] D. H., Tsai. The virial theorem and stress calculation inmolecular dynamics. J. Chem. Phys., 70:1375–1382, 1979.Google Scholar
[TSBK99] E. B., Tadmor, G. S., Smith, N., Bernstein and E., Kaxiras. Mixed finite element and atomistic formulation for complex crystals. Phys. Rev. B, 59(1):235–245, 1999.Google Scholar
[TT60] C., Truesdell and R., Toupin. The classical field theories. In S., Flügge, editor, Handbuch der Physik, Volume III/1, pages 226–793. Berlin: Springer, 1960.Google Scholar
[Tuc10] M. E., Tuckerman. Statistical Mechanics: Theory and Molecular Simulations. Oxford: Oxford University Press, 2010.Google Scholar
[Tuc11] M. E., Tuckerman. Statistical mechanics course (G25.2651) lecture notes. http://www.nyu.edu/classes/tuckerman/stat.mech/lectures.html, 2011.
[TWSK02] E. B., Tadmor, U.V., Waghmare, G. S., Smith and E., Kaxiras. Polarization switching in PbTiO3: An ab initio finite element simulation. Acta Mater., 50:2989–3002, 2002.Google Scholar
[Uff07] J., Uffink. Compendium of the foundations of classical statistical physics. In J., Butterfield and J., Earman, editors, Handbook for Philsophy of Physics, pages 923–1074. Amsterdam: Elsevier, 2007.Google Scholar
[UoC09] ,Department of Chemistry University of Cambridge. History of the theory sector of the chemistry department. www-theor.ch.cam.ac.uk/history.html, 2009.
[Var57] Y. P., Varshni. Comparative study of potential energy functions for diatomic molecules. Rev. Mod. Phys., 29(4):664–682, 1957.Google Scholar
[VAR+03] M., Veleva, S., Arsene, M. C., Record, J. L., Bechade and J., Bai. Hydride embrittlement and irradiation effects on the hoop mechanical properties of pressurized water reactor (PWR) and boiling-water reactor (BWR) ZIRCALOY cladding tubes. Part II. Morphology of hydrides investigated at different magnifications and their interaction with the processes of plastic deformation. Metall. Mater. Trans. A, 34(3):567–578, 2003.Google Scholar
[VAS09] VASP, . VASP website. http://cms.mpi.univie.ac.at/vasp, 2009.
[VC87] A. F., Voter and S. P., Chen. High temperature ordered intermetallic alloys. In R.W., Siegal, J.R., Weertmong, and R., Sinclair, editors, Characterization of Defects in Materials, Mater. Res. Soc. Symp. Proc., Volume 82, page 175, Pittsburgh: Materials Research Society, 1987.Google Scholar
[vDDLG01] 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, 105:9396–9409, 2001.Google Scholar
[vdGN95] E., van der Giessen and A., Needleman. Discrete dislocation plasticity: A simple planar model. Modell. Simul. Mater. Sci. Eng., 3:689–735, 1995.Google Scholar
[vDMH+08] A. C. T., van Duin, B.V., Merinov, S. S., Han, C.O., Dorso and W. A., Goddard, III. ReaxFF reactive force field for the Y-doped BaZrO3 proton conductor with applications to diffusion rates for multigranular systems. J. Phys. Chem. A, 112(45):11414–11422, 2008.Google Scholar
[vDSS+03] A. C. T., van Duin, A., Strachan, S., Stewman, Q. S., Zhang, X., Xu, and W. A., Goddard, III. ReaxFF(SiO) reactive force field for silicon and silicon oxide systems. J. Phys. Chem. A, 107(19):3803–3811, 2003.Google Scholar
[vdZ07] H., van der Zant. Molecular electronics and devices website. http://www.med.tn.tudelft.nl, 2007.
[Ver67] L., Verlet. Computer “experiments” on classical fluids. I. thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 159(1):98, 1967.Google Scholar
[VFG98] M., Verdier, M., Fivel, and I., Groma. Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications. Modell. Simul. Mater. Sci. Eng., 6(6):755–770, 1998.Google Scholar
[vH49] L., van Hove. Quelques propriétés générales de l'intégrale de configuration d'un système de particules avec interaction. Physica, 15(11–12):951–961, 1949.Google Scholar
[Vit68] V., Vitek. Intrinsic stacking faults in body-centered cubic crystals. Philos. Mag., 18:773–786, 1968.Google Scholar
[VKS96] A. F., Voter, J. D., Kress and R. N., Silver. Linear-scaling tight binding from a truncated-moment approach. Phys. Rev. B, 53(19):12733–12741, 1996.Google Scholar
[vL01] J. H., van Lith. Stir in stillness: A study in the foundations of equilibrium statistical mechanics. PhD thesis, Universiteit Utrecht, 2001. Full text available at http://igitur-archive.library.uu.nl/dissertations/1957294/UUindex.html.
[vVLZ+03] K. J., van Vliet, J., Li, T., Zhu, S., Yip, and S., Suresh. Quantifying the early stages of plasticity through nanoscale experiments and simulations. Phys. Rev. B, 67:104105, 2003.Google Scholar
[VMG02] A. F., Voter, F., Montalenti, and T. C., Germann. Extending the time scale in atomistic simulation of materials. Annu. Rev. Mater. Res., 32:321–346, 2002.Google Scholar
[vN32] J., von Neaumann. Physical applications of the ergodic hypothesis. Proc. Nat. Acad. Sci. USA, 18:263–266, 1932.Google Scholar
[Vot94] A. F., Voter. The embedded atom method. In J. H., Westbrook and R. L., Fleischer, editors, Intermetallic Compounds: Principles and Practice, pages 77–90. London: John Wiley and Sons, Ltd, 1994.Google Scholar
[Vot97] A. F., Voter. Hyperdynamics: Accelerated molecular dynamics of infrequent events. Phys. Rev. Lett., 78:3908–3911, 1997.Google Scholar
[Vot98] A. F., Voter. Parallel replica method for dynamics of infrequent events. Phys. Rev. B, 57(22):13985–13988, 1998.Google Scholar
[VRSK98] L., Vitos, A. V., Ruban, H. L., Skriver, and J., Kollár. The surface energy of metals. Surf. Sci., 411(1–2):186–202, 1998.Google Scholar
[VS82] A. R., Verma and O. N., Srivastava. Crystallography for Solid State Physics. New Delhi: Wiley Eastern Ltd., 1982.Google Scholar
[vVS02] K. J., van Vliet and S., Suresh. Simulations of cyclic normal indentation of crystal surfaces using the bubble-raft model. Philos. Mag. A, 82(10):1993–2001. 2002.Google Scholar
[WAD95] E., Wajnryb, A. R., Altenberger and J. S., Dahler. Uniqueness of the microscopic stress tensor. J. Chem. Phys., 103(22):9782–9787, 1995.Google Scholar
[Wal72] D. C., Wallace. Thermodynamics of Crystals. Mineola: Dover, 1972.Google Scholar
[Wal94] D. J., Wales. Rearrangements of 55-atom Lennard-Jones and (C60)55 clusters. J. Chem. Phys., 101(5):3750–3762, 1994.Google Scholar
[Wal03] D. J., Wales. Energy Landscapes. Cambridge: Cambridge University Press, 2003.Google Scholar
[Wei83] J. H., Weiner. Statistical Mechanics of Elasticity. New York: John Wiley and Sons, 1983.Google Scholar
[Wen91] R. M., Wentzcovitch. Invariant molecular-dynamics approach to structural phase transitions. Phys. Rev. B, 44(5):2358–2361, 1991.Google Scholar
[WFvdGN02] D., Weygand, L. H., Friedman, E., van der Giessen and A., Needleman. Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Modell. Simul. Mater. Sci. Eng., 10(4):437–468, 2002.Google Scholar
[WGC98] Y. A., Wang, N., Govind, and E. A., Carter. Orbital-free kinetic-energy functionals for the nearly free electron gas. Phys. Rev. B, 58(20):13465–13471, 1998.Google Scholar
[Wik05] Wikipedia, . Photograph of Boltzmann's grave in central cemetery of Vienna – Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/File:Zentralfriedhof_Vienna_-_Boltzmann.JPG, 2005. [Online; accessed March 05, 2009].
[Wik08] Wikipedia, . Macrostructure of rolled and annealed brass; magnification 400x – Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/File:SDC10257.JPG, 2008. [Online; accessed 11-Aug-2010].
[Wim96] E., Wimmer. Computational materials design and processing: perspectives for atomistic approaches. Mater. Sci. Eng., B37:72–82, 1996.Google Scholar
[WJTP08] G. J., Wagner, R. E., Jones, J. A., Templeton and M. L., Parks. An atomistic-to-continuum coupling method for heat transfer in solids. Comput. Meth. Appl. Mech. Eng., 197(41–42):3351–3365, 2008.Google Scholar
[WKL04] G. J., Wagner, E. G., Karpov and W. K., Liu. Molecular dynamics boundary conditions for regular crystal lattices. Comput. Meth. Appl. Mech. Eng., 193:1579–1601, 2004.Google Scholar
[WL03] G. J., Wagner and W. K., Liu. Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys., 190:249–274, 2003.Google Scholar
[WM92] D., Wolf and K. L., Merkle. Correlation between the structure and energy of grain boundaries in metals. In D., Wolf and S., Yip, editors, Materials Interfaces: Atomic Level Structure and Properties, Chapter 3, pages 87–150. London: Chapman and Hall, 1992.Google Scholar
[WW96a] D. J., Wales and T. R., Walsh. Theoretical study of the water pentamer. J. Chem. Phys., 105(16):6957–6971, 1996.Google Scholar
[WW96b] T. R., Walsh and D. J., Wales. Rearrangements of the water trimer. J. Chem. Soc., Faraday Trans., 92(14):2505–2517, 1996.Google Scholar
[WWN05] S. C., Wu, D. T., Wasan, and A. D., Nikolov. Structural transitions in two-dimensional hard-sphere systems. Phys. Rev. E, 71(5):056112, 2005.Google Scholar
[WYPW93] J., Wang, S., Yip, S. R., Phillpot and D., Wolf. Crystal instabilities at finite strain. Phys. Rev. Lett., 71(25):4182–4185, 1993.Google Scholar
[WYW10] R. M., Wentzcovitch, Y. G., Yu and Z., Wu. Thermodynamic properties and phase relations in mantle minerals investigated by first principles quasiharmonic theory. Rev. Mineral. Geochem., 71:59–98, 2010.Google Scholar
[XAO95] X.-P., Xu, A. S., Argon, and M., Ortiz. Nucleation of dislocations from crack tips under mixed modes of loading: Implications for brittle versus ductile behaviour of crystals. Philos. Mag. A, 72:415, 1995.Google Scholar
[XB04] S. P., Xiao and T., Belytschko. A bridging domain method for coupling continua with molecular dynamics. Comput. Meth. Appl. Mech. Eng., 193:1645–69, 2004.Google Scholar
[XM96] W., Xu and J. A., Moriarty. Atomistic simulation of ideal shear strength, point defects and screw dislocations in bcc transition metals: Molybdenum as a prototype. Phys. Rev. B, 54(10):6941–6951, 1996.Google Scholar
[XM98] W., Xu and J. A., Moriarty. Accurate atomistic simulations of the Peierls barrier and kink-pair formation energy for 〈111〉 screw dislocations in bcc Mo. Comput. Mater. Sci., 9(3–4):348–356, 1998.Google Scholar
[XMG09] Y., Xing, A. J., Majda, and W. W., Grabowski. New efficient sparse space-time algorithms for superparameterization on mesoscales. Mon. Weather Rev., 137(12):4307–4324, 2009.Google Scholar
[YC82] M. T., Yin and M. L., Cohen. Theory of lattice-dynamical properties of solids: Application to Si and Ge. Phys. Rev. B, 26(6):3259–3272, 1982.Google Scholar
[YE06] J. Z., Yang and W. E., GeneralizedCauchy–Born rules for elastic deformation of sheets, plates and rods. Phys. Rev. B, 74:184110, 2006.Google Scholar
[Yip06] S., Yip, editor. Handbook of Materials Modeling, Part A. Methods. New York: Springer Science and Business Media, 2006.Google Scholar
[YL52] C. N., Yang and T. D., Lee. Statistical theory of equations of state and phase transitions. I. theory of condensation. Phys. Rev., 87(3):404–409, 1952.Google Scholar
[YSM01a] L. H., Yang, P., Soderlind, and J. A., Moriarty. Accurate atomistic simulation of (a/2) 〈111〉 screw dislocations and other defects in bcc tantalum. Philos. Mag. A, 81:1355–1385, 2001.Google Scholar
[YSM01b] L. H., Yang, P., Soderlind and J. A., Moriarty. Atomistic simulation of pressure-dependent screw dislocation properties in bcc tantalum. Mater. Sci. Eng. A, 309(Sp. Iss. SI):102–107, 2001.Google Scholar
[Yuk91] V. I., Yukalov. Phase transitions and heterophase fluctuations. Phys. Rep., 208(6):395–489, 1991.Google Scholar
[Zan92] G., Zanzotto. On the material symmetry group of elastic crystals and the Born rule. Arch. Ration. Mech. Anal., 121:1–36, 1992.Google Scholar
[Zan96] G., Zanzotto. The Cauchy–Born hypothesis, nonlinear elasticity and mechanical twinning in crystals. Acta Crystallogr., Sect. A, 52:839–849, 1996.Google Scholar
[ZBG09] J. A., Zimmerman, D. J., Bammann and H., Gao. Deformation gradients for continuum mechanical analysis of atomistic simulations. Int. J. Solids Struct., 46:238–253, 2009.Google Scholar
[ZCvD+04] Q., Zhang, T., Cagin, A., van Duin, W. A., Goddard, III Y., Qi and L. G., Hector. Adhesion and nonwetting-wetting transition in the Al/α-Al2O3 interface. Phys. Rev. B, 69(4), 2004.Google Scholar
[ZHG+02] P., Zhang, Y., Huang, P. H., Geubelle, P. A., Klein and K. C., Hwang. The elastic modulus of single-wall carbon nanotubes: A continuum analysis incorporating interatomic potentials. Int. J. Solids Struct., 39:3893–3906, 2002.Google Scholar
[Zho03] M., Zhou. A new look at the atomic level virial stress: On continuum-molecular system equivalence. Proc. R. Soc. London, Ser. A, 459:2347–2392. 2003.Google Scholar
[ZJ05] J., Zinn-Justin. Path Integrals in Quantum Mechanics. Oxford: Oxford University Press, 2005.Google Scholar
[ZJZ+08] R., Zhu, F., Janetzko, Y., Zhang, A. C. T., van Duin, W. A., Goddard, III and D. R., Salahub. Characterization of the active site of yeast RNA polymerase II by DFT and ReaxFF calculations. Theor. Chem. Acc., 120(4–6):479–489, 2008.Google Scholar
[ZLC05] B. J., Zhou, V. L., Ligneres and E. A., Carter. Improving the orbital-free density functional theory description of covalent materials. J. Chem. Phys., 122(4), 2005.Google Scholar
[ZM67] H., Ziegler and D., McVean. On the notion of an elastic solids. In B., Broberg, J., Hult, and F., Niordson, editors, Recent Progress in Applied Mechanics (The Folke Odquist Volume), pages 561–572. Stockholm: Almquist and Wiksell, 1967.Google Scholar
[ZM03] R. R., Zope and Y., Mishin. Interatomic potentials for atomistic simulations of the Ti–Al system. Phys. Rev. B, 68(2), 2003.Google Scholar
[ZRH98] H. M., Zbib, M., Rhee, and J. P., Hirth. On plastic deformation and the dynamics of 3D dislocations. Int. J. Mech. Sci., 40:113–127, 1998.Google Scholar
[ZT05] O. C., Zienkiewicz and R. L., Taylor. The Finite Element Method. London: McGraw-Hill, sixth edition, 2005.
[Zun02] J. D., Zund. George David Birkhoff and John von Neumann: A question of priority and the ergodic theorems, 1931–1932. Historia Mathematica, 29:138–156, 2002.Google Scholar
[Zwa01] R., Zwanzig. Nonequilibrium Statistical Mechanics. Oxford: Oxford Univ. Press, 2001.Google Scholar
[ZWH+04] J. A., Zimmerman, E. B., Webb, III J. J., Hoyt, R. E., Johnson and D. J., Bammann. Calculation of stress in atomistic simulation. Modell. Simul. Mater. Sci. Eng., 12:S319–S332, 2004.Google Scholar
[ZZ87] O. C., Zienkiewicz and J. Z., Zhu. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng., 24:337–357, 1987.Google Scholar

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  • References
  • Ellad B. Tadmor, University of Minnesota, Ronald E. Miller, Carleton University, Ottawa
  • Book: Modeling Materials
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003582.017
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  • References
  • Ellad B. Tadmor, University of Minnesota, Ronald E. Miller, Carleton University, Ottawa
  • Book: Modeling Materials
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003582.017
Available formats
×

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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Ellad B. Tadmor, University of Minnesota, Ronald E. Miller, Carleton University, Ottawa
  • Book: Modeling Materials
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003582.017
Available formats
×