On multiscale non-equilibrium molecular dynamics simulations

International Journal for Numerical Methods in Engineering

Volumn 83, Issue 8-9, 2010, Pages 998-1038

  Li, Shaofan ^a   Sheng, Ni ^b  

^a 109 McLaughlin Hall   (United States)

^b MACAU UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Macao)

Author keywords

Dislocation; Molecular dynamics; Multiscale simulation; Nanomechanics; Non equilibrium thermodynamics

Indexed keywords

BOLTZMANN EQUATION; DISLOCATIONS (CRYSTALS); DISTRIBUTION FUNCTIONS; NANOMECHANICS; SHOCK WAVES; THERMODYNAMICS;

BOLTZMANN DISTRIBUTION; CONTINUUM THERMODYNAMICS; LOCAL EQUILIBRIUM STATE; MULTI-SCALE SIMULATION; NON EQUILIBRIUM MOLECULAR DYNAMIC (NEMD); NON EQUILIBRIUM THERMODYNAMICS; THERMODYNAMIC TEMPERATURE; THREE DIMENSIONAL SIMULATIONS;

MOLECULAR DYNAMICS;

EID: 77956120169     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2849     Document Type: Article

References (94)

1. Progogine I. Introduction to Thermodynamics of Irreversible Processes (3rd edn). Wiley: New York, 1967.
2. Zubarev DN, Morozov V, Ropke G. Statistical Mechanics of Nonequilibrium Processes: Basic Concepts, Kinetic Theory. Wiley: New York, 1996.
3. Hoover WG. Canonical dynamics: equilibrium phase-space distributions. Physical Review A 1985; 31:1695-1697.
4. Baranyai A. Heat flow studies for large temperature gradients by molecular dynamics simulation. Physical Review E 1996; 54:6911-6917.
5. Müller-Plathe F. A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity. Journal of Chemical Physics 1997; 106:6082-6085.
6. Lepri S, Livi R, Politi A. Thermal conduction in classical low-dimensional lattices. Physics Reports 2003; 377:1-80.
7. Poulikakos D, Arcidacono S. Molecular dynamics simulation in nanoscale heat transfer: a review. Microscale Thermophysical Engineering 2003; 7:181-206.
8. Castejon HJ. Nonequilibrium molecular dynamics calculation of the thermal conductivity of solid materials. Journal of Physics Chemistry, B 2003; 107:826-828.
9. Tokumasu T, Kamijo K. Molecular dynamics study for the thermal conducitivy of diatomic liquid. Superlattice and Microstructure 2004; 35:217-225.
10. Chantrenne P, Barrat JL. Finite size effects in determination of thermal conductivities: comparing molecular dynamics with simple models. ASME Journal of Heat Transfer 2004; 126:577-585.
11. Baalss D, Hess S. Nonequilibrium molecular dynamics studies on the anisotropic viscosity of perfectly aligned nematic liquid crystals. Physical Review Letters 1986; 57:86-89.
12. Kröger M, Makhloufi R. Wormlike micelles under shear flow: a microscopic model studied by nonequilibrium-molecular-dynamics simulations. Physical Review E 1995; 53:2531-2536.
13. Kröger M, Hess S. Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics. Physics Review Letters 2000; 85:1128-1131.
14. Xu L, Sedigh MG, Sahimi M, Tsotsis TT. Nonequilibrium molecular dynamics simulation of transport of gas mixtures in nanopores. Physical Review Letters 1998; 80:3511-3514.
15. Jansen TIC, Snijders JG. The third- and fifth-order nonlinear Raman response of liquid CS2 calculated using a finite field nonequilibrium dynamics method. Journal of Chemical Physics 2000; 113:307-311.
16. MacElroy JMD, Boyle MJ. Nonequilibrium molecular dynamics simulation of a model carbon membrane separation of CH4/H2 mistures. Chemical Engineering Journal 1999; 74:85-97.
17. Hoover WG. Systems far from equilibrium. In Systems Far from Equilibrium, Garrido L (ed.). Springer: Berlin, 1980; 373-380.
18. Hoover WG, Evans DJ, Hickman RB, Ladd AJC, Ashurst WT, Moran B. Lennar-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics. Physical Review A 1980; 22:1690-1697.
19. Hoover WG. Nonequilibrium molecular dynamics. Annual Review of Physical Chemistry 1983; 34:103-127.
20. Evans DJ, Morriss GP. Nonlinear-response theory for steady planar Couette flow. Physics Review A 1984; 30:1528-1530.
21. Evans DJ, Morriss GP. Statistical Mechanics of Nonequilibrium Liquids. Academic Press Inc: San Diego, 1990.
22. Tuckerman ME, Mundy CJ, Balasubramanian S, Klein ML. Modified nonequilibrium molecular dynamics for fluid flows with energy conservation. Journal of Chemical Physics 1997; 106:5616.
23. Edwards BJ, Dressler M. A reversible problem in non-equilibrium thermodynamics: Hamiltonian evolution equations for non-equilibrium molecular dynamics simulations. Journal of Non-Newtonian Fluid Mechanics 2001; 96:163-175.
24. Edwards BJ, Baig C, Keffer DJ. An examination of the validity of nonequilibrium molecular-dynamics simulation algorithms for arbitrary steady-state flows. Journal of Chemical Physics 2005; 123. Article no. 1141106.
25. Edwards BJ, Baig C, Keffer DJ. A validation of the p-SLLOD equations of motion for homogeneous steady-state flows. Journal of Chemical Physics 2006; 124. Article no. 194104.
26. Baig C, Edwards BJ, Keffer DJ, Cochran HD. A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow. Journal of Chemical Physics 2005; 122. Article no. 114103.
27. Evans DJ. Homogeneous NEMD algorithm for thermal conductivity-application of non-canonical linear response theory. Physics Letters 1983; 91A:457-460.
28. Zhang F, Isbister DJ, Evans DJ. Nonequlibrium molecular dynamics simulations of heat flow in one-dimensional lattices. Physical Review E 2000; 61:3541-3546.
29. Zhang M, Lussetti E, de Souza LES, Müller-Plathe F. Thermal conductivities of molecular liquids by reverse nonequilibrium molecular dynamics. Journal of Physical Chemistry B 2005; 109:15060-15067.
30. Hoover WG, Ladd AJC, Moran B. High-strain-rate plastic flow studied via nonequilibrium molecular dynamics. Physics Review Letters 1982; 48:1818-1820.
31. Holian BL, Lomdahl PS. Plasticity induced by shock waves in nonequilibrium molecular-dynamics simulations. Science 1998; 280:2085-2088.
32. Evans DJ, Hoover WG, Failor BH, Moran B, Ladd AJC. Nonequilibrium molecular dynamics via Gauss's principle of least constraint. Physical Review A 1983; 8:1016.
33. Galea TM, Attard P. Constraint method for deriving nonequilibrium molecular dynamics equations of motion. Physical Review E 2002; 66. Article No. 041207.
34. Bright JN, Evans DJ. New observations regarding deterministic, time-reversible thermostats and Gauss's principle of least constraint. Journal of Chemical Physics 2005; 122. Article no. 194106.
35. Martyna GJ, Klein ML, Tuckerman ME. Noseé-Hoover chains: the canonical ensemble via continuous dynamics. Journal of Chemical Physics 1992; 97:2635-2645.
36. Chen G. Nanoscale Energy Transport Sand Conversion. Oxford University Press: Oxford, 2005.
37. Volz SG, Saulnier JB, Chen G, Beauchamp P. Computation of thermal conductivity of Si/Ge superlattices by molecular dynamics techniques. Microelectronics Journal 2000; 31:815-819.
38. Gomes CJ, Madrid M, Goicochea JV, Amon CH. In-plane sand out-of-planr thermal conductivity of silicon thin films predicted by molecular dynamics. ASME Journal of Heat Transfer 2006; 128:1114-1121.
39. E W, Huang Z. Matching conditions in atomistic-continuum modeling materials. Physical Review Letters 2001; 87:135501-1-4.
40. E W, Huang Z. A dynamic atomistic-continuum method for the simulation of crystalline materials. Journal of Computational Physics 2002; 182:234-260.
41. Wagner GJ, Liu WK. Coupling of atomistic sand continuum simulations using a bridging scale decomposition. Journal of Computational Physics 2003; 190:249-274.
42. Wagner GJ, Karpov EG, Liu WK. Molecular dynamics boundary conditions for regular crystal lattices. Computer Method in Applied Mechanics and Engineering 2004; 193:1579-1601.
43. Park HS, Karpov EG, Liu WK. Non-reflecting boundary conditions for atomistic, continuum and coupled atomistic/continuum simulations. International Journal for Numerical Methods in Engineering 2005; 64: 237-259.
44. Tang Z, Zhao H, Li G, Aluru NR. Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures. Physical Review B 2006; 74. Article no. 064110.
45. Yun G, Park HS. A multiscale, finite deformation formulation for surface stress effects on the coupled thermomechanical behavior of nanomaterials. Computer Methods in Applied Mechanics and Engineering 2008; 197:3337-3350.
46. Xiao SP, Belytschko T. A bridging domain method for coupling continua with molecular dynamics. Computer Methods in Applied Mechanics and Engineering 2004; 193:1645-1669.
47. To A, Li S. Perfectly matched multiscale simulations. Physics Review B 2005; 72. Article no. 035414.
48. Li S, Liu X, Agrawal A, To A. The perfectly matched multisclae simulation revised. Physical Review B 2006; 74. Article no. 045418.
49. Liu X, Li S. Nonequilibrium multiscale computational model. Journal of Chemical Physics 2007; 126. Article no. 124105.
50. Li S, Sheng N, Liu X. A non-equilibrium multiscale simulation paradigm. Chemical Physics Letters 2008; 451:293-300.
51. Park HS, Karpov EG, Liu WK. A temperature equation for coupled atomistic/continuum simulations. Computer Methods in Applied Mechanics and Engineering 2004; 193:1713-1732.
52. Karpov EG, Park HS, Liu WK. A phonon heat bath approach for the atomistic and multiscale simulation of solids. International Journal for Numerical Methods in Engineering 2007; 70:351-378.
53. Keffer DJ, Baig C, Adhangale P, Edwards BJ. A generalized Hamiltonian-based algorithm for rigorous equilibrium molecular dynamics simulation in the canonical ensemble. Journal of Non-Newtonian Fluid Mechanics 2008; 152:129-139.
54. Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn), vol. 1. Butterworth-Heinemann: Oxford, U.K., 2000.
55. Rudd RE, Broughton JQ. Coarse-grained molecular dynamics: nonlinear finite elements and finite temperature. Physical Review B 2005; 72. Article no. 144104.
56. Qiang D, Faber V, Gunzburger M. Centroidal voronoi tesselations: application and algorithm. SIAM Review 1999; 41:637-676.
57. Taniguchi T. Thermodynamical properties in nonequilibrium statistical mechanics. Physica A 1997; 236:448-484.
58. Bathe KJ. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996.
59. Nosé S. A molecular dynamics method for simulations in the canonical ensemble. Molecular Physics 1984; 52:255-268.
60. Nosé S. An extension of the canonical ensemble molecular dynamics method. Molecular Physics 1986; 57: 187-191.
61. Liu WK, Karpov EG, Park HS. Nano Mechanics Sand Materials. Wiley: The Atrium, Southern Gate, Chichester, 2006.
62. Kawasaki K, Gunton D. Theory of nonlinear transport processes: nonlinear shear viscosity and normal stress effects. Physical Review A 1973; 8:2048-2064.
63. Taniguchi T, Morriss G. Steady shear flow thermodynamics based on a canonical distribution approach. Physics Review E 2004; 70. Article no. 056124.
64. Gaveau B, Schulman LS. Master equation based formulation of nonequilibrium statistical mechanics. Journal of Mathematical Physics 1996; 37:3897-3932.
65. Schulman LS, Gaveau B. Coarse grains: the emergence of space sand order. Foundations of Physics 2001; 31:713-731.
66. Weiner JH. Statistical Mechanics of Elasticity. Wiley: New York, 1983.
67. LeSar R, Najafabadi R, Srolovitz DJ. Finite-temperature defect properties from free-energy minimization. Physical Review Letters 1989; 63:624-627.
68. Foiles S. Evaluation of harmonic methods for calculating the free energy of defects in solids. Physical Review B 1994; 49:14930-14939.
69. Jiang H, Huang Y, Hwang KC. A finite-temperature continuum theory based on interatomic potentials. ASME Journal of Engineering Materials and Technology 2005; 127:408-416.
70. Silhavy M. The Mechanics and Thermodynamics of Continuous Media. Springer: Berlin, 1997.
71. Maugin GA. The Thermomechanics of Nonlinear Irreversible Behaviors-An Introduction. World Scientific: Singapore, 1999.
72. Tadmor E, Ortiz M, Phillips R. Quasicontinuum analysis of defects in solids. Philosophycal Magazine A 1996; 73:1529-1563.
73. Diestler DJ. Coarse-grained description of multiple scale processes in solid systems. Phyiscal Review B 2002; 66. Article no. 184104.
74. Wu ZB, Diestler DJ, Feng R, Zeng XC. Coarse-graining description of solid systems at nonzero temperature. Journal of Computational Physics 2003; 119:8013-8023.
75. Kittel C. Introduction to Solid State Physics (8th edn). Wiley: Hoboken, NJ, 2005.
76. Hoplzapfel GA. Nonlinear Solid Mechanics. Wiley: Chichester, Weinheim, New York, 2000.
77. Nowacki W. Thermoelasticity (2nd edn). Pergamon Press: Stanford, 1986.
78. Hughes TJR. The Finite Element Method: Linear Static sand Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
79. Jang S, Voth GA. Simple reversible molecular dynamics algorithms for Nosé-Hoover chain dynamics. Journal of Chemical Physics 1997; 107:9514-9526.
80. Jang S, Voth GA. Response to comment on 'Simple reversible molecular dynamics algorithms for Nosé-Hoover chain dynamics' [J. Chem. Phys. 110, 3623 (1999)]. Journal of Chemical Physics 1999; 110:3626-3628.
81. Brańka AC. Nosé-Hoover chain method for nonequilibrium molecular dynamics simulation. Physical Review E 2000; 61:4769-4773.
82. Liu WK, Belytschko T. Mixed-time implicit-explicit finite elements for transient analysis. Computers and Structures 1982; 15:445-450.
83. Torrens IM. Interatomic Potentials. Academic Press: New York, London, 1972.
84. Frenkel YI, Kontorova T. The model of dislocation in solid body. Zh. Eksp. Teor. Fiz. 1938; 8:1340 (in Russian).
85. E W, Engquist B, Huang Z. Heterogeneous multiscale method: a general methodology for multiscale modelling. Physical Review B 2002; 67:092101-1-4.
86. Dupuy L, Tadmor EB, Miller RE, Phillips R. Finite-temperature quasicontinuum: molecular dynamics without all the atoms. Physical Review Letters 2005; 95:060202.
87. Sheng N, Li S. A non-equilibrium multiscale simulation of shock wave propagation. Mechanics Research Communications 2008; 35:10-16.
88. Mori H. Statistical-mechanics theory of transport in fluids. Physical Review 1958; 112:1829-1842.
89. Yamada T, Kawasaki K. Nonlinear effects in the shear viscosity of critical mixtures. Progress in Theoretical Physics 1967; 38:1031-1051.
90. Mavrantzas VG, Öttinger HC. Atomistic Monte Carlo simulation of polymer melt elasticity: their nonequilibrium thermodynamics GENERIC formulation in a generalized canonical ensemble. Macromolecules 2002; 35:960-975.
91. Broido DA, Ward A, Mingo N. Lattice thermal conductivity of silicon from empirical interatomic potentials. Physical Review B 2005; 72. Article no. 014308.
92. Cahill DG, Ford WK, Goodson KE, Mahan GD, Majumdar A, Maris HJ, Merlin R, Phillpot SR. Nanoscale thermal transport. Applied Physics Reviews 2003; 93:793-811.
93. Zeng X, Li S. A multiscale cohesive zone model and simulations of fracture. Computer Methods in Applied Mechanics and Engineering 2010; 199:547-556.
94. Li S, Fan H, Sheng N. Multiscale nonequilibrium molecular dynamics simulations: heat transfer and crack propagation. 2009; 1-20. Unpublished.