Finite-temperature extension of the quasicontinuum method using Langevin dynamics: Entropy losses and analysis of errors

Modelling and Simulation in Materials Science and Engineering

Volumn 18, Issue 1, 2010, Pages

  Marian, J ^a   Venturini, G ^b   Hansen, B L ^b   Knap, J ^c   Ortiz, M ^b   Campbell, G H ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b California Institute of Technology   (United States)

^c U S ARMY RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CANONICAL ENSEMBLE; CLUSTER DIAMETER; CLUSTER SIZES; COMPUTATIONAL CELL; CONTINUUM THERMODYNAMICS; DOMAIN BOUNDARY; DYNAMIC SYSTEMS; ENERGY TRANSMISSION; ENTROPY LOSS; LAGRANGIAN MECHANICS; LANGEVIN; LANGEVIN DYNAMICS; LENGTH SCALE; NON EQUILIBRIUM; QUASICONTINUUM METHOD; THERMAL EXPANSION COEFFICIENTS; TIME-SCALES; UNIFORM MESH; VIBRATIONAL ENTROPY;

DYNAMICAL SYSTEMS; DYNAMICS; ERRORS; MOLECULAR DYNAMICS; QUANTUM THEORY; THERMAL EXPANSION;

EQUATIONS OF MOTION;

EID: 77149180787     PISSN: 09650393     EISSN: 1361651X     Source Type: Journal    
DOI: 10.1088/0965-0393/18/1/015003     Document Type: Article

References (71)

1. Ortiz M, Cuitiño A M, Knap J and Koslowski M 2001 MRS Bull. 26 16
2. Curtin W A and Miller R E 2003 Modelling Simul. Mater. Sci. Eng. 11 R33
3. Miller R R and Tadmor E B 2009 Modelling Simul. Mater. Sci. Eng. 17 053001
4. Medina F and Rosales F 1987 Eng. Comput. 4 139
5. Rudd R E and Broughton J Q 2005 Phys. Rev. B 72 144104
6. Cai W, de Koning M, Bulatov V V and Yip S 2000 Phys. Rev. Lett. 85 3213
7. E W and Zhongyi H 2001 Phys. Rev. Lett. 87 135501
8. Park H S, Karpov E G, Liu W K and Klein P A 2005 Phil. Mag. 85 79
9. Curtaloro S and Ceder G 2002 Phys. Rev. Lett. 88 255504
10. Wagner G J, Jones R E, Templeton J A and Parks M L 2008 Comput. Methods Appl. Mech. Eng. 197 3351
11. Qu S, Shastry V, Curtin W A and Miller R E 2005 Modelling Simul. Mater. Sci. Eng. 13 1101
12. Tadmor E B, Ortiz M and Phillips R 1996 Phil. Mag. A 73 1529
13. Knap J and Ortiz M 2001 J. Mech. Phys. Solids 49 1899
14. LeSar R, Najafabadi R and Srolovitz D J 1989 Phys. Rev. Lett. 63 624
15. Althoff J D, Morgan D, De Fontaine D, Asta M, Foiles S M and Johnson D D 1998 Comput. Mater. Sci. 10 411
16. Baranyai A and Evans D 1991 Mol. Phys. 74 353
17. Shenoy V, Shenoy V and Phillips R 1999 Mater. Res. Soc. Symp. Proc. 538 465-71
18. Wu Z-B, Diestler D J, Feng R and Zeng X C 2003 J. Chem. Phys. 111 8013
19. Dupuy L M, Tadmor E B, Miller R E and Phillips R 2005 Phys. Rev. Lett. 95 060202
20. Tang Z, Zhao H, Li G and Aluru N R 2006 Phys. Rev. B 74 064110
21. Kulkarni Y, Knap J and Ortiz M 2008 J. Mech. Phys. Solids 56 1417
22. Knap J, Marian J and Ortiz M 2004 Mesh optimization for the Quasicontinuum method: a generalization of VALE Presented at the 21st Int. Congress on Theoretical and Applied Mechanics (ICTAM) (Warsaw, Poland, 15-21 August 2004)
23. Knap J and Ortiz M 2001 Phys. Rev. Lett. 90 226102
24. Marian J, Knap J and Ortiz M 2004 Phys. Rev. Lett. 93 165503
25. Marian J, Knap J and Campbell G H 2008 Acta Mater. 56 2389
26. Marian J and Knap J 2007 Int. J. Multiscale Comput. Eng. 5 287
27. Vujanovic B D and Jones S E 1989 Variational methods in nonconservative phenomena Mathematics in Science and Engineering vol 182 (San Diego, CA: Academic)
28. Eringen A C and Suhubi E S 1974 Elastodynamics vol 1 (New York: Academic)
29. Hughes T J R 2000 The Finite Element Method (New York: Dover)
30. Coffey W T, Kalmykov Yu P and Waldron J T 2004 The Langevin Equation (World Scientific Series in Contemporary Chemical Physics) vol 14 (Singapore: World Scientific)
31. Kirkwood J G 1935 J. Chem. Phys. 3 300
32. Gardiner C W 2003 Handbook of Stochastic Methods 3rd edn (New York: Springer)
33. Kubo R 1966 Rep. Prog. Phys. 29 255
34. Leimkuhler B and Reich S 2005 Simulating Hamiltonian Dynamics (Cambridge: Cambridge University Press)
35. Melchionna S 2007 J. Chem. Phys. 127 044108
36. Newmark N M 1959 ASCE J. Eng. Mech. Division 85 67-94
37. Simo J C, Tarnow N and Wong K K 1992 Comput. Methods Appl. Mech. Eng. 100 63
38. Kane C, Marsden J E, Ortiz M and West M 2000 Int. J. Numer. Methods Eng. 49 1295
39. Courant R, Friedrichs K and Lewy H 1967 IBM J. 215-34 (March)
40. Zhang G and Schlick T 1994 J. Chem. Phys. 101 4995
41. Bussi G and Parrinello M 2007 Phys. Rev. E 75 056707
42. Nilsson L G and Padro J A 1990 Mol. Phys. 71 355
43. Helfand E 1979 Bell Syst. Tech. J. 58 2289
44. Greenside H S and Helfand E 1981 Bell Syst. Tech. J. 60 1927
45. Box G E P and Muller M E 1958 Ann. Math. Stat. 29 610
46. Biswas R and Hamann D R 1986 Phys. Rev. B 34 895
47. Kittel C 1996 Introduction to Solid State Physics 7th edn (Hoboken, NJ: Wiley)
48. Maradudin A A, Montroll E W and Weiss G H 1963 Theory of lattice dynamics in the harmonic approximation Solid State Physics (New York: Academic) Suppl. 3
49. Cole H 1959 IBM J. 126 (April)
50. MacDonald R A 1972 Phys. Rev. B 5 4139
51. Hill T L 1986 An Introduction to Statistical Thermodynamics (New York: Dover)
52. Grimvall G 1986 Thermophysical properties of materials Selected Topics in Solid State Physics vol XVIII ed E P Wohlfarth (Amsterdam: North-Holland)
53. A Authier (ed) 2006 International Tables for Crystallography, Vol D: Physical Properties of Crystals (Norwell, MA: Kluwer Academic) (International Union of Crystallography) (Section 1.4.2)
54. Srivastava G P 1990 The Physics of Phonons (New York: Taylor and Francis)
55. Ho C Y and Taylor R E 1998 Thermal Expansion of Solids (OH: ASM International)
56. Maranganti R and Sharma P 2007 J. Mech. Phys. Solids 55 1823
57. Diethelm K, Ford N J, Freed A D and Luchko Y 2005 Comput. Methods Appl. Mech. Eng. 194 743
58. Touloukian Y S, Kirby R K, Taylor R E and Lee T Y R 1977 Thermal expansion of non-metallic solids Thermophysical Properties Matter vol 13 (New York: Plenum)
59. Biegalski M D, Haeni J H, Trolier-McKinstry S and Schlom D G 2005 J. Mater. Res. 20 952
60. Born M and Huang K 1956 Dynamical Theory of Crystal Lattices (Oxford: Oxford University Press)
61. Ercolessi F and Adams J B 1994 Europhys. Lett. 26 583
62. Liu X-Y, Ercolessi F and Adams J B 2004 Modelling Simul. Mater. Sci. Eng. 12 665
63. Pearson W B 1958 A Handbook of Lattice Spacings and Structures of Metals and Alloys (New York: Pergamon)
64. Szeftel J 1985 Surf. Sci. 152/153 797
65. Li Y, Siegel D J, Adams J B and Liu X-Y 2003 Phys. Rev. B 67 125101
66. MacDonald R A and Shukla R C 1985 Phys. Rev. B 32 4961
67. Mishin Y and Lozovoy A Y 2006 Acta Mater. 54 5013
68. Ozaki K, Fukutani A and Honda K 2001 JSME Int. J. 44 199
69. Lew A, Marsden J E, Ortiz M and West M 2003 Arch. Ration. Mech. Anal. 167 85
70. Foiles F M 1994 Phys. Rev. B 49 14930
71. Rodney D 2003 Proc. NATO Conf. Thermodynamics, Microstructures and Plasticity ed A Finel et al (Dortrecht: Kluwer)