Smooth particle applied mechanics: The state of the art

Smooth Particle Applied Mechanics: The State of the Art

Volumn , Issue , 2006, Pages 1-300

  Hoover, William Graham ^a  

^a Great Basin College   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85115672681     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6218     Document Type: Book

References (150)

1. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge University Press, London, 1986).
2. R. A. Gingold and J. J. Monaghan, “Smoothed Particle Hydrodynamics: Theory and Application to Nonspherical Stars”, Monthly Notices of the Royal Astronomical Society 181, 375-389 (1977).
3. L. B. Lucy, “A Numerical Approach to the Testing of the Fission Hypothesis”, The Astronomical Journal 82, 1013-1024 (1977).
4. J. Gleick, Chaos, Making a New Science (Viking, New York, 1989).
5. Wm. G. Hoover, Computational Statistical Mechanics (Elsevier, New York, 1991). [Keisan Toukei Rikigaku, Japanese translation by Koichiro Shida with the supervision of Susumu Kotake (Morikita Shupan, 1999)].
6. R. Preston, “Capturing the Unicorn”, New Yorker Magazine, 11 April 2005.
7. J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, “Dynamics of Radiation Damage”, Physical Review 120, 1229-1253 (1960).
8. B. J. Alder and T. E. Wainwright, “Molecular Dynamics by Electronic Computers”, pages 97-131 in Transport Processes in Statistical Mechanics, I. Prigogine, Editor (Interscience, New York, 1958).
9. The “Fermi-Pasta-Ulam” problem is reviewed and extended in J. L. Tuck and M. T. Menzel, “The Superperiod of the Nonlinear Weighted String Problem”, Advances in Mathematics 9, 399-407 (1972).
10. Wm. G. Hoover, “Mécanique de Nonéquilibre à la Californienne”, Physica A 240, 1-11 (1997).
11. S. Nosé, “Constant Temperature Molecular Dynamics Methods”, Progress in Theoretical Physics Supplement 103, 1-117 (1991).
12. Wm. G. Hoover, “Liouville’s Theorems, Gibbs’ Entropy, and Mul-tifractal Distributions for Nonequilibrium Steady States”, Journal of Chemical Physics109, 4164-4170 (1998).
13. J. W. Gibbs, Elementary Principles in Statistical Mechanics (Oxbow Press, 1991) [first published in 1902]
14. C. Cercignani, Ludwig Boltzmann, the Man Who Trusted Atoms (Oxford University Press, 1998).
15. B. Moran, W. G. Hoover, and S. Bestiale, “Diffusion in a Periodic Lorentz Gas”, Journal of Statistical Physics48, 709-726 (1987).
16. Wm. G. Hoover and C. G. Hoover, “Searching for Auxetics with Dyna3d and ParaDyn”, Physica Status Solidi242b, 585-594 (2005).
17. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).
18. T. J. Ahrens, T. Takata, J. D. O’Keefe, and G. S. Orton, “Impact of Comet Shoemaker-Levy 9 on Jupiter”, Geophysical Research Letters21, 1087-1090 (1994).
19. D. Levesque and L. Verlet, “Molecular Dynamics and Time Reversibility”, Journal of Statistical Physics72, 519-537 (1993).
20. O. Kum and W. G. Hoover, “Time-Reversible Continuum Mechanics”, Journal of Statistical Physics76, 1075-1081 (1994).
21. Wm. G. Hoover and H. A. Posch, “Shear Viscosity via Local Control of Spatiotemporal Chaos in Two-Dimensional Isoenergetic Dense Fluids”, Physical Review E51, 273-279 (1995).
22. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, 1952).
23. C. G. Hoover, A. J. DeGroot, and R. J. Sherwood, “ParaDyn: a Parallel Nonlinear Explicit Three-Dimensional Finite-Element Code for Solid and Structural Mechanics”, Report UCRL-MA-140943 (Lawrence Livermore National Laboratory, 2004). ParaDyn is the export controlled parallel version of Dyna3d. For a description of the serial code, which is available to everyone, see J. L. Lin, “Dyna3d, A Nonlinear, Explicit, Three-dimensional Finite Element Code for Solid and Structural Mechanics” (Lawrence Livermore National Laboratory, 2004).
24. D. A. Young, Phase Diagrams of the Elements (University of California, Berkeley, 1991).
25. J. von Neumann and R. Richtmyer, “A Method for the Numerical Calculation of Hydrodynamic Shocks”, Journal of Applied Physics21, 232-257 (1950).
26. B. L. Holian, W. G. Hoover, B. Moran, and G. K. Straub, “Shockwave Structure via Nonequilibrium Molecular Dynamics and Navier-Stokes Continuum Mechanics”, Physical Review A22, 2798-2808 (1987).
27. W. G. Hoover, W. T. Ashurst, and R. J. Olness, “Two-Dimensional Computer Studies of Crystal Stability and Fluid Viscosity”, Journal of Chemical Physics60, 4043-4047 (1974).
28. A. Puhl, M. M. Mansour, and M. Mareschal, “Quantitive Comparison of Molecular Dynamics with Hydrodynamics in Rayleigh-Benard Convection”, Physical Review A40, 1999-2012 (1989).
29. V. M. Castillo, Wm. G. Hoover, and C. G. Hoover, “Coexisting At-tractors in Compressible Rayleigh-Benard Flow”, Physical Review E55, 5546-5550 (1997).
30. O. Kum, Wm. G. Hoover, and H. A. Posch, “Viscous Conducting Flows with Smooth Particle Applied Mechanics”, Physical Review E52, 4899-4908 (1995).
31. M. L. Wilkins, “Finite Difference Scheme for Calculating Problems in Two Space Dimensions and Time”, Journal of Computational Physics 5, 406-414 (1970).
32. H. A. Posch, W. G. Hoover, and O. Kum, “Steady State Shear Flows via Nonequilibrium Molecular Dynamics and Smooth Particle Applied Mechanics”, Physical Review E 52, 1711-1720 (1995).
33. J. von Neumann and R. Richtmyer, “A Method for the Numerical Calculation of Hydrodynamic Shocks”, Journal of Applied Physics 21, 232-257 (1950).
34. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1985).
35. Wm. G. Hoover and C. G. Hoover, “Smooth-Particle Phase Stability with Generalized Density-Dependent Potentials”, Physical Review E73, 016702 (2006).
36. O. Kum, W. G. Hoover, and C. G. Hoover, “Smooth Particle Boundary Conditions”, Physical Review E 68, 017701 (2003).
37. W. T. Ashurst and W. G. Hoover, “Dense-Fluid Shear Viscosity via Nonequilibrium Molecular Dynamics”, Physical Review A11, 658-678 (1975).
38. R. W. Zwanzig, “Time Correlation Functions and Transport Coefficients”, Annual Review of Physical Chemistry16, 67-102 (1965).
39. Wm. G. Hoover and H. A. Posch, “Numerical Heat Conductivity in Smooth Particle Applied Mechanics”, Physical Review E 54, 5142-5145 (1996).
40. V. M. Castillo, Wm. G. Hoover, and C. G. Hoover, “Coexisting At-tractors in Compressible Rayleigh-Benard Flow”, Physical Review E 55, 5546-5550 (1997).
41. Wm. G. Hoover, Time Reversibility, Computer Simulation, and Chaos (World Scientific, Singapore, 2001).
42. W. G. Hoover, C. G. Tull (C. G. Hoover as of 10 November 1988!), and H. A. Posch, “Negative Lyapunov Exponents for Dissipative Systems”, Physics Letters A 131, 211-215 (1988).
43. Wm. G. Hoover, Computational Statistical Mechanics (Elsevier, 1991).
44. T. Watanabe and H. Kaburaki, “Increase in Chaotic Motions of Atoms in a Large-Scale Self-Organized Motion”, Physical Review E 54, 1504-1509 (1996).
45. V. M. Castillo and Wm. G. Hoover, “Entropy Production and Lyapunov Instability at the Onset of Turbulent Convection”, Physical Review E 58, 7350-7354 (1998).
46. H. A. Posch, W. G. Hoover, and F. J. Vesely, “Canonical Dynamics of the Nose Oscillator: Stability, Order, and Chaos”, Physical Review A33, 4253-4265 (1986).
47. H. A. Posch and W. G. Hoover, “Equilibrium and Nonequilibrium Lyapunov Spectra for Dense Fluids”, Physical Review A39, 2175-2188 (1989).
48. Wm. G. Hoover and C. G. Hoover, “Smooth Particle Phase Stability with Generalized Density-Dependent Potentials”, Physical Review E73, 016702 (2006).
49. Wm. G. Hoover and H. A. Posch, “Shear Viscosity via Global Control of Spatiotemporal Chaos in Two-Dimensional Isoenergetic Dense Fluids”, Physical Review E51, 273-279 (1995).
50. W. G. Hoover and M. Ross, “Statistical Theories of Melting”, Contemporary Physics12, 339-356 (1971).
51. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1985).
52. J. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977).
53. Wm. G. Hoover and S. Hess, “Equilibrium and Nonequilibrium Ther-momechanics for an Effective Pair Potential used in Smooth Particle Applied Mechanics”, Physica A231, 425-438 (1996).
54. 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”, Physical Review B33, 7983-7991 (1986).
55. Wm. G. Hoover and H. A. Posch, “Entropy Increase in Confined Free Expansions via Molecular Dynamics and Smooth-Particle Applied Mechanics”, Physical Review E59, 1770-1776 (1999).
56. Wm. G. Hoover, H. A. Posch, V. M. Castillo, and C. G. Hoover, “Computer Simulation of Irreversible Expansions via Molecular Dynamics, Smooth Particle Applied Mechanics, Eulerian, and Lagrangian Continuum Mechanics”, Journal of Statistical Physics100, 313-326 (2000).
57. Wm. G. Hoover and C. G. Hoover, “SPAM-Based Recipes for Continuum Simulations”, Computers in Science and Engineering3, 78-85(2001).
58. B. L. Holian, W. G. Hoover, B. Moran, and G. K. Straub, “Shockwave Structure via Nonequilibrium Molecular Dynamics and Navier-Stokes Continuum Mechanics”, Physical Review A22, 2798-2808 (1987).
59. O. Kum, Wm. G. Hoover, and C. G. Hoover, “Temperature Maxima in Stable Two-Dimensional Shockwaves”, Physical Review E 56, 462-465 (1997).
60. R. W. Zwanzig, “Time Correlation Functions and Transport Coefficients”, Annual Review of Physical Chemistry16, 67-102 (1965).
61. J. W. Swegle, D. L. Hicks, and S. W. Attaway, “Smooth Particle Hydrodynamics Stability Analysis”, Journal of Computational Physics116, 123-134 (1995).
62. J. J. Monaghan, “On the Problem of Penetration in Particle Methods”, Journal of Computational Physics 82, 1-15 (1989).
63. J. J. Monaghan, “Smooth Particle Hydrodynamics without a Tensile Instability”, Journal of Computational Physics159, 290-311 (2000).
64. W. Prager, Introduction to the Mechanics of Continua (Ginn & Company, Boston, 1961 [Dover reprint, 1973]).
65. T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Element Analysis for Continua and Structures (Wiley, New York, 2000).
66. Wm. G. Hoover, C. G. Hoover, and E. C. Merritt, “Smooth Particle Applied Mechanics: Conservation of Angular Momentum with Tensile Stability and Velocity Averaging”, Physical Review E69, 016702 (2004).
67. Wm. G. Hoover and H. A. Posch, “Numerical Heat Conductivity in Smooth Particle Applied Mechanics”, Physical Review E 54, 5142-5145 (1996)
68. “Auxetic and Related Systems”, Physica Status Solidi242b, March 2005 (K. W. Wojciechowski, A. Alderson, A. Brarika, and K. L. Anderson, editors).
69. Wm. G. Hoover, and S. Hess, “Equilibrium and Nonequilibrium Ther-momechanics for an Effective Pair Potential used in Smooth Particle Applied Mechanics”, Physica A231, 425-438 (1996).
70. M. Heinstein and D. Segalman, “Simulation of Orthogonal Cutting with Smooth Particle Hydrodynamics”, Sandia Report SAND97-1961 (1997).
71. R. Cartwright, J. Xia, S. Cannon, D. McGuckin, and P. Gronenboom, “Motion Prediction of Ships and Yachts by Smoothed Particle Hy-drodyamics”, Proceedings of the Second High Performance Yacht Design Conference (Auckland, New Zealand, 2006).
72. R. W. Lindsay and H. L. Stern, “A New Lagrangian Model of Arctic Sea Ice”, Journal of Physical Oceanography34, 272-283 (2004).
73. L. B. Lucy, “A Numerical Approach to the Testing of the Fission Hypothesis”, The Astronomical Journal82, 1013-1024 (1977).
74. R. A. Gingold and J. J. Monaghan, “Smoothed Particle Hydrodynamics: Theory and Application to Nonspherical Stars”, Monthly Notices of the Royal Astronomical Society181, 375-389 (1977).
75. J. A. Faber and F. A. Rasio, “Post-Newtonian SPH Calculation of Binary Neutron Star Coalescence: Method and First Results”, Physical Review D, 62, 064012 (2000).
76. A. P. Boss and L. P. Bodenheimer, “Fragmentation in a Rotating Protostar. A Comparison of Two 3D Computer Codes”, Astrophysical Journal234, 289-295 (1979).
77. S. Kitsionas and A. P. Whitworth, “Smoothed Particle Hydrodynamics with Particle Splitting, Applied to Self-Gravitating Collapse”, Monthly Noices of the Royal Astronomical Society330, 129-136 (2002).
78. T. J. Ahrens, T. Takata, J. D. O’Keefe, and G. S. Orton, “Impact of Comet Shoemaker-Levy 9 on Jupiter”, Geophysical Research Letters21, 1087-1090 (1994).
79. B. J. Alder and T. E. Wainwright, “Molecular Dynamics by Electronic Computers”, pages 97-131 in Transport Processes in Statistical Mechanics, I. Prigogine, Editor (Interscience, New York, 1958).
80. W. T. Ashurst and W. G. Hoover, “Dense-Fluid Shear Viscosity via Nonequilibrium Molecular Dynamics”, Physical Review A11, 658-678 (1975).
81. T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Element Analysis for Continua and Structures (Wiley, New York, 2000).
82. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).
83. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1985).
84. A. P. Boss and L. P. Bodenheimer, “Fragmentation in a Rotating Protostar. A Comparison of Two 3D Computer Codes”, Astrophysical Journal234, 289-295 (1979).
85. R. Cartwright, J. Xia, S. Cannon, D. McGuckin, and P. Grönenboom, “Motion Prediction of Ships and Yachts by Smoothed Particle Hydrodyamics”, Proceedings of the Second High Performance Yacht Design Conference (Auckland, New Zealand, 2006).
86. V. M. Castillo, Wm. G. Hoover, and C. G. Hoover, “Coexisting Attractors in Compressible Rayleigh-Benard Flow”, Physical Review E55, 5546-5550 (1997).
87. V. M. Castillo and Wm. G. Hoover, “Entropy Production and Lyapunov Instability at the Onset of Turbulent Convection”, Physical Review E58, 7350-7354 (1998).
88. C. Cercignani, Ludwig Boltzmann, the Man Who Trusted Atoms (Oxford University Press, 1998).
89. S. J. Chapman, Fortran 90 and 95 for Scientists and Engineers (McGraw Hill, 1997).
90. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, 1952).
91. J. A. Faber and F. A. Rasio, “Post-Newtonian SPH Calculation of Binary Neutron Star Coalescence: Method and First Results”, Physical Review D, 62, 064012 (2000).
92. 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”, Physical Review B33, 7983-7991 (1986).
93. J. W. Gibbs, Elementary Principles in Statistical Mechanics (Oxbow Press, 1991) [first published in 1902]
94. J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, “Dynamics of Radiation Damage”, Physical Review120, 1229-1253 (1960).
95. R. A. Gingold and J. J. Monaghan, “Smoothed Particle Hydrodynamics: Theory and Application to Nonspherical Stars”, Monthly Notices of the Royal Astronomical Society181, 375-389 (1977).
96. J. Gleick, Chaos, Making a New Science (Viking, New York, 1989).
97. J. L. Gross and J. Yellen, Graph Theory and its Applications (CRC Press LLC, Second Edition, 2005).
98. M. Heinstein and D. Segalman, “Simulation of Orthogonal Cutting with Smooth Particle Hydrodynamics”, Sandia Report SAND97-1961 (1997).
99. B. L. Holian, W. G. Hoover, B. Moran, and G. K. Straub, “Shockwave Structure via Nonequilibrium Molecular Dynamics and Navier-Stokes Continuum Mechanics”, Physical Review A22, 2798-2808 (1987).
100. C. G. Hoover, A. J. DeGroot, and R. J. Sherwood, “ParaDyn: a Parallel Nonlinear Explicit Three-Dimensional Finite-Element Code for Solid and Structural Mechanics”, Report UCRL-MA-140943 (Lawrence Livermore National Laboratory, 2004). ParaDyn is the export controlled parallel version of Dyna3d. For a description of the serial code, which is available to everyone, see J. L. Lin, “Dyna3d, A Nonlinear, Explicit, Three-dimensional Finite Element Code for Solid and Structural Mechanics” (Lawrence Liver-more National Laboratory, 2004).
101. W. G. Hoover and M. Ross, “Statistical Theories of Melting”, Contemporary Physics12339-356 (1971).
102. W. G. Hoover, W. T. Ashurst, and R. J. Olness, “Two-Dimensional Computer Studies of Crystal Stability and Fluid Viscosity”, Journal of Chemical Physics60, 4043-4047 (1974).
103. W. G. Hoover, C. G. Tull (now C. G. Hoover), and H. A. Posch, “Negative Lyapunov Exponents for Dissipative Systems”, Physics Letters A131, 211-215 (1988).
104. Wm. G. Hoover and H. A. Posch, “Shear Viscosity via Local Control of Spatiotemporal Chaos in Two-Dimensional Isoenergetic Dense Fluids”, Physical Review E51, 273-279 (1995).
105. Wm. G. Hoover and S. Hess, “Equilibrium and Nonequilibrium Thermo-mechanics for an Effective Pair Potential used in Smooth Particle Applied Mechanics”, Physica A231425-438 (1996).
106. Wm. G. Hoover and H. A. Posch, “Numerical Heat Conductivity in Smooth Particle Applied Mechanics”, Physical Review E54, 5142-5145 (1996).
107. Wm. G. Hoover, “Mécanique de Nonéquilibre à la Californienne”, Physica A 240, 1-11 (1997).
108. Wm. G. Hoover, “Isomorphism Linking Smooth Particles and Embedded Atoms”, Physica A260, 244-254 (1998).
109. Wm. G. Hoover, “Liouville’s Theorems, Gibbs’ Entropy, and Multifrac-tal Distributions for Nonequilibrium Steady States”, Journal of Chemical Physics109, 4164-4170 (1998).
110. Wm. G. Hoover, Computational Statistical Mechanics (Elsevier, New York, 1991), available at http://williamhoover.info. [Keisan Toukei Rikigaku, Japanese translation by Koichiro Shida with the supervision of Susumu Kotake (Morikita Shupan, 1999) ISBN: 4627840918].
111. Wm. G. Hoover and H. A. Posch, “Entropy Increase in Confined Free Expansions via Molecular Dynamics and Smooth Particle Applied Mechanics”, Physical Review E59, 1770-1776 (1999).
112. Wm. G. Hoover, H. A. Posch, V. M. Castillo, and C. G. Hoover, “Computer Simulation of Irreversible Expansions via Molecular Dynamics, Smooth Particle Applied Mechanics, Eulerian, and Lagrangian Continuum Mechanics”, Journal of Statistical Physics100, 313-326 (2000).
113. Wm. G. Hoover, Time Reversibility, Computer Simulation, and Chaos (World Scientific, Singapore, 2001) [ Jikan no ya, Kompyutah Shimyureis-hon, Kaosu, Japanese translation by Koichiro Shida (Morikita Shuppan, 2002) ISBN: 4627153015].
114. Wm. G. Hoover, C. G. Hoover, and E. C. Merritt, “Smooth Particle Applied Mechanics: Conservation of Angular Momentum with Tensile Stability and Velocity Averaging”, Physical Review E69, 016702 (2004).
115. Wm. G. Hoover and C. G. Hoover, “Searching for Auxetics with Dyna3d and ParaDyn”, Physica Status Solidi242b, 585-594 (2005).
116. Wm. G. Hoover and C. G. Hoover, “Smooth Particle Phase Stability with Generalized Density-Dependent Potentials”, Physical Review E73, 016702 (2006).
117. B. Kernighan and D. Ritchie, The C Programming Language (Prentice Hall, 1988).
118. S. Kitsionas and A. P. Whitworth, “Smoothed Particle Hydrodynamics with Particle Splitting, Applied to Self-Gravitating Collapse”, Monthly Noices of the Royal Astronomical Society330, 129-136 (2002).
119. S. Kochan, Programming in C (Sams, Prentice-Hall, Indianapolis, 2004).
120. O. Kum and W. G. Hoover, “Time-Reversible Continuum Mechanics”, Journal of Statistical Physics76, 1075-1081 (1994).
121. O. Kum, Wm. G. Hoover, and H. A. Posch, “Viscous Conducting Flows with Smooth Particle Applied Mechanics”, Physical Review E52, 4899-4908 (1995).
122. O. Kum, Wm. G. Hoover, and C. G. Hoover, “Temperature Maxima in Stable Two-Dimensional Shockwaves”. Physical Review E56, 462-465 (1997).
123. O. Kum, W. G. Hoover, and C. G. Hoover, “Smooth Particle Boundary Conditions”, Physical Review E68, 017701 (2003).
124. D. Levesque and L. Verlet, “Molecular Dynamics and Time Reversibility”, Journal of Statistical Physics72, 519-537 (1993).
125. ParaDyn is an export controlled parallel version of Dyna3d. For a description of the serial code, which is available to everyone, see J. L. Lin, “Dyna3d, A Nonlinear, Explicit, Three-dimensional Finite Element Code for Solid and Structural Mechanics” (LLNL, Livermore, California, February 2004).
126. R. W. Lindsay and H. L. Stern, “A New Lagrangian Model of Arctic Sea Ice”, Journal of Physical Oceanography34, 272-283 (2004).
127. E. N. Lorenz, “Deterministic Nonperiodic Flow”, Journal of Atmospheric Science20, 130-141 (1963).
128. For an interesting variant representation of this classic method see page 186 of Lorenz’ otherwise fine book, The Essence of Chaos (University of Washington Press, 1993).
129. L. B. Lucy, “A Numerical Approach to the Testing of the Fission Hypothesis”, The Astronomical Journal82, 1013-1024 (1977).
130. J. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977).
131. D. D. McCracken and W. Salmon, Computing for Engineers & Scientists with Fortran 77 (Wiley, 1990).
132. J. J. Monaghan, “On the Problem of Penetration in Particle Methods”, Journal of Computational Physics82, 1-15 (1989).
133. J.J. Monaghan, “Smooth Particle Hydrodynamics without a Tensile Instability”, Journal of Computational Physics159, 290-311 (2000).
134. B. Moran, W. G. Hoover, and S. Bestiale, “Diffusion in a Periodic Lorentz Gas”, Journal of Statistical Physics48, 709-726 (1987).
135. S. Nose, “Constant Temperature Molecular Dynamics Methods”, Progress in Theoretical Physics Supplement103, 1-117 (1991).
136. H. A. Posch, W. G. Hoover, and F. J. Vesely, “Canonical Dynamics of the Nose Oscillator: Stability, Order, and Chaos”, Physical Review A33, 4253-4265 (1986).
137. H. A. Posch and W. G. Hoover, “Equilibrium and Nonequilibrium Lyapunov Spectra for Dense Fluids”, Physical Review A39, 2175-2188 (1989).
138. H. A. Posch, W. G. Hoover, and O. Kum, “Steady State Shear Flows via Nonequilibrium Molecular Dynamics and Smooth Particle Applied Mechanics”, Physical Review E52, 1711-1720 (1995).
139. W. Prager, Introduction to the Mechanics of Continua (Ginn & Company, Boston, 1961 [Dover reprint, 1973]).
140. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge University Press, London, 1986).
141. R. Preston, “Capturing the Unicorn”, New Yorker Magazine, 11 April 2005.
142. A. Puhl, M. M. Mansour, and M. Mareschal, “Quantitive Comparison of Molecular Dynamics with Hydrodynamics in Rayleigh-Benard Convection”, Physical Review A40, 1999-2012 (1989).
143. J. W. Swegle, D. L. Hicks, and S. W. Attaway, “Smooth Particle Hydrodynamics Stability Analysis”, Journal of Computational Physics116, 123-134 (1995).
144. The “Fermi-Pasta-Ulam” problem is reviewed and extended in J. L. Tuck and M. T. Menzel, “The Superperiod of the Nonlinear Weighted String Problem”, Advances in Mathematics 9, 399-407 (1972).
145. J. von Neumann and R. Richtmyer, “A Method for the Numerical Calculation of Hydrodynamic Shocks”, Journal of Applied Physics21232-257 (1950).
146. T. Watanabe and H. Kaburaki, “Increase in Chaotic Motions of Atoms in a Large-Scale Self-Organized Motion”, Physical Review E54, 1504-1509 (1996).
147. M. L. Wilkins, “Finite Difference Scheme for Calculating Problems in Two Space Dimensions and Time”, Journal of Computational Physics 5, 406-414 (1970).
148. K. W. Wojciechowski, A. Alderson, A. Branka, and K. L. Anderson, editors, “Auxetic and Related Systems”, Physica Status Solidi 242b, (March, 2005).
149. D. A. Young, Phase Diagrams of the Elements (University of California, Berkeley, 1991).
150. R. W. Zwanzig, “Time Correlation Functions and Transport Coefficients”, Annual Review of Physical Chemistry16, 67-102 (1965).