Understanding the Discrete Element Method: Simulation of Non-Spherical Particles for Granular and Multi-body Systems

Understanding the Discrete Element Method: Simulation of Non-Spherical Particles for Granular and Multi-body Systems

Volumn 9781118567203, Issue , 2014, Pages 1-456

  Matuttis, Hans Georg ^a   Chen, Jian ^b  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^b RIKEN   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; MATLAB; NUMERICAL METHODS; STUDENTS; TWO PHASE FLOW;

ANGULAR PARTICLES; FUNDAMENTAL CONCEPTS; GRADUATE STUDENTS; LOGICAL APPROACHES; MULTI BODY SYSTEMS; NONSPHERICAL PARTICLE; POLYGONAL PARTICLES; SIMULATION CODE;

PARTICLES (PARTICULATE MATTER);

EID: 84927580012     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118567210     Document Type: Book

References (389)

1. M. Nagasawa, Schrödinger Equations and Diffusion Theory. Monographs in Mathematics, Birkhäuser, 1993.
2. G. Emch and C. Liu, The Logic of Thermo-Statistical Physics. Physics and Astronomy Online Library, Springer, 2002.
3. H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics, 3rd ed. Pearson, 2001.
4. M. P. Allen and D. Tildesley, Computer Simulation of Liquids. Oxford University Press, 1987.
5. J. Myers, Handbook of Equations for Mass and Area Properties of Various Geometrical Shapes. NAVWEPS Report 7827, U.S. Naval Ordnance Test Station, 1962.
6. J. Wittenburg, Dynamics of Systems of Rigid Bodies. Teubner, 1977.
7. D. Greenwood, Advanced Dynamics. Cambridge University Press, 2006.
8. H. Corben and P. Stehle, Classical Mechanics. Wiley, 1960.
9. W. Benenson, J. Harris, H. Stöcker, and H. Lutz (eds.), Handbook of Physics. Springer, 2002.
10. J. Hartog, "LXXIII. Forced vibrations with combined viscous and coulomb damping", Philosophical Magazine Series 7, vol. 9, no. 59, pp. 801-817, 1930.
11. R. Reissig, "Erzwungene Schwingungen mit zäher und trockener Reibung", Mathematische Nachrichten, vol. 11, no. 6, pp. 345-384, 1954.
12. J. Knudsen and P. Hjorth, Elements of Newtonian Mechanics: Including Nonlinear Dynamics, 3rd ed. Advanced Texts in Physics, Springer, 2000.
13. V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. Graduate Texts in Mathematics, Springer, 1989.
14. S. Zdravkovska and P. Duren, Golden Years of Moscow Mathematics. History of Mathematics, American Mathematical Society, 2007.
15. B. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2004.
16. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed. Springer, 2006.
17. S.-H. Chong, M. Otsuki, and H. Hayakawa, "Generalized Green-Kubo relation and integral fluctuation theorem for driven dissipative systems without microscopic time reversibility", Physical Review E, vol. 81, 041130, 2010.
18. A. Filippov, Differential Equations with Discontinuous Righthand Sides. Mathematics and its Applications, Springer, 1988.
19. K. Johnson, Contact Mechanics. Cambridge University Press, 1987.
20. W. C. Cheng, J. Chen, and H.-G. Matuttis, "Granular acoustics of polyhedral particles", AIP Conference Proceedings, vol. 1542, pp. 567-570, 2013.
21. S. A. E. Shourbagy, S. Okeda, and H. G. Matuttis, "Acoustic of sound propagation in granular materials in one, two, and three dimensions", Journal of the Physical Society of Japan, vol. 77, no. 3, article 034606, 2008.
22. N. Fletcher and T. Rossing, The Physics of Musical Instruments. Springer, 1998.
23. M. Kunze, "Rigorous methods and numerical results for dry friction problems", in Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities (M. Wiercigroch and B. De Kraker, eds.), World Scientific Series on Nonlinear Science Series A, pp. 207-235, World Scientific, 2000.
24. D. Knuth, The Art of Computer Programming, Volumes 1-4A. Addison-Wesley, 2011.
25. Y. Tokura and H. Maekawa, "Direct numerical simulation of impinging shock wave/transitional boundary layer interaction with separation flow", Journal of Fluid Science and Technology, vol. 6, no. 5, pp. 765-779, 2011.
26. L. Bunimovich, "On the ergodic properties of nowhere dispersing billiards", Communications in Mathematical Physics, vol. 65, pp. 295-312, 1979.
27. S. T. Maddison, J. R. Murray, and J. J. Monaghan, "SPH simulations of accretion disks and narrow rings", Publications of the Astronomical Society of Australia, vol. 13, pp. 66-70, 1996.
28. R. Speith and W. Kley, "Stability of the viscously spreading ring", Astronomy and Astrophysics, vol. 399, no. 2, pp. 395-407, 2003.
29. T. Shinbrot, C. Grebogi, J. Widsom, and J. A. Yorke, "Chaos in a double pendulum", American Journal of Physics, vol. 60, pp. 491-499, 1992.
30. E. N. Lorenz, "Deterministic nonperiodic flow", Journal of the Atmospheric Sciences, vol. 20, pp. 130-141, 1963.
31. I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics, 5th ed. Springer, 2007.
32. F. R. Gantmaher, Lectures in Analytical Mechanics. MIR Publishers, 1970.
33. D. Merkin, F. Afagh, and A. Smirnov, Introduction to the Theory of Stability. Texts in Applied Mathematics, Springer, 1997.
34. W. Greiner, Classical Mechanics: Systems of Particles and Hamiltonian Dynamics. Classical Theoretical Physics, Springer, 2010.
35. L. Poinsot, Théorie nouvelle de la rotation des corps. Bachelier, 1851.
36. J. P. Vinti, "Conservation laws and Liapounov stability of the free rotation of a rigid body", Celestial Mechanics, vol. 1, pp. 59-71, 1969.
37. M. H. Kaplan, Modern Spacecraft Dynamics & Control. Wiley, 1976.
38. R. Gregory, Classical Mechanics. Cambridge University Press, 2006.
39. R. Mickens, Truly Nonlinear Oscillations: Harmonic Balance, Parameter Expansions, Iteration, and Averaging Methods. World Scientific, 2010.
40. M. Ardema, Newton-Euler Dynamics. Springer, 2006.
41. A. Manevich and L. Manevich, The Mechanics of Nonlinear Systems with Internal Resonances. Imperial College Press, 2005.
42. A. L. Garcia, Numerical Methods for Physics, 2nd ed. Prentice Hall, 1999.
43. S. B. Santra, S. Schwarzer, and H. Herrmann, "Fluid-induced particle-size segregation in sheared granular assemblies", Physical Review E, vol. 54, pp. 5066-5072, Nov 1996.
44. Maplesoft, Maple, http://www.maplesoft.com/products/maple/, last visited December 2013.
45. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Artech House Antennas and Propagation Library, Artech House, 2005.
46. P. Saha and S. Tremaine, "Symplectic integrators for solar system dynamics", Astronomical Journal, vol. 104, pp. 1633-1640, 1992.
47. B. Leonard, "A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation", in Finite Element Methods for Convection Dominated Flows (Winter Annual Meeting of the American Society of Mechanical Engineers, New York, December 2-7, 1979), pp. 1-17. ASME, 1979.
48. N. J. Higham, "The accuracy of floating point summation", SIAM Journal on Scientific Computation, vol. 14, pp. 783-799, 1993.
49. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed. Vol. 8 of Springer Series in Computational Mathematics, Springer, 1993.
50. E. Hairer and G.Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd ed. Vol. 14 of Springer Series in Computational Mathematics, Springer, 1996.
51. X. Wang and H.-G. Matuttis, "Numerical irreversibility in energy-conserving many particle systems", Theoretical and Applied Mechanics Japan (NCTAM), vol. 59, pp. 309-321, 2010.
52. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed. Springer, 2006.
53. B. J. Alder and T. Wainwright, "Studies in molecular dynamics", Journal of Chemical Physics, vol. 31, pp. 495-466, 1959.
54. Y. Hiwatari and M. Isobe, eds., The 50th Anniversary of the Alder Transition: Recent Progress on Computational Statistical Physiscs; Proceedings of the Symposium on the 50th Anniversary of the Alder Transition, Kanazawa, Japan, November 28-30, 2007. (Proceedings of papers presented at two successive conferences held in Kanazawa, Japan: one was the special session "The 50th Anniversary of the Alder Transition - Dawn and Historical Review of the Molecular Simulation" as part of the 21st Annual Meeting of the Molecular Simulation Society of Japan (MSSJ), November 28, 2007; the other was the "Symposium on the 50th Anniversary of the Alder Transition - Recent Progress on Computational Statistical Physics", November 29-30, 2007.) Publ. Office, Progress of Theoretical Physics, 2009.
55. C. Störmer, "Méthode d'intégration numérique des équations différentielles ordinaires", in Comptes rendus du Congrès international des Mathématiciens (Strasbourg), pp. 243-257, 1921.
56. L. Verlet, "Computer "experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules", Physical Review, vol. 159, pp. 98-103, Jul 1967.
57. Wikimedia, "Verlet integration", http://en.wikipedia.org/wiki/Verlet_integration, last visited December 2013.
58. J. A. C. Gallas, H. J. Herrmann, and S. Sokolowski, "Granular media on a vibrating plate: a molecular dynamics simulation", International Journal of Modern Physics B, vol. 7, no. 9-10, pp. 1779-1788, 1993.
59. R. I. McLachlan and P. Atela, "The accuracy of symplectic integrators", Nonlinearity, vol. 5, pp. 541-562, 1992.
60. D. Okunbor and R. D. Skeel, "Explicit canonical methods for Hamiltonian systems", Mathematics of Computation, vol. 59, pp. 439-455, 1992.
61. R. D. Ruth, "A canonical integration technique", IEEE Transactions on Nuclear Science, vol. NS-30, pp. 2669-2671, 1983.
62. E. Forest and R. D. Ruth, "Fourth-order symplectic integration", Physica D, vol. 43, pp. 105-117, 1990.
63. J. Candy andW. Rozmus, "A symplectic integration algorithm for separable Hamiltonian functions", Journal of Computational Physics, vol. 92, pp. 230-256, 1991.
64. J. E. Chambers and M. A. Murison, "Pseudo-high-order symplectic integrators", The Astronomical Journal, vol. 119, pp. 425-433, 2000.
65. J. Laskar and P. Robutel, "High order symplectic integrators for perturbed Hamiltonian systems", Celestial Mechanics and Dynamical Astronomy, vol. 80, pp. 39-62, 2001.
66. R. I. McLachlan, "Composition methods in the presence of small parameters", BIT Numerical Mathematics, vol. 35, pp. 258-268, 1995.
67. M. Suzuki, "Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations", Physics Letters A, vol. 146, pp. 319-323, 1990.
68. M. Suzuki and K. Umeno, "Higher-order decomposition theory of exponential operators and its applications to QMC and nonlinear dynamics", in Computer Simulation Studies in Condensed-Matter Physics VI (D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds.), pp. 74-86. Springer, 1993.
69. N. Hatano and M. Suzuki, "Finding exponential product formulas of higher orders", in Quantum Annealing and Related Optimization Methods (A. Das and B. K. Chakrabarti, eds.), pp. 37-68. Springer, 2005.
70. K. Tselios and T. E. Simos, "Symplectic methods of fifth order for the numerical solution of the radial Schrödinger equation", Journal of Mathematical Chemistry, vol. 35, pp. 55-63, 2004.
71. H. Yoshida, "Construction of higher order symplectic integrators", Physics Letters A, vol. 150, pp. 262-268, 1990.
72. H. Yoshida, "Symplectic integrators for Hamiltonian systems: basic theory", in Chaos, Resonance and Collective Dynamical Phenomena in the Solar System (S. Ferraz-Mello, ed.), pp. 407-411. Springer, 1992.
73. M. Suzuki, "General theory of fractal path integrals with applications to many-body theories and statistical physics", Journal of Mathematical Physics, vol. 32, pp. 400-407, 1991.
74. H. Yoshida, "Recent progress in the theory and application of symplectic integrators", Celestial Mechanics and Dynamical Astronomy, vol. 56, pp. 27-43, 1993.
75. M. P. Allen and D. Tildesley, Computer Simulation of Liquids. Oxford University Press, 1987.
76. X. Wang and H.-G. Matuttis, "The fermionic minus-sign problem for the ground state, revisited with higher order Suzuki-Trotter decompositions", Journal of the Physical Society of Japan, vol. 81, no. 10, article 104002, 2012.
77. K. Feng, Symplectic Geometric Algorithms for Hamiltonian Systems. Zhejiang Publishing United Group, 2010.
78. R. D. Skeel and C. W. Gear, "Does variable step size ruin a symplectic integrator?", Physica D, vol. 60, pp. 311-313, Nov 1992.
79. L. F. Shampine and C. W. Gear, "A user's view of solving stiff ordinary differential equations", SIAM Review, vol. 21, pp. 1-16, 1979.
80. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations. Prentice Hall, 1971.
81. L. F. Shampine and M. W. Reichelt, "The Matlab ODE suite", SIAM Journal on Scientific Computing, vol. 18, pp. 1-22, 1997.
82. J. Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis. John Wiley & Sons, 1993.
83. P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations. Applications of Mathematics, Springer, 2011.
84. R. Bulirsch and J. Stoer, "Numerical treatment of ordinary differential equations by extrapolation methods", Numerische Mathematik, vol. 8, no. 1, pp. 1-13, 1966.
85. C. Lubich, "Linearly implicit extrapolation methods for differential-algebraic systems", Numerische Mathematik, vol. 55, no. 2, pp. 197-211, 1989.
86. K. C. Smith, T. S. Fisher, and M. Alam, "Quasistatic compaction of polyhedra by the discrete element method", in Powders and Grains 2009: Proceedings of the 6th International Conference on Micromechanics of Granular Media (M. Nakagawa and S. Luding, eds.). AIP Conference Proceedings, American Institute of Physics, 2009.
87. L. Petzold, "Differential/algebraic equations are not ODEs", SIAM Journal on Scientific and Statistical Computing, vol. 3, pp. 367-384, 1982.
88. J. Baumgarte, "Stabilization of constraints and integrals of motion in dynamical systems", Computational Methods in Applied Mechanical Engineering, vol. 1, pp. 11-16, 1972.
89. C. Lubich, "On projected Runge-Kutta methods for differential-algebraic equations", BIT Numerical Mathematics, vol. 31, no. 3, pp. 545-550, 1991.
90. M. Overton, Numerical Computing with IEEE Floating Point Arithmetic. Society for Industrial and Applied Mathematics, 2001.
91. N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed. Society for Industrial and Applied Mathematics, 2002.
92. C. W. Gear and R. D. Skeel, "The development of ODE methods: a symbiosis between hardware and numerical analysis", in A History of Scientific Computing (S. G. Nash, ed.), pp. 88-105. Association for Computing Machinery (ACM), 1990.
93. J. Chen, A. Schinner, and H.-G. Matuttis, "Static friction, differential algebraic systems and numerical stability", Physics Procedia, vol. 6, pp. 65-75, 2010.
94. E. Cheney and D. Kincaid, Numerical Mathematics and Computing. Brooks/Cole, 2007.
95. G. Engeln-Müllges and F. Uhlig, Numerical Algorithms With C. Springer, 1996.
96. G. Engeln-Müllges and F. Uhlig, Numerical Algorithms with Fortran. Springer, 1996.
97. L. F. Shampine, I. Gladwell, and R. W. Brankin, "Reliable solution of special event location problems for ODEs", ACM Transactions on Mathematical Software, vol. 17, pp. 11-25, 1987.
98. K. Brenan, S. Campbell, and L. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, 1987.
99. U. Ascher and L. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations.Miscellaneous Titles in Applied Mathematics, Society for Industrial and Applied Mathematics, 1998.
100. P. Kunkel and V. Mehrmann, Differential-Algebraic Equations: Analysis and Numerical Solution. EMS Textbooks in Mathematics, European Mathematical Society, 2006.
101. W. Schiesser, The Numerical Method of Lines: Integration of Partial Differential Equations. Academic Press, 1991.
102. W. E. Schiesser and G. W. Griffiths, A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab. Cambridge University Press, 2009.
103. G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations. Prentice Hall, 1977.
104. E. Kreyszig, Advanced Engineering Mathematics, 9th ed. John Wiley & Sons, 2006.
105. F. Klein and A. Sommerfeld, Über die Theorie des Kreisels. III. Die störenden Einflüsse. Astronomische und geophysikalische Anwendungen, 2nd ed. B.G. Teubner, 1923.
106. A. J. Morin, Nouvelles expériences sur le frottement: faites á Metz en 1831 [-1833]. Bachelier, 1834.
107. P. Conti, "Sulla resistenza di attrito", Atti della Reale Accademia dei Lincei, Serie 2, vol. 272, no. 2, pp. 16-200, 1875.
108. D. Galton, The Effect of Brakes Upon Railway Trains. Westinghouse Air Brake Company, 1894.
109. J. A. Hammerschmidt, B. Moasser, W. L. Gladfelter, G. Haugstad, and R. R. Jones, "Polymer viscoelastic properties measured byfriction force microscopy", Macromolecules, vol. 29, pp. 8996-8998, 1996.
110. R. W. Stark, G. Schitter, and A. Stemmer, "Velocity dependent friction laws in contact mode atomic force microscopy", Ultramicroscopy, vol. 100, no. 34, pp. 309-317, 2004.
111. B. Bhushan and B. Gupta, Handbook of Tribology: Materials, Coatings, and Surface Treatments. McGraw-Hill, 1991.
112. E. Booser, ed., Tribology Data Handbook: An Excellent Friction, Lubrication, and Wear Resource. Taylor & Francis, 2010.
113. P. Blau, Friction Science and Technology: From Concepts to Applications, 2nd ed. Taylor & Francis, 2010.
114. B. Bhushan, Modern Tribology Handbook, Two Volumes. Mechanics & Materials Science, Taylor & Francis, 2010.
115. U. Gedde, Polymer Physics. Springer, 1995.
116. E. Rabinowicz, Friction and Wear of Materials, 2nd ed. Wiley, 1995.
117. V. Popov, Contact Mechanics and Friction: Physical Principles and Applications. Springer, 2010.
118. J. H. Dieterich and G. Conrad, "Effect of humidity on time- and velocity-dependent friction in rocks", Journal of Geophysical Research: Solid Earth, vol. 89, no. B6, pp. 4196-4202, 1984.
119. L. Bocquet, E. Charlaix, S. Ciliberto, and J. Crassous, "Moisture-induced ageing in granular media and the kinetics of capillary condensation", Nature, vol. 396, no. 6713, pp. 735-737, 1998.
120. T. Akiyama. Personal communication.
121. E. Rabinowicz, Friction and Wear of Materials. Wiley, 1965.
122. Y. Sang, M. Dubé, and M. Grant, "Dependence of friction on roughness, velocity, and temperature", Physical Review E, vol. 77, article 036123, Mar 2008.
123. T. Pöschel and H. Herrmann, "A simple geometrical model for solid friction", Physica A: Statistical Mechanics and its Applications, vol. 198, no. 3, pp. 441-448, 1993.
124. E. Rouèche, E. Serris, G. Thomas, and L. Périer-Camby, "Influence of temperature on the compaction of an organic powder and the mechanical strength of tablets", Powder Technology, vol. 162, no. 2, pp. 138-144, 2006.
125. V. Gorodnichev and G. Borisov, "Influence of temperature on the equilibrium moisture content of medicinal granulations", Pharmaceutical Chemistry Journal, vol. 11, pp. 1410-1412, 1977.
126. H. Jones and D. Scott (eds.), Industrial Tribology: The Practical Aspects of Friction, Lubrication and Wear. Elsevier Science, 1983.
127. F. Klein and A. Sommerfeld, The Theory of the Top. Volume III: Perturbations, Astronomical and Geophysical Applications. Birkhäuser Boston, 2012.
128. H. Ziegler (ed.), Kreiselprobleme / Gyrodynamics: Symposion Celerina, 20-23 August 1962. Springer, 1963.
129. Y. Sakamoto, Experimental Investigation of Drilling Friction for Axial Symmetric Bodies with Planes (in Japanese). Master's thesis, The University of Electro-Communications, 2008.
130. A. Sommerfeld, Mechanics. Lectures on Theoretical Physics, Academic Press, 1964.
131. F. Radjai, Dynamique des rotations et frottement colllectiv dans les systémes granulaires. PhD thesis, University Paris Orsay, 1995.
132. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed. Vol. 8 of Springer Series in Computational Mathematics, Springer, 1993.
133. G. Hamel, Theoretische Mechanik: eine einheitliche Einfhrung in die gesamte Mechanik. Springer, 1945.
134. U. Ascher and L. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Miscellaneous Titles in Applied Mathematics, Society for Industrial and Applied Mathematics, 1998.
135. M. Kunze andM. Marques, "An introduction to Moreau's sweeping process", in Impacts in Mechanical Systems, B. Brogliato, ed., vol. 551 of Lecture Notes in Physics, pp. 1-60. Springer, 2000.
136. J. J. Moreau and P. D. Panagiotopoulos, eds., Nonsmooth Mechanics and Applications. Vol. 302 of CISM Courses and Lectures, Springer, 1988.
137. J. J. Moreau, P. D. Panagiotopoulos, and G. Strang, eds., Topics in Nonsmooth Mechanics. Birkhäuser, 1988.
138. P. A. Cundall and O. D. L. Strack, "A discrete numerical model for granular assemblies", Geotéchnique, vol. 29, no. 1, pp. 47-65, 1979.
139. Z. Zhong, Finite Element Procedures for Contact-Impact Problems. Oxford Science Publications, Oxford University Press, 1993.
140. P. Wriggers, Computational Contact Mechanics. John Wiley & Sons, 2002.
141. T. Laursen, Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Engineering Online Library, Springer, 2003.
142. A. Munjiza, The Combined Finite-Discrete Element Method. John Wiley & Sons, 2004.
143. V. Matrosov and I. Finogenko, "The solvability of the equations of motion of mechanical systems with sliding friction", Journal of Applied Mathematics and Mechanics, vol. 58, no. 6, pp. 945-954, 1994.
144. P. Haff and B. Werner, "Computer simulation of the mechanical sorting of grains", Powder Technology, vol. 48, no. 3, pp. 239-245, 1986.
145. D. Zhao, E. G. Nezami, Y. M. Hashash, and J. Ghaboussi, "Three-dimensional discrete element simulation for granular materials", Engineering Computations, vol. 23, no. 7, pp. 749-770, 2006.
146. L. Pars, A Treatise on Analytical Dynamics. Heinemann, 1965.
147. S. L. Loney, An Elementary Treatise On the Dynamics of a Particle and of Rigid Bodies. Cambridge University Press, 1930.
148. F. Klein, "Zu Painlevés Kritik der Coulombschen Reibungsgesetze", Zeitschrift für Mathematik und Physik, no. 58, pp. 704-709, 1910.
149. Z. P. Wiercigroch M., "On the Painleve paradoxes", in Proceedings of the XXVII Summer School 'Nonlinear Oscillations in Mechanical Systems', St. Petersburg, Russia, pp. 89-111, 2000.
150. K. L. Johnson, Contact Mechanics. Cambridge University Press, 1987.
151. T. S. Komatsu, S. Inagaki, N. Nakagawa, and S. Nasuno, "Creep motion in a granular pile exhibiting steady surface flow", Physical Review Letters, vol. 86, pp. 1757-1760, Feb 2001.
152. W. Stronge, Impact Mechanics. Cambridge University Press, 2000.
153. F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts. Wiley Interscience, 1997.
154. D. Weaire, V. Langlois, M. Saadatfar, and S. Hutzler, "Foam as granular matter", in Granular and Complex Materials, T. Aste, T. Di Matteo, and A. Tordesillas, eds., World Scientific Lecture Notes in Complex Systems, pp. 1-26, World Scientific, 2008.
155. P. K. Haff, "Grain flow as a fluid-mechanical phenomenon", Journal of Fluid Mechanics, vol. 134, pp. 401-430, 1983.
156. R. Gingold and J. Monaghan, "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society, vol. 181, pp. 375-389, 1977.
157. S. Koshizuka and Y. Oka, "Moving-particle semi-implicit method for fragmentation of incompressible fluid", Nuclear Science Engineering, vol. 123, no. 3, pp. 421-434, 1996.
158. G. R. Liu and M. B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, 2003.
159. I. Goldhirsch and G. Zanetti, "Clustering instability in dissipative gases", Physical Review Letters, vol. 70, pp. 1619-1622, Mar 1993.
160. D. Krengel, S. Strobl, A. Sack, M. Heckel, and T. Pschel, "Pattern formation in a horizontally shaken granular submonolayer", Granular Matter, vol. 15, no. 3, pp. 377-387, 2013.
161. J. Lee and H. Herrmann, "Angle of repose and angle of marginal stability: molecular dynamics of granular particles", Journal of Physics A, vol. 26, no. 2, pp. 373-383, 1993.
162. S. A. M. El Shourbagy, S. Morita, and H.-G. Matuttis, "Simulation of the dependence of the bulk-stress-strain relations of granular materials on the particle shape", Journal of the Physical Society of Japan, vol. 75, no. 10, article 104602, 2006.
163. T. Doanh, M. Hoang, J.-N. Roux, and C. Dequeker, "Stick-slip behaviour of model granular materials in drained triaxial compression", Granular Matter, vol. 15, no. 1, pp. 1-23, 2013.
164. R. Brockbank, J. Huntley, and R. Ball, "Contact force distribution beneath a three-dimensional granular pile", Journal de Physique II, vol. 7, no. 10, pp. 1521-1532, 1997.
165. M. Huber-Burnand, "Über das Ausfliessen und den Druck des Sandes", Annalen der Physik, vol. 92, no. 6, pp. 316-328, 1829.
166. G. H. L. Hagen, "Über den Druck und die Bewegung des trockenen Sandes", Monatsberichte der königlich, Preußischen Akademie der Wissenschaften zu Berlin, p. 35, Jan 1852.
167. F. Engesser, "Über den Erddruck gegen innere Stützwände", Deutsche Bauzeitung, 1882.
168. P. Forchheimer, "Über Sanddruck und Bewegungserscheinungen im inneren trockenen Sandes", Zeitschrift des österreichischen Ingenieurs- und Architekten-Vereins, 1883.
169. H. A. Janssen, "Versuche über Getreidedruck in Silozellen", Zeitschrift des Vereines deutscher Ingenieure, vol. 39, no. 35, pp. 1045-1049, 1895.
170. G. Darwin, On the Horizontal Thrust of a Mass of Sand. Institution of Civil Engineers, 1883.
171. C. Terzaghi, "Old earth-pressure theories and new test results", Engineering News-Record, vol. 85, no. 14, pp. 632-637, 1920.
172. G. Gudehus, "Earth pressure determination", in Geotechnical Engineering Handbook. Volume 1: Fundamentals, pp. 407-436. Wiley, 2002.
173. G. Gudehus, Physical Soil Mechanics. Springer, 2010.
174. H.-G. Matuttis, "Simulation of the pressure distribution under a two-dimensional heap of polygonal particles", Granular Matter, vol. 1, pp. 83-91, 1998.
175. T. Jotaki and R. Moriyama, "On the bottom pressure distribution of the bulk materials piled with the angle of repose", Journal of the Society of Powder Technology, Japan, vol. 16, no. 4, pp. 184-191, 1979.
176. O. Reynolds, "On the dilatancy of media composed of rigid particles in contact", Philosophical Magazine Series 5, vol. 20, pp. 469-482, 1885.
177. J. Šmid and J. Novosad, "Pressure distribution under heaped bulk solids", International Chemical Engineering Symposium Series, vol. 63, pp. D3/V/1-12, 1981.
178. I. K. Lee and J. Herrington, "Stresses beneath granular embarkments", Proceedings of the first Australian-New Zealand Conference on Geomechanics, Melbourne, vol. 1, pp. 291-296, August 1971.
179. B. Lackinger, Das Tragverhalten von Staudämmen mit membranartigen Dichtungen. PhD thesis, Mitteilungen des Instituts für Bodenmechanik, Felsmechanik und Grundbau an der Fakultät für Bauingenieurwesen und Architekture der Universität Innsbruck, 1980.
180. S. Savage, "Modelling and granular material boundary value problems", in Physics of Dry Granular Media, H. J. Herrmann, J.-P. Hovi, and S.Luding, eds., vol. 350 of NATO Advanced Science Institutes Series E, Kluwer Academic Publishers, 1998.
181. L. Vanel, D. Howell, D. Clark, R. P. Behringer, and E. Clement, "Memories in sand: Experimental tests of construction history on stress distributions under sandpiles", Physical Review E, vol. 60, no. 5, pp. R5040-R5043, 1999.
182. A. Schinner, H.-G. Mattutis, J. Aoki, S. Takahashi, K. M. Aoki, T. Akiyama, and K. Kassner, "Towards a micromechanic understanding of the pressure distribution under heaps", in Mathematical Aspects of Complex Fluids II, vol. 1184 of Kokyuroku (Kyoto University), pp. 123-139, Research Insitute for Mathematical Sciences, 2001.
183. J. Chen and H.-G. Matuttis, "Study of quasi two dimensional granular heaps", Theoretical and Applied Mechanics Japan, vol. 60, pp. 225-238, 2012.
184. J. Gordon and P. Ball, The New Science of Strong Materials: Or Why You Don't Fall Through the Floor. Alix G. Mautner Memorial Lectures, Princeton University Press, 2006.
185. H.-J. Tillemans and H. J. Herrmann, "Simulating deformations of granular solids under shear", Physica A, vol. 217, pp. 261-288, 1995.
186. S. H. Ng and H.-G. Matuttis, "Adaptive mesh generation for two-dimensional simulation of polygonal particles in fluid", Theoretical and Applied Mechanics Japan, vol. 59, pp. 323-333, 2011.
187. S. H. Ng and H.-G. Matuttis, "Two-dimensional microscopic simulation of granular particles in fluid", Theoretical and Applied Mechanics Japan, vol. 60, pp. 105-115, 2012.
188. D. Baraff, "Curved surfaces and coherence for non-penetrating rigid body simulation", Computer Graphics, vol. 24, no. 4, pp. 19-28, 1990.
189. M. C. Lin, Efficient Collision Detection for Animation and Robotics. PhD thesis, University of California, Berkeley, 1993.
190. D. J. Muder, "Putting the best face on a Voronoi polyhedron", Proceedings of the London Mathematical Society, vol. 56, pp. 329-348, 1988.
191. P. Mott, J. Dorgan, and C. Roland, "The bulk modulus and Poisson's ratio of "incompressible" materials", Journal of Sound and Vibration, vol. 312, no. 4-5, pp. 572-575, 2008.
192. P. Mott and C. Roland, "Response to "Comment on paper 'The bulk modulus and Poisson's ratio of "incompressible" materials' " ", Journal of Sound and Vibration, vol. 329, no. 3, pp. 368-369, 2010.
193. D. J. Hart and H. F. Wang, "Laboratory measurements of a complete set of poroelastic moduli for Berea sandstone and Indiana limestone", Journal of Geophysical Research: Solid Earth, vol. 100, no. B9, pp. 17741-17751, 1995.
194. W. S. Cheng, J. Chen, and H.-G. Matuttis, "Granular acoustics of polyhedral particles", in Proceedings of the 7th International Conference on Micromechanics of Granular Media, Sydney, Australia, A. Yu, K. Dong, R. Yang, and S. Luding, eds., vol. 1542 of American Institute of Physics Conference Series, pp. 567-570, American Institute of Physics, 2013.
195. Z. Zeravcic, N. Xu, A. J. Liu, S. R. Nagel, and W. van Saarloos, "Excitations of ellipsoid packings near jamming", Europhysics Letters, vol. 87, no. 2, article 26001, 2009.
196. E. Clément, L. Vanel, J. Rajchenbach, and J. Duran, "Pattern formation in a vibrated two-dimensional granular layer", Physical Review E, vol. 53, pp. 2972-2975, Mar 1996.
197. P. B. Umbanhowar, F. Melo, and H. L. Swinney, "Localized excitations in a vertically vibrated granular layer", Nature, vol. 382, pp. 793-796, Aug 1996.
198. C. Coste and B. Gilles, "On the validity of Hertz contact law for granular material acoustics", The European Physical Journal B, vol. 7, no. 1, pp. 155-168, 1999.
199. C. Coste, E. Falcon, and S. Fauve, "Solitary waves in a chain of beads under Hertz contact", Physical Review E, vol. 56, pp. 6104-6117, Nov 1997.
200. M. A. Porter, C. Daraio, E. B. Herbold, I. Szelengowicz, and P. G. Kevrekidis, "Highly nonlinear solitary waves in periodic dimer granular chains", Physical Review E, vol. 77, article 015601, Jan 2008.
201. N. Ashcroft and N. Mermin, Solid State Physics. Saunders College, 1976.
202. C. Kittel, Introduction to Solid State Physics, 6th ed. John Wiley & Sons, 1986.
203. S. Elliott, The Physics and Chemistry of Solids. Wiley, 1998.
204. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. Cambridge University Press, 2002.
205. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. Cambridge University Press, 1992.
206. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, 1992.
207. A. L. Garcia, Numerical Methods for Physics, 2nd ed. Prentice-Hall, 1999.
208. F. S. Crawford, Jr, Waves and Oscillations. Vol. 3 of Berkeley Physics Course, McGraw-Hill, 1966.
209. H. J. Pain, The Physics of Vibrations and Waves, 6th ed. John Wiley & Sons, 2005.
210. M. Remoissenet,Waves Called Solitons: Concepts and Experiments. Advanced Texts in Physics, Springer, 1999.
211. R. Landau, M. Meĵaia, and C. Bordeianu, Computational Physics: Problem Solving with Computers. Wiley, 2007.
212. A. Manevich and L. Manevich, The Mechanics of Nonlinear Systems with Internal Resonances. Imperial College Press, 2005.
213. P. Gresho and R. Sani, Incompressible Flow and the Finite Element Method, Volume 2: Isothermal Laminar Flow. John Wiley & Sons, 2000.
214. B. Leonard, "A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation", in Finite Element Methods for Convection Dominated Flows (Winter Annual Meeting of the American Society of Mechanical Engineers, New York, December 2-7, 1979), pp. 1-17. ASME, 1979.
215. K. Popper, The World of Parmenides: Essays on the Presocratic Enlightenment. Routledge Classics, Taylor & Francis, 2012.
216. H. Hertz, Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt: Mit einem Vorworte. Johann Ambrosius Barth (Arthur Meiner), 1894.
217. H. Hertz, The Principles of Mechanics Presented in a New Form. Dover Phoenix Editions, Dover Publications, 2004.
218. G. Darwin, On the Horizontal Thrust of a Mass of Sand. Institution of Civil Engineers, 1883.
219. H.-G. Matuttis, "Simulation of the pressure distribution under a two-dimensional heap of polygonal particles", Granular Matter, vol. 1, pp. 83-91, 1998.
220. D. Frenkel, "Simulations: The dark side", The European Physical Journal Plus, vol. 128, article 10, 2013.
221. R. Gingold and J. Monaghan, "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society, vol. 181, pp. 375-389, 1977.
222. S. Koshizuka and Y. Oka, "Moving-particle semi-implicit method for fragmentation of incompressible fluid", Nuclear Science Engineering, vol. 123, no. 3, pp. 421-434, 1996.
223. G. W. Baxter and R. P. Behringer, "Cellular automata models of granular flow", Physical Review A, vol. 42, pp. 1017-1020, Jul 1990.
224. P. Bak, C. Tang, and K. Wiesenfeld, "Self-organized criticality: An explanation of the 1/f noise", Physical Review Letters, vol. 59, pp. 381-384, Jul 1987.
225. H. M. Jaeger, C.-H. Liu, and S. R. Nagel, "Relaxation at the angle of repose", Physical Review Letters, vol. 62, pp. 40-43, Jan 1989.
226. N. Yoshioka, "A sandpile experiment and its implications for self-organized criticality and characteristic earthquake", Earth, Planets and Space, vol. 55, pp. 283-289, 2003.
227. M. Kendall and B. B. Smith, Tables of Random Sampling Numbers. Cambridge University Press, 1939.
228. C. Wenzler, Das Roulette-Spiel. Taschenbuch und Ratgeber für alle Interessenten dieses Spieles. Leupoldt, 1890.
229. R. R. Coveyou, J. G. Sullivan, H. P. Carter, D. C. Irving, R. M. Freestone, Jr, and F. B. K. Kam, O5R, a General-Purpose Monte Carlo Neutron Transport Code. Oak Ridge National Laboratory, 1965.
230. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "Equation of state calculations by fast computing machines", Journal of Chemical Physics, vol. 21, pp. 1087-1092, 1953.
231. T. Duke, G. Barker, and A. Mehta, "Monte Carlo study of granular relaxation", Europhysics Letters, vol. 13, pp. 19-24, 1990.
232. A. Mehta, ed.,Granular Matter: An Interdisciplinary Approach. Springer, 1994.
233. M. Müller, S. Luding, and H. J. Herrmann, "Simulations of vibrated granular media in two and three dimensional systems", in Friction, Arching and Contact Dynamics, D. E. Wolf and P. Grassberger, eds., pp. 335-340, World Scientific, 1997.
234. T. Laursen, Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Engineering Online Library, Springer, 2002.
235. G. Zavarise and P. Wriggers, Trends in Computational Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, Springer, 2011.
236. P. Wriggers and T. Laursen, eds., Computational Contact Mechanics. Vol. 498 of CISM International Centre for Mechanical Sciences, Springer, 2008.
237. S. Luding, E. Clément, A. Blumen, J. Rajchenbach, and J. Duran, "Anomalous energy dissipation in molecular dynamics simulations of grains: The "detachment effect" ", Physical Review E, vol. 50, pp. 4113-4122, 1994.
238. J. Schäfer and D. E. Wolf, "Bistability in simulated granular flow along corrugated walls", Physical Review E, vol. 51, pp. 6154-6157, Jun 1995.
239. T. Scheffler and D. E. Wolf, "Molecular dynamics simulation of a charged granular medium", in Workshop on Molecular Dynamics on Parallel Computers, John Von Neumann Institute for Computing (NIC) Research Centre, Jülich, Germany, 8-10 February 1999, R. Esser, P. Grassberger, J. Grotendorst, and M. Lewerenz, eds., pp. 233-238, World Scientific, 2000.
240. H.-G. Matuttis, "Simulation of the pressure distribution under a two-dimensional heap of polygonal particles", Granular Matter, vol. 1, pp. 83-91, 1998.
241. G. Kuwabara and K. Kono, "Restitution coefficient in a collision between two spheres", Japanese Journal of Applied Physics, vol. 26, pp. 1230-1233, 1987.
242. O. R. Walton, "Explicit particle dynamics model for granular materials", in Numerical Methods in Geomechanics:Edmonton 1982 (Proceedings of the Fourth International Conference on Numerical Methods in Geomechanics, Edmonton, Canada, May 31-June 4, 1982), H. Rathmayer, Z. Eisenstein, and K. Saari, eds., A. A. Balkema, 1982.
243. J. Kepler, De Fundamentis Astrologiae Certioris. 1601.
244. G. Schneebeli, "Une analogie mécanique pour les terres sans cohésion", Comptes Rendus de l'Académie des Sciences, vol. 243, no. 1, pp. 125-126, 1956.
245. K. Johnson, Contact Mechanics. Cambridge University Press, 1987.
246. M. A. Porter, C. Daraio, E. B. Herbold, I. Szelengowicz, and P. G. Kevrekidis, "Highly nonlinear solitary waves in periodic dimer granular chains", Physical Review E, vol. 77, article 015601, Jan 2008.
247. J. A. Greenwood, "Contact of rough surfaces", in Fundamentals of Friction: Macroscopic and Microscopic Processes, I. L. Singer and H. Pollock, eds., NATO Advanced Study Institutes Series E: Applied sciences, Kluwer, 1992.
248. S. A. El Shourbagy, S. Okeda, and H.-G. Matuttis, "Acoustic of sound propagation in granular materials in one, two, and three dimensions", Journal of the Physical Society of Japan, vol. 77, no. 3, article 034606, 2008.
249. J. O'Rourke, "comp.graphics.algorithms Frequently Asked Questions", http://www.faqs.org/faqs/graphics/ algorithms-faq/, last visited December 2013.
250. A. Schinner, "Fast algorithms for the simulation of polygonal particles", Granular Matter, vol. 2, no. 1, pp. 35-43, 1999.
251. H.-G. Matuttis and A. Schinner, "Particle simulation for cohesive granular materials", International Journal of Modern Physics C, vol. 12, no. 7, pp. 1011-1022, 2001.
252. R. Albert, I. Albert, D. Hornbaker, P. Schiffer, and A.-L. Barabási, "Maximum angle of stability in wet and dry spherical granular media", Physical Review E, vol. 56, pp. R6271-R6274, Dec 1997.
253. H.-J. Tillemanns, Molekulardynamik beliebig geformter Teilchen in zwei Dimensionen. PhD thesis, Universität Köln, 1995.
254. S. A. M. El Shourbagy, S. Morita, and H.-G. Matuttis, "Simulation of the dependence of the bulk-stress-strain relations of granular materials on the particle shape", Journal of the Physical Society of Japan, vol. 75, no. 10, article 104602, 2006.
255. L. Verlet, "Computer "experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules", Physical Review, vol. 159, pp. 98-103, Jul 1967.
256. C. Störmer, "Méthode d'intégration numérique des équations différentielles ordinaires", in Comptes Rendus du Congrès International des Mathématiciens, Strasbourg, pp. 243-257, 1921.
257. W. Vermöhlen and N. Ito, "State diagram of polydisperse elastic-disk systems", Physical Review E, vol. 51, pp. 4325-4334, May 1995.
258. P. Jiménez, F. Thomas, and C. Torras, "3D collision detection: a survey", Computers & Graphics, vol. 25, pp. 269-285, 2001.
259. D. Baraff, "Rigid body simulation", in SIGGRAPH 93: An Introduction to Physical Modeling, M. Kass, ed., pp. H1-H68, Association for Computing Machinery, 1993.
260. D. Baraff, "An introduction to physically based modeling: Rigid body simulation II-nonpenetration constraints", in SIGGRAPH Course Notes, pp. D31-D68, Association for Computing Machinery, 1997.
261. N. K. Mitani, H.-G. Matuttis, and T. Kadono, "Density and size segregation in deposits of pyroclastic flow", Geophysical Research Letters, vol. 31, article L15606, 2004.
262. J. Chen and H.-G. Matuttis, "Optimization and OpenMP parallelization of a discrete element code for convex polyhedra on multi-core machines", International Journal of Modern Physics C, vol. 24, no. 2, article 1350001, 2013.
263. B. C. Vemuri, L. Chen, L. Vu-Quoc, X. Zhang, and O. Walton, "Efficient and accurate collision detection for granular flow simulation", in Graphical Models And Image Processing, vol. 60, pp. 403-422, 1998.
264. R. J. Bathurst and L. Rothenburg, "Observations on stress-force-fabric relationships in idealized granular materials", Mechanics of Materials, vol. 9, no. 1, pp. 65-80, 1990.
265. K. Binder and D. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction. Graduate Texts in Physics, Springer, 2010.
266. J. O'Rourke, Computational Geometry in C, 2nd ed. Cambridge University Press, 1998.
267. Wikimedia Foundation, http://www.wikipedia.org, last visited December 2013.
268. D. Knuth, The Art of Computer Programming, Volumes 1-4A. Addison-Wesley, 2011.
269. M. P. Allen and D. Tildesley, Computer Simulation of Liquids. Oxford University Press, 1987.
270. M. P. Allen and D. Tildesley, Program library of 'Computer Simulation of Liquids, http://www.ccl.net/cca/ software/SOURCES/FORTRAN/allen-tildesley-book/index.shtml, last visited December 2013.
271. D. Zhao, E. G. Nezami, Y. M. Hashash, and J. Ghaboussi, "Three-dimensional discrete element simulation for granular materials", Engineering Computations, vol. 23, no. 7, pp. 749-770, 2006.
272. P. Cundall, "Formulation of a three-dimensional distinct element model-Part I. A scheme to represent contacts in a system composed of many polyhedral blocks", International Journal of Rock Mechanics and Mining Sciences & Geomechanics, vol. 25, no. 3, pp. 107-116, 1988.
273. F. Preparata and M. I. Shamos, Computational Geometry: An Introduction. Springer, 1985.
274. M. C. Lin, Efficient Collision Detection for Animation and Robotics. PhD thesis, University of California, Berkeley, 1993.
275. C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, "The quickhull algorithm for convex hulls", ACMTransactions on Mathematical Software, vol. 22, no. 4, pp. 469-483, 1996. http://www.qhull.org.
276. A. Schinner, "Numerische simulationen für granulare medien", Master's thesis, University of Regensburg, 1995.
277. G. H. Golub and C. F. van Loan, Matrix Computations, 3rd ed. Johns Hopkins Studies in Mathematical Sciences, Johns Hopkins University Press, 1996.
278. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users' Guide. Society for Industrial and Applied Mathematics, 1992.
279. S. McConnell, Code Complete: A Practical Handbook of Software Construction. Microsoft Press, 1993.
280. J. Chen, Discrete Element Method for 3D Simulations of Mechanical Systems of Non-Spherical Granular Materials. PhD thesis, The University of Electro-Communications, 2011.
281. J. Chen and H.-G. Matuttis, "Optimization and OpenMP parallelization of a discrete element code for convex polyhedra on multi-core machines", International Journal of Modern Physics C, vol. 24, no. 2, article 1350001, 2013.
282. M. P. Allen, "A molecular dynamics simulation study of octopoles in the field of a planar surface", Molecular Physics, vol. 52, no. 3, pp. 717-732, 1984.
283. M. P. Allen and D. Tildesley, Computer Simulation of Liquids. Oxford University Press, 1987.
284. S. A. El Shourbagy, S. Okeda, and H.-G. Matuttis, "Acoustic of sound propagation in granular materials in one, two, and three dimensions", Journal of the Physical Society of Japan, vol. 77, no. 3, article 034606, 2008.
285. W. S. Cheng, J. Chen, and H.-G. Matuttis, "Granular acoustics of polyhedral particles", in Proceedings of the 7th International Conference on Micromechanics of Granular Media, Sydney, Australia, A. Yu, K. Dong, R. Yang, and S. Luding, eds., vol. 1542 of American Institute of Physics Conference Series, pp. 567-570, American Institute of Physics, 2013.
286. S. Sokolowski and J. A. C. Gallas, "Grain non-sphericity effects on the angle of repose of granular materials", International Journal of Modern Physics B, vol. 7, no. 9-10, pp. 2037-2046, 1993.
287. D. Negrut, A. Tasora, H. Mazhar, T. Heyn, and P. Hahn, "Leveraging parallel computing in multibody dynamics", Multibody System Dynamics, vol. 27, no. 1, pp. 95-117, 2012.
288. J.W. Perram andM. S.Wertheim, "Statistical mechanics of hard ellipsoids. I. Overlap algorithm and the contact function", Journal of Computational Physics, vol. 58, pp. 409-416, 1985.
289. J.W. Perram, J. Rasmussen, E. Præstgaard, and J. L. Lebowitz, "Ellipsoid contact potential: Theory and relation to overlap potentials", Physical Review E, vol. 54, pp. 6565-6572, Dec 1996.
290. R. Everaers and M. R. Ejtehadi, "Interaction potentials for soft and hard ellipsoids", Physical Review E, vol. 67, article 041710, Apr 2003.
291. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. Cambridge University Press, 2002.
292. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. Cambridge University Press, 1992.
293. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, 1992.
294. H. G. Matuttis, N. Ito, H. Watanabe, and K. M. Aoki, "Vectorizable overlap computation for ellipse-based discrete element method", Powders & Grains 2001, Y. Kishino, ed., pp. 173-176, Balkema, 2001.
295. J. Viellard-Baron, Thése de Doctorat d'Etat. PhD thesis, Faculté des Sciences d'Orsay, 1970.
296. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users' Guide. Society for Industrial and Applied Mathematics, 1992.
297. A. V. Potapov and C. S. Campbell, "A fast model for the simulation of non-round particles", Granular Matter, vol. 1, pp. 9-14, 1998.
298. P. Fu, O. R. Walton, and J. T. Harvey, "Polyarc discrete element for efficiently simulating arbitrarily shaped 2D particles", International Journal for Numerical Methods in Engineering, vol. 89, no. 5, pp. 537-670, 2012.
299. S. Rémond, J. L. Gallias, and A. Mizrahi, "Simulation of the packing of granular mixtures of non-convex particles and voids characterization", Granular Matter, vol. 10, pp. 157-170, 2008.
300. G. S. Fishman, Principles of Discrete Event Simulation. Wiley, 1978.
301. D. C. Rapaport, The Art of Molecular Dynamics Simulation. Cambridge University Press, 2004.
302. S. Luding, Die Physik trockener granularer Medien (Habilitation thesis, in German). Logos Verlag, 1998.
303. J. J. Moreau, "Unilateral contact and dry friction in finite freedom dynamics", in Nonsmooth Mechanics and Applications, J. J. Moreau. and P. D. Panagiotopoulos, eds., vol. 302 of CISM Courses and Lectures, pp. 1-82, Springer, 1988.
304. M. Raous, M. Jean, and J. J. Moreau, eds., Contact Mechanics, Plenum, 1995.
305. T. Laursen, Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Engineering Online Library, Springer, 2002.
306. G. Zavarise and P. Wriggers, Trends in Computational Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, Springer, 2011.
307. P. Wriggers and T. Laursen, eds., Computational Contact Mechanics. Vol. 498 of CISM International Centre for Mechanical Sciences, Springer, 2008.
308. J. Moreau, "Evolution problem associated with a moving convex set in a Hilbert space", Journal of Differential Equations, vol. 26, pp. 347-374, 1977.
309. J. J. Moreau, "Application de la methode "contact dynamics" á des collections de solides polygonaux", in 4ème Réunion annuelle du Réseau de Laboratoires G.E.O, Aussois, France, 24-28 Novembre, 1997.
310. E. Azéma, F. Radjai, R. Peyroux, V. Richefeu, and G. Saussine, "Short-time dynamics of a packing of polyhedral grains under horizontal vibrations", The European Physical Journal E, vol. 26, no. 3, pp. 327-335, 2008.
311. E. Azéma, F. Radjai, and F. Dubois, "Packings of irregular polyhedral particles: Strength, structure, and effects of angularity", Physical Review E, vol. 87, article 062203, Jun 2013.
312. G.-H. Shi, "Discontinous deformation analysis: A new numerical model for the statics and dynamics of deformable block structures", Engineering Computations, vol. 9, pp. 157-168, 1992.
313. G. Shi, Block System Modeling by Discontinuous Deformation Analysis. Topics in Engineering, Computational Mechanics Publications, 1993.
314. A. Aikawa and F. Urakawa, "Modeling techniques for three-dimensional discrete element analysis of a conventional ballasted railway track and its application" (in Japanese), Technical Report 2, Railway Technical Research Institute, Kunitachi, Tokyo, Japan, 2009.
315. M. Kunze andM. Marques, "An introduction to Moreau's sweeping process", in Impacts in Mechanical Systems, B. Brogliato, ed., vol. 551 of Lecture Notes in Physics, pp. 1-60, Springer, 2000.
316. W. Boehm and H. Prautzsch, Geometric Concepts for Geometric Design. A.K. Peters, 1994.
317. C. Gibson, Elementary Geometry of Algebraic Curves: An Undergraduate Introduction. Cambridge University Press, 1998.
318. R. Bix, Conics and Cubics: A Concrete Introduction to Algebraic Curves. Springer, 2006.
319. M. Mortenson, Geometric Modeling, 3rd ed. Industrial Press, 2006.
320. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design. A.K. Peters, 1993.
321. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences, Springer, 2003.
322. J. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 1999.
323. The International Obfuscated C Code Contest, http://www.ioccc.org, last visited December 2013.
324. N. Wirth, "The programming language Pascal", Acta Informatica, vol. 1, pp. 35-63, 1971.
325. D. Knuth, The Art of Computer Programming, Volumes 1-4A. Addison-Wesley, 2011.
326. S. McConnell, Code Complete, 2nd ed. Microsoft Press, 2009.
327. A. Hunt and D. Thomas, The Pragmatic Programmer: From Journeyman to Master. Pearson Education, 1999.
328. J. Bentley, Programming Pearls, 2nd ed. ACM Press Series, Prentice Hall, 2000.
329. F. P. Brooks, Jr, The Mythical Man-Month: Essays On Software Engineering, Anniversary Edition, 2nd ed. Pearson Education, 1995.
330. E. Yourdon, Death March. Yourdon Press Computing Series, Prentice Hall, 2004.
331. S. Maguire, Debugging the Development Process: Practical Strategies for Staying Focused, Hitting Ship Dates, and Building Solid Teams. Microsoft Press, 1994.
332. S. McConnell, Code Complete, 1st ed. Microsoft Press, 1993.
333. L. Null and J. Lobur, The Essentials of Computer Organization and Architecture. Jones & Bartlett Learning, 2010.
334. HPL - A Portable Implementation of the High-Performance Linpack Benchmark for Distributed-Memory Computers, http://www.netlib.org/benchmark/hpl/, last visited December 2013.
335. J. Dongarra, J. Bunch, G. Moler, and G. Stewart, LINPACK Users' Guide. Society for Industrial and Applied Mathematics, 1987.
336. R. Himeno, Himeno Benchmark, http://openbenchmarking.org/test/pts/himeno, last visited December 2013.
337. J. Chen and H.-G. Matuttis, "Optimization and OpenMP parallelization of a discrete element code for convex polyhedra on multi-core machines", International Journal of Modern Physics C, vol. 24, no. 2, article 1350001, 2013.
338. R. Hackl, H.-G. Matuttis, J. M. Singer, T. Husslein, and I. Morgenstern, "Parallelization of the 2D Swendsen-Wang algorithm", International Journal of Modern Physics C, vol. 4, no. 6, pp. 1117-1130, 1993.
339. M. Flanigan and P. Tamayo, "A parallel cluster labeling method for Monte Carlo dynamics", International Journal of Modern Physics C, vol. 3, no. 6, pp. 1235-1249, 1992.
340. R. Mecklenburg, Managing Projects with GNU Make. O'Reilly Media, 2009.
341. Cygwin, http://www.cygwin.com, last visited December 2013.
342. I. S. Duff, M. A. Heroux, and R. Pozo, "An overview of the sparse basic linear algebra subprograms: The new standard from the BLAS technical forum", ACM Transactions on Mathematical Software, vol. 28, no. 2. pp. 239-267, 2002.
343. BLAS (Basic Linear Algebra Subprograms), http://www.netlib.org/blas/, last visited December 2013.
344. The OpenMP API specification for parallel programming, http://openmp.org/wp/, last visited December 2013.
345. A. Aho and J. Ullman, Foundations of Computer Science: C Edition. Principles of Computer Science Series, W. H. Freeman, 1994.
346. T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction To Algorithms. MIT Press, 2001.
347. R. Sedgewick, Algorithms in C++: Graph Algorithms. Addison-Wesley, 2002.
348. R. Sedgewick, Algorithms in Java. Parts 1-4: Fundamentals, Data Structures, Sorting, Searching. Prentice Hall, 2003.
349. R. Sedgewick and K. Wayne, Algorithms. Prentice Hall, 2011.
350. B. Chapman, G. Jost, and R. Van Der Pas, Using OpenMP: Portable Shared Memory Parallel Programming. Scientific and Engineering Computation Series, MIT Press, 2008.
351. R. Chandra, L. Dagum, D. Kohr, D. Maydan, J. McDonald, and R. Menon, Parallel Programming in OpenMP. Academic Press, 2001.
352. K. Johnson, Contact Mechanics. Cambridge University Press, 1987.
353. V. Popov, Contact Mechanics and Friction: Physical Principles and Applications. Springer, 2010.
354. J. J. Moreau, "Unilateral contact and dry friction in finite freedom dynamics", in Nonsmooth Mechanics and Applications, J. J. Moreau and P. D. Panagiotopoulos, eds., CISM Courses and Lectures, vol. 302, pp. 1-82, Springer, 1988.
355. J. J. Moreau and P. D. Panagiotopoulos, eds., Nonsmooth Mechanics and Applications, CISM Courses and Lectures, vol. 302, Springer, 1988.
356. E. Azéma, F. Radjai, R. Peyroux, V. Richefeu, and G. Saussine, "Short-time dynamics of a packing of polyhedral grains under horizontal vibrations", The European Physical Journal E, vol. 26, no. 3, pp. 327-335, 2008.
357. T. Laursen, Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Engineering Online Library, Springer, 2003.
358. P. Wriggers, Computational Contact Mechanics. John Wiley & Sons, 2002.
359. R. M. Brach, Mechanical Impact Dynamics: Rigid Body Collisions. Brach Engineering, 2007.
360. W. Stronge, Impact Mechanics. Cambridge University Press, 2000.
361. F. Kun and H. J. Herrmann, "Transition from damage to fragmentation in collision of solids", Physical Review E, vol. 59, pp. 2623-2632, Mar 1999.
362. B. Behera, F. Kun, S. McNamara, and H. J. Herrmann, "Fragmentation of a circular disc by impact on a frictionless plate", Journal of Physics: Condensed Matter, vol. 17, no. 24, article S2439, 2005.
363. H. J. Pain, The Physics of Vibrations and Waves, 6th ed. John Wiley & Sons, 2005.
364. M. Fuhr, Hybrid FE-DE Simulation of Notched Bar Impact Testing, Master's thesis, Swiss Federal Institute of Technology (ETH), 2008.
365. A. B. Richou, A. Ambari, M. Lebey, and J. Naciri, "Drag force on a circular cylinder midway between two parallel plates at Re_ 1. Part 2: moving uniformly (numerical and experimental)", Chemical Engineering Science, vol. 60, no. 10, pp. 2535-2543, 2005.
366. S. H. Ng and H.-G. Matuttis, "Two-dimensional microscopic simulation of granular particles in fluid", Theoretical and Applied Mechanics Japan, vol. 60, pp. 105-115, 2012.
367. R. G. Watts and R. Ferrer, "The lateral force on a spinning sphere: Aerodynamics of a curveball", American Journal of Physics, vol. 55, no. 1, pp. 40-44, 1987.
368. T. Taniguchi, T. Miyazaki, T. Shimizu, and R. Himeno, "Measurement of aerodynamic forces exerted on baseball using a high-speed video camera", in The Impact of Technology on Sport: Proceedings of the Asia-Pacific Congress on Sports Technology, A. Subic and S. Ujihashi, eds., pp. 269-279, Australasian Sports Technology Alliance Pty, 2005.
369. Y. Pan, T. Tanaka, and Y. Tsuji, "Direct numerical simulation of particle-laden rotating turbulent channel flow", Physics of Fluids, vol. 13, no. 8, pp. 2320-2337, 2001.
370. K. Höfler and S. Schwarzer, "Navier-Stokes simulation with constraint forces: Finite-difference method for particle-laden flows and complex geometries", Physical Review E, vol. 61, pp. 7146-7160, Jun 2000.
371. M. Hillairet, "Do Navier-Stokes equations enable to predict contact between immersed solid particles?", in Analysis and Simulation of Fluid Dynamics, C. Calgaro, J.-F. Coulombel, and T. Goudon, eds., pp. 109-127, Advances in Mathematical Fluid Mechanics, Birkhäuser, 2007.
372. P. Gresho and R. Sani, Incompressible Flow and the Finite Element Method, Volume Two: Isothermal Laminar Flow. John Wiley & Sons, 2000.
373. G. H. Ristow, "Wall correction factor for sinking cylinders in fluids", Physical Review E, vol. 55, pp. 2808-2813, Mar 1997.
374. S. H. Ng and H.-G. Matuttis, "Adaptive mesh generation for two-dimensional simulation of polygonal particles in fluid", Theoretical and Applied Mechanics Japan, vol. 59, pp. 323-333, 2011.
375. R. Gingold and J. Monaghan, "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society, vol. 181, pp. 375-389, 1977.
376. S. Koshizuka and Y. Oka, "Moving-particle semi-implicit method for fragmentation of incompressible fluid", Nuclear Science Engineering, vol. 123, no. 3, pp. 421-434, 1996.
377. C. Gauger, P. Leinen, and H. Yserentant, "The finite mass method", SIAM Journal on Numerical Analysis, vol. 37, pp. 1768-1799, 2000.
378. H. Yserentant, "The convergence of the finite mass method for flows in given force and velocity fields", in Meshfree Methods for Partial Differential Equations, M. Griebel and M. A. Schweitzer, eds., vol. 26 of Lecture Notes in Computational Science and Engineering, Springer, 2003.
379. A. V. Potapov, M. L. Hunt, and C. S. Campbell, "Liquid-solid flows using smoothed particle hydrodynamics and the discrete element method", Powder Technology, vol. 116, pp. 204-213, 2001.
380. M. S. Shadloo, A. Zainali, S. H. Sadek, and M. Yildiz, "Improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies", Computer Methods in Applied Mechanics and Engineering, vol. 200, pp. 1008-1020, 2011.
381. G. R. Liu and M. B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, 2003.
382. P. W. Cleary and M. Prakash, "Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences", Philosophical Transactions of the Royal Society A, vol. 362, pp. 2003-2030, 2004.
383. U. Frisch, B. Hasslacher, and Y. Pomeau, "Lattice-gas automata for the Navier-Stokes equation", Physical Review Letters, vol. 56, pp. 1505-1508, 1986.
384. S. Succi, The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Numerical Mathematics and Scientific Computation, Clarendon Press, 2001.
385. R. Hockney and J. Eastwood, Computer Simulation Using Particles. Adam Hilger, 1988.
386. T. Darden, D. York, and L. Pedersen, "Particle mesh Ewald: An N • log(N) method for Ewald sums in large systems", Journal of Chemical Physics, vol. 98, pp. 10089-10092, 1993.
387. U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, "A smooth particle mesh Ewald method", Journal of Chemical Physics, vol. 103, pp. 8577-8593, 1995.
388. D. York and W. Yang, "The fast Fourier Poisson method for calculating Ewald sums", Journal of Chemical Physics, vol. 101, no. 4, pp. 3298-3300, 1994.
389. T. Schlick, Molecular Modeling and Simulation: An Interdisciplinary Guide. Interdisciplinary Applied Mathematics, Springer, 2010.