Abstract
We considered the complex problem of how to simulate dynamics of multiparticle contacts under the molecular dynamics method. The understanding of interaction process is therefore crucial in order to develop theoretical studies and also to perform simulations of motion of a granular material. In opposite to binary collisions, where several contacts between particles are independent, multiparticle contacts depend on some history including several two-particle contacts. To solve this problem we applied fractional interaction law, where fractional derivatives accumulate the whole history of the function in weighted form. We proposed a novel algorithm which allows to perform calculations for an arbitrary form of multiparticle contacts.
Chapter PDF
Similar content being viewed by others
References
Allen M.P. and Tidesley D.J.: Computer simulation of liquids, Oxford Univ. Press, New York (1989)
Cundall P.A. and Strack O.D.L.: A discrete numerical model for granular assemblies, Geotechnique 29 (1979) pp. 47–65
Gidaspow D.: Multiphase flow and fluidization. Continuum and kinetic theory descriptions, Academic Press, San Diego (1994)
Greenspan D.: Discrete models, Addison-Wesley, London (1973)
Kuwabara G., Kono K.: Restitution coefficient in a collision between two spheres, Jap. J. Appl. Phys. 26 Part 1 (1987) pp. 1230–1233
Leszczynski J.S.: A numerical method for solution of ordinary differential equations of fractional order, LNCS Vol. 2328, Springer-Verlag (2001) pp. 695–702
Leszczynski J.S.: The calculation of a normal force between multiparticle contacts using fractional operators, arXiv:physics/0209085, to appear in The Second MIT Conference on Computational Fluid and Solid Mechanics, MIT (2003); Leszczynski J.S.: A discrete model of a two-particle contact applied to cohesive granular materials, (to appear in Granular Matter, 2003)
Luding S. et al: Anomalous energy dissipation in molecular dynamics simulations of grains, Phys. Rev. E 50 (1994) pp. 4113–4122
McNamara S. and Young W.R.: Inelastic collapse and clumping in a one dimensional granular medium, Phys. Fluids A 4 (1992) pp. 496–504
Oldham K.B., Spanier J.: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order, Academic Press, New York (1974)
Palczewski A.: Ordinary differential equations, WNT, Warsaw (1999) (in Polish)
Pournin L., Liebling Th.M.: Molecular dynamics force models for better control of energy dissipation in numerical simulations of dense granular media, Phys. Rev. E 65 (2001) pp. 011302-1–011302-7
Rappaport D.C.: The art of molecular dynamics simulation, Cambridge Univ. Press, Cambridge (1995)
Walton O.R., Braun R.L.: Viscosity, granular-temperature and stress calculations for shearing assemblies of inelastic frictional disks, J. Rheol. 30 (1986) pp. 949–980
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Leszczynski, J.S. (2003). Computer Simulations of Multiparticle-Contacts Dynamics. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Dongarra, J.J., Zomaya, A.Y., Gorbachev, Y.E. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44860-8_11
Download citation
DOI: https://doi.org/10.1007/3-540-44860-8_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40194-0
Online ISBN: 978-3-540-44860-0
eBook Packages: Springer Book Archive