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Dynamics and Thermodynamics of a system with multiple length scales

Published online by Cambridge University Press:  01 February 2011

Stefano Curtarolo  and
Gerbrand Ceder
Stefano Curtarolo
Affiliation:
Department of Materials Science and Engineering, MIT, Cambridge, MA 02139
Gerbrand Ceder
Affiliation:
Department of Materials Science and Engineering, MIT, Cambridge, MA 02139 Center for Materials Science and Engineering, MIT, Cambridge, MA 02139
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Abstract

Descriptions, in which matter can be coarse grained to arbitrary levels, are necessary to study materials phenomenal simultaneously at various length scales. Attempts to do this in the static regime have already been developed. In this work, we present an approach that leads to dynamics for such coarse-grained models. Renormalization group theory is used to create new local potentials between nodes. Assuming that these potentials give an averaged description of node dynamics, we calculate thermal, mechanical and transport properties. If this method can be sufficiently generalized it may form the basis of a Molecular Dynamics method with time and spatial coarse-graining.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 731: Symposium W – Modeling and Numerical Simulation of Materials Behavior and Evolution , 2002 , W4.4
Copyright
Copyright © Materials Research Society 2002

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References

[1] Tadmor, E. B., Ortiz, M., and Phillips, R., Philos. Mag. A 73, 1529 (1996); V. B. Shenoy, R. Miller, E. B. Tadmor, R. Phillips, and M. Ortiz, Phys. Rev. Lett. 80, 742 (1998); R. Miller, E. B. Tadmor, R. Phillips, and M. Ortiz, Model, Simul. Mater. Sc. 6, 607 (198); V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips, and M. Ortiz, J. Mech. and Phys. of Solids 47, 611 (1999); V. B. Shenoy, R. V. Kukta, and R. Phillips, Phys. Rev. Lett. 84, 1491 (2000).Google Scholar
[2] Shenoy, V., Shenoy, V., and Phillips, R., Multiscale Modeling of Materials. Symposium. Mater. Res. Soc. 1999, pp.465–71. Warrendale, PA, USA; R. Najafabadi and D. J. Srolovitz, Surf. Sci. 284, 104 (1993).Google Scholar
[3] Hadjiconstantinou, N. G., Phys. Rev. E 59, 2475 (1999), J. Comp. Physics 154, 245 (1999).Google Scholar
[4] Rudd, R.E., and Broughton, J.W., Phys. Rev. B 58, R5893 (1998), Phys. Stat. Sol. (b) 217, 251 (2000).Google Scholar
[5] Mori-Zwanzig projection operators method: Zwanzig, R., “Nonequilibrium Statistica Mechanics”, Oxford, (2001).Google Scholar
[6] Voter, A. F., J. Chem. Phys., 106, 4665 (1997), Phys. Rev. Lett. 78, 3908 (1997)Google Scholar
[7] Olender, R., Elber, R., J. Mol. Struct., 398-399, 63 (1997), J. Chem. Phys. 105, 9299 (1996)Google Scholar
[8] Migdal, A. A., Zh. Eksp. Teor. Fiz. 69, 1457 (1975); L. P. Kadanoff, Ann. Phys. 100, 359 (1976), Rev. Mod. Phys. 49, 267 (1977).Google Scholar
[9] Ferrek, R. A., Monyhard, N., Schmidt, H., and Szepfalusy, P., Ann. Phys. (NY) 47, 565 (1968); B. I. Halperin and P. C. Hohemberg, Phys. Rev. 177, 952 (1969).Google Scholar
[10] equation (9.23) in Yeomans, J. M., “Statistical Mechanics of phase transitions” Oxford Science Publications (1992).Google Scholar