Multibody interactions in coarse-graining schemes for extended systems

SIAM Journal on Scientific Computing

Volumn 31, Issue 2, 2008, Pages 987-1015

  Are, Sasanka ^a   Katsoulakis, Markos A ^a   Plechac, Petr ^b   Luc, Rey Bellet ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Cluster expansion; Coarse graining, relative entropy; Gibbs measure; Lattice spin systems; Monte carlo method; Multibody interactions; Renormalization group map

Indexed keywords

MONTE CARLO METHODS; STATISTICAL MECHANICS; STOCHASTIC SYSTEMS;

CLUSTER EXPANSION; COARSE GRAINING; COARSE-GRAINING, RELATIVE ENTROPY; GIBBS MEASURE; INTERACTION POTENTIALS; LATTICE SPIN SYSTEMS; MONTECARLO METHODS; MULTI-BODY INTERACTIONS; RELATIVE ENTROPY; RENORMALIZATION GROUP MAP;

ERROR ANALYSIS;

EID: 67649543899     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/080713276     Document Type: Article

References (24)

1. C. F. ABRAMS AND K. KREMER, The effect of bond length on the structure of dense bead-spring polymer melts, J. Chem. Phys., 115 (2001), pp. 2776-2785.
2. R. L. C. AKKERMANS AND W. J. BRIELS, Coarse-grained interactions in polymer melts: A variational approach, J. Chem. Phys., 115 (2001), pp. 6210-6219.
3. A. CHATTERJEE AND D. VLACHOS, An overview of spatial microscopic and accelerated kinetic Monte Carlo methods, J. Comput. Aided Mater. Des., 14 (2007), pp. 253-308.
4. H. FUKUNAGA, J.-iCHi TAKIMOTO, AND M. DOI, A coarse-graining procedure for flexible polymer chains with bonded and nonbonded interactions, J. Chem. Phys., 116 (2002), pp. 8183-8190.
5. N. GOLDENFELD, Lectures on Phase Transitions and the Renormalization Group, Vol. 85, Addison-Wesley, New York, 1992.
6. V. A. HARMANDARIS, N. P. ADHIKARI, N. F. A. VAN DER VEGT, AND K. KREMER, Hierarchical modeling of polysterene: From atomistic to coarse-grained simulations, Macromolecules, 39 (2006), pp. 6708-6719.
7. L. KADANOFF, Scaling laws for Ising models near tc, Physics, 2 (1966), pp. 263-272.
8. M. KARDAR, Crossover to equivalent-neighbor multicritical behavior in arbitrary dimensions, Phys. Rev. B, 28 (1983), pp. 244-246.
9. M. A. KATSOULAKIS, A. J. MAJDA, AND D. G. VLACHOS, Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems, J. Comput. Phys., 112 (2003), pp. 250-278.
10. M. A. KATSOULAKIS, A. J. MAJDA, AND D. G. VLACHOS, Coarse-grained stochastic processes for microscopic lattice systems, Proc. Natl. Acad. Sci. USA, 100 (2003), pp. 782-787.
11. M. A. KATSOULAKIS, P. PLECHÁČ, AND A. SOPASAKIS, Error analysis of coarse-graining for stochastic lattice dynamics, SIAM J. Numer. Anal., 44 (2006), pp. 2270-2296.
12. M. A. KATSOULAKIS, P. PLECHÁČ, L. REY-BELLET, AND D. K. TSAGKAROGIANNIS, Mathematical strategies in the coarse-graining of extensive systems: Error quantification and adaptivity, J. Non-Newtonian Fluid Mech., 152 (2008), pp. 101-112.
13. M. A. KATSOULAKIS, L. REY-BELLET, P. PLECHÁČ, AND D. K. TSAGKAROGIANNIS, Coarse- Graining Schemes for Stochastic Lattice Systems with Short and Long Range Interactions, preprint.
14. M. A. KATSOULAKIS, L. REY-BELLET, P. PLECHÁČ, AND D. TSAGKAROGIANNIS, Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems, M2AN Math. Model. Numer. Anal., 41 (2006), pp. 627-660.
15. M. A. KATSOULAKIS AND A. SZEPESSY, Stochastic hydrodynamic limits of particle systems, Commun. Math. Sci., 4 (2006), pp. 513-549.
16. M. A. KATSOULAKIS AND J. TRASHORRAS, Information loss in coarse-graining of stochastic particle dynamics, J. Stat. Phys., 122 (2006), pp. 115-135.
17. K. KREMER AND F. MULLER-PLATHE, Multiscale problems in polymer science: Simulation approaches, MRS Bull., 26 (2001), pp. 205-210.
18. D. P. LANDAU AND K. BINDER, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press, Cambridge, UK, 2000.
19. J. MCCOY AND J. CURRO, Mapping of explicit atom onto united atom potentials,Macro- molecules, 31 (1998), pp. 9362-9368.
20. F. MULLER-PLATHE, Coarse-graining in polymer simulation: From the atomistic to the mesoscale and back, Chem. Phys. Chem., 3 (2002), pp. 754-769.
21. I. PIVKIN AND G. KARNIADAKIS, Coarse-graining limits in open and wall-bounded dissipative particle dynamics systems, J. Chem. Phys., 124 (2006), 184101.
22. B. SIMON, The Statistical Mechanics of Lattice Gases. Vol. I, Princeton Ser. Phys., Princeton University Press, Princeton, NJ, 1993.
23. W. TSCHÖP, K. KREMER, O. HAHN, J. BATOULIS, AND T. BÜRGER, Simulation of polymer melts. I. Coarse-graining procedure for polycarbonates, Acta Polym., 49 (1998), pp. 61-74.
24. B. TURKINGTON, Statistical equilibrium measures and coherent states in two-dimensional turbulence, Comm. Pure Appl. Math., 52 (1999), pp. 781-809.