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Mathematical strategies in the coarsegraining of extensive systems : error quantification and adaptivity
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Katsoulakis, Markos A., Plechac, Petr, ReyBellet, Luc and Tsagkarogiannis, Dimitrios K. (2008) Mathematical strategies in the coarsegraining of extensive systems : error quantification and adaptivity. In: 4th International Workshop on Equilibrium Thermodynamics and Complex Fluids, Rhodes, Greece, Sep 0307, 2006. Published in: Journal of NonNewtonian Fluid Mechanics, Vol.152 (No.13). pp. 101112.
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Official URL: http://dx.doi.org/10.1016/j.jnnfm.2007.05.005
Abstract
In this paper we continue our study of coarsegraining schemes for stochastic manybody microscopic models started in Katsoulakis et al. [M. Katsoulakis, A. Majda, D. Vlachos, Coarsegrained stochastic processes for microscopic lattice systems, Proc. Natl. Acad. Sci. 100 (2003) 782782, M.A. Katsoulakis, L. ReyBellet, P. Plechac, D. Tsagkarogiannis, Coarsegraining schemes and a posteriori error estimates for stochastic lattice systems, M2AN Math. Model. Numer. Anal., in press], focusing on equilibrium stochastic lattice systems. Using cluster expansion techniques we expand the exact coarsegrained Hamiltonian around a first approximation and derive higher accuracy schemes by including more terms in the expansion. The accuracy of the coarsegraining schemes is measured in terms of information loss, i.e., relative entropy, between the exact and approximate coarsegrained Gibbs measures. We test the effectiveness of our schemes in systems with competing short and longrange interactions, using an analytically solvable model as a computational benchmark. Furthermore, the cluster expansion in Katsoulakis et al. [M.A. Katsoulakis, L. ReyBellet, P. Plechac, D. Tsagkarogiannis, Coarsegraining schemes and a posteriori error estimates for stochastic lattice systems, M2AN Math. Model. Numer. Anal., in press] yields sharp a posteriori error estimates for the coarsegrained approximations that can be computed onthefly during the simulation. Based on these estimates we develop a numerical strategy to assess the quality of the coarsegraining and suitably refine or coarsen the simulations. We demonstrate the use of this diagnostic tool in the numerical calculation of phase diagrams. (C) 2007 Elsevier B.V. All rights reserved.
Item Type:  Conference Item (UNSPECIFIED)  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Error analysis (Mathematics), Entropy, Lattice theory, Monte Carlo method, Stochastic processes  
Journal or Publication Title:  Journal of NonNewtonian Fluid Mechanics  
Publisher:  Elsevier BV  
ISSN:  03770257  
Official Date:  June 2008  
Dates: 


Volume:  Vol.152  
Number:  No.13  
Number of Pages:  12  
Page Range:  pp. 101112  
Identification Number:  10.1016/j.jnnfm.2007.05.005  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  Deutsche Forschungsgemeinschaft (DFG), National Science Foundation (U.S.) (NSF)  
Grant number:  DEFG0205ER25702 (DFG), NSFDMS0413864 (NSF), NSFITR0219211 (NSF), NSFDMS0303565 (NSF), NSFDMS0605058 (NSF)  
Title of Event:  4th International Workshop on Equilibrium Thermodynamics and Complex Fluids  
Type of Event:  Workshop  
Location of Event:  Rhodes, Greece  
Date(s) of Event:  Sep 0307, 2006  
References:  [1] C.F. Abrams, K. Kremer, The effect of bond length on the structure of dense 

URI:  http://wrap.warwick.ac.uk/id/eprint/29832 
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