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Volumn 44, Issue 6, 2006, Pages 2270-2296

Error analysis of coarse-graining for stochastic lattice dynamics

Author keywords

Arrhenius dynamics; Birth death process; Coarse grained stochastic processes; Detailed balance; Gibbs measures; Microscopic reconstruction; Monte Carlo simulations; Weak error estimates

Indexed keywords

ARRHENIUS DYNAMICS; BIRTH-DEATH PROCESS; COARSE-GRAINED STOCHASTIC PROCESSES; GIBBS MEASURES; MICROSCOPIC RECONSTRUCTION; WEAK ERROR ESTIMATES;

EID: 34547927269     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050637339     Document Type: Article
Times cited : (28)

References (36)
  • 2
    • 84968498705 scopus 로고
    • Rate of convergence of a stochastic particle method for the Kolmogorov equation with variable coefficients
    • P. BERNARD, D. TALAY, AND L. TUBARO, Rate of convergence of a stochastic particle method for the Kolmogorov equation with variable coefficients, Math. Comp., 63 (1994), pp. 555-587, S11-S17.
    • (1994) Math. Comp , vol.63
    • BERNARD, P.1    TALAY, D.2    TUBARO, L.3
  • 3
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms
    • G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms. I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
    • (1991) I, Comm. Pure Appl. Math , vol.44 , pp. 141-183
    • BEYLKIN, G.1    COIFMAN, R.2    ROKHLIN, V.3
  • 4
    • 0038708036 scopus 로고
    • Multigrid methods in lattice field computations
    • A. BRANDT, Multigrid methods in lattice field computations, Nucl. Phys. B, 26 (1992), pp. 137-180.
    • (1992) Nucl. Phys. B , vol.26 , pp. 137-180
    • BRANDT, A.1
  • 5
    • 0038369196 scopus 로고    scopus 로고
    • Multilevel Monte Carlo methods for studying large-scale phenomena in fluids
    • A. BRANDT AND V. ILYIN, Multilevel Monte Carlo methods for studying large-scale phenomena in fluids, J. Molecular Liquids, 105 (2003), pp. 253-256.
    • (2003) J. Molecular Liquids , vol.105 , pp. 253-256
    • BRANDT, A.1    ILYIN, V.2
  • 6
    • 0035530280 scopus 로고    scopus 로고
    • Renormalization multigrid: Statistically optimal renormalization group flow and coarse-to-fine Monte Carlo acceleration
    • A. BRANDT AND D. RON, Renormalization multigrid: Statistically optimal renormalization group flow and coarse-to-fine Monte Carlo acceleration, J. Stat. Phys., 102 (2001), pp. 231-257.
    • (2001) J. Stat. Phys , vol.102 , pp. 231-257
    • BRANDT, A.1    RON, D.2
  • 7
    • 0039456891 scopus 로고
    • Multilevel approaches to discrete-state and stochastic problems
    • W. Hackbusch and U. Trottenberg, eds, Springer-Verlag, Berlin
    • A. BRANDT, D. RON, AND D. J. AMIT, Multilevel approaches to discrete-state and stochastic problems, in Multigrid Methods, II, W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, Berlin, 1986, pp. 66-99.
    • (1986) Multigrid Methods, II , pp. 66-99
    • BRANDT, A.1    RON, D.2    AMIT, D.J.3
  • 11
    • 37849013985 scopus 로고    scopus 로고
    • W. E AND B. ENGQUIST, Multiscale modeling and computation, Notices Amer. Math. Soc., 50 (2003), pp. 1062-1070.
    • W. E AND B. ENGQUIST, Multiscale modeling and computation, Notices Amer. Math. Soc., 50 (2003), pp. 1062-1070.
  • 12
    • 0000589894 scopus 로고
    • Multigrid Monte Carlo methods for lattice field theories
    • J. GOODMAN AND A. D. SOKAL, Multigrid Monte Carlo methods for lattice field theories, Phys. Rev. Lett., 56 (1986), pp. 1015-1018.
    • (1986) Phys. Rev. Lett , vol.56 , pp. 1015-1018
    • GOODMAN, J.1    SOKAL, A.D.2
  • 13
    • 0035275704 scopus 로고    scopus 로고
    • Renormalization group and perfect operators for stochastic differential equations
    • Q. HOU, N. GOLDENFELD, AND A. MCKANE, Renormalization group and perfect operators for stochastic differential equations, Phys. Rev. E, 63 (2001), 036125.
    • (2001) Phys. Rev. E , vol.63 , pp. 036125
    • HOU, Q.1    GOLDENFELD, N.2    MCKANE, A.3
  • 14
    • 0013004246 scopus 로고    scopus 로고
    • A multiscale finite element method for PDEs with oscillatory coefficients
    • Kiel, Notes Numer. Fluid Mech. 70, Vieweg, Braunschweig, Germany
    • T. Y. HOU AND X.-H. WU, A multiscale finite element method for PDEs with oscillatory coefficients, in Numerical Treatment of Multi-scale Problems (Kiel, 1997), Notes Numer. Fluid Mech. 70, Vieweg, Braunschweig, Germany, 1999, pp. 58-69.
    • (1997) Numerical Treatment of Multi-scale Problems , pp. 58-69
    • HOU, T.Y.1    WU, X.-H.2
  • 18
    • 33644605731 scopus 로고    scopus 로고
    • Multiscale couplings in prototype hybrid deterministic/stochastic systems. Part I. Deterministic closures
    • M. A. KATSOULAKIS, A. J. MAJDA, AND A. SOPASAKIS, Multiscale couplings in prototype hybrid deterministic/stochastic systems. Part I. Deterministic closures, Commun. Math. Sci., 2 (2004), pp. 255-294.
    • (2004) Commun. Math. Sci , vol.2 , pp. 255-294
    • KATSOULAKIS, M.A.1    MAJDA, A.J.2    SOPASAKIS, A.3
  • 19
    • 0037456891 scopus 로고    scopus 로고
    • Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems
    • M. A. KATSOULAKIS, A. J. MAJDA, AND D. G. VLACHOS, Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems, J. Comput. Phys., 186 (2003), pp. 250-278.
    • (2003) J. Comput. Phys , vol.186 , pp. 250-278
    • KATSOULAKIS, M.A.1    MAJDA, A.J.2    VLACHOS, D.G.3
  • 20
    • 0037417955 scopus 로고    scopus 로고
    • Coarse-grained stochastic processes for microscopic lattice systems
    • 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.
    • (2003) Proc. Natl. Acad. Sci. USA , vol.100 , pp. 782-787
    • KATSOULAKIS, M.A.1    MAJDA, A.J.2    VLACHOS, D.G.3
  • 21
    • 37849031632 scopus 로고    scopus 로고
    • Stochastic hydrodynamical limits of particle systems
    • M. A. KATSOULAKIS AND A. SZEPESSY, Stochastic hydrodynamical limits of particle systems, Comm. Math. Sci., 4 (2006), pp. 513-549.
    • (2006) Comm. Math. Sci , vol.4 , pp. 513-549
    • KATSOULAKIS, M.A.1    SZEPESSY, A.2
  • 22
    • 33644583624 scopus 로고    scopus 로고
    • Information loss in coarse-graining of stochastic particle dynamics
    • M. A. KATSOULAKIS AND J. TRASHORRAS, Information loss in coarse-graining of stochastic particle dynamics, J. Stat. Phys., 122 (2006), pp. 115-135.
    • (2006) J. Stat. Phys , vol.122 , pp. 115-135
    • KATSOULAKIS, M.A.1    TRASHORRAS, J.2
  • 23
    • 0345529914 scopus 로고    scopus 로고
    • Coarse-grained stochastic processes and kinetic Monte Carlo simulations for diffusion of interacting molecules
    • M. A. KATSOULAKIS AND D. G. VLACHOS, Coarse-grained stochastic processes and kinetic Monte Carlo simulations for diffusion of interacting molecules, J. Chem. Phys., 119 (2003), pp. 9412-9427.
    • (2003) J. Chem. Phys , vol.119 , pp. 9412-9427
    • KATSOULAKIS, M.A.1    VLACHOS, D.G.2
  • 24
    • 3042720018 scopus 로고    scopus 로고
    • Equation-free: The computer aided analysis of complex multiscale systems
    • I. G. KEVREKIDIS, C. W. GEAR, AND G. HUMMER, Equation-free: The computer aided analysis of complex multiscale systems, AIChE J., 50 (2004), pp. 1346-1355.
    • (2004) AIChE J , vol.50 , pp. 1346-1355
    • KEVREKIDIS, I.G.1    GEAR, C.W.2    HUMMER, G.3
  • 28
    • 0035607876 scopus 로고    scopus 로고
    • A mathematical framework for stochastic climate models
    • A. J. MAJDA, I. TIMOFEYEV, AND E. V. EIJNDEN, A mathematical framework for stochastic climate models, Comm. Pure Appl. Math., 54 (2001), pp. 891-974.
    • (2001) Comm. Pure Appl. Math , vol.54 , pp. 891-974
    • MAJDA, A.J.1    TIMOFEYEV, I.2    EIJNDEN, E.V.3
  • 29
    • 0037120092 scopus 로고    scopus 로고
    • Coarse-graining in polymer simulation: From the atomistic to the mesoscale and back
    • F. MULLER-PLATHE, Coarse-graining in polymer simulation: From the atomistic to the mesoscale and back, Chem. Phys. Chem., 3 (2002), pp. 754-769.
    • (2002) Chem. Phys. Chem , vol.3 , pp. 754-769
    • MULLER-PLATHE, F.1
  • 31
    • 0000764037 scopus 로고    scopus 로고
    • Dynamics of adatom motion under influence of mutual interactions
    • S. RENISCH, R. SCHUSTER, J. WINTTERLIN, AND G. ERTL, Dynamics of adatom motion under influence of mutual interactions, Phys. Rev. Lett., 82 (1999), pp. 3839-3842.
    • (1999) Phys. Rev. Lett , vol.82 , pp. 3839-3842
    • RENISCH, S.1    SCHUSTER, R.2    WINTTERLIN, J.3    ERTL, G.4
  • 32
    • 0000573002 scopus 로고    scopus 로고
    • A direct approach to conformational dynamics based on hybrid Monte Carlo
    • C. SCHÜTTE, A. FISCHER, W. HUISINGA, AND P. DEUFLHARD, A direct approach to conformational dynamics based on hybrid Monte Carlo, J. Comput. Phys., 151 (1999), pp. 146-168.
    • (1999) J. Comput. Phys , vol.151 , pp. 146-168
    • SCHÜTTE, C.1    FISCHER, A.2    HUISINGA, W.3    DEUFLHARD, P.4
  • 33
    • 0035641113 scopus 로고    scopus 로고
    • Adaptive weak approximation of stochastic differential equations
    • A. SZEPESSY, R. TEMPONE, AND G. E. ZOURARIS, Adaptive weak approximation of stochastic differential equations, Comm. Pure Appl. Math., 54 (2001), pp. 1169-1214.
    • (2001) Comm. Pure Appl. Math , vol.54 , pp. 1169-1214
    • SZEPESSY, A.1    TEMPONE, R.2    ZOURARIS, G.E.3
  • 34
    • 0000124397 scopus 로고
    • Expansion of the global error for numerical schemes solving stochastic differential equations
    • 1991
    • D. TALAY AND L. TUBARO, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Anal. Appl., 8 (1990), pp. 483-509 (1991).
    • (1990) Stochastic Anal. Appl , vol.8 , pp. 483-509
    • TALAY, D.1    TUBARO, L.2
  • 35
    • 0001000232 scopus 로고
    • The effects of phase transitions, surface diffusion, and defects on surface catalyzed reactions: Fluctuations and oscillations
    • D. G. VLACHOS, L. D. SCHMIDT, AND R. ARIS, The effects of phase transitions, surface diffusion, and defects on surface catalyzed reactions: Fluctuations and oscillations, J. Chem. Phys., 93 (1990), pp. 8306-8313.
    • (1990) J. Chem. Phys , vol.93 , pp. 8306-8313
    • VLACHOS, D.G.1    SCHMIDT, L.D.2    ARIS, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.