메뉴 건너뛰기




Volumn 17, Issue 6, 2004, Pages

Extracting macroscopic dynamics: Model problems and algorithms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 3042793188     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/6/R01     Document Type: Article
Times cited : (353)

References (170)
  • 1
    • 0003781238 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press
    • Norris J 1997 Markov Chains (Cambridge: Cambridge University Press)
    • (1997) Markov Chains
    • Norris, J.1
  • 5
    • 19744369999 scopus 로고    scopus 로고
    • Diffusions, Markov processes and martingales
    • Cambridge: Cambridge University Press
    • Rogers L C G and Williams D 2000 Diffusions, Markov processes and martingales Itô Calculus 2nd edn, vol 2 (Cambridge: Cambridge University Press)
    • (2000) Itô Calculus 2nd Edn , vol.2
    • Rogers, L.C.G.1    Williams, D.2
  • 6
    • 0002157780 scopus 로고
    • Elimination of fast variables
    • van Kampen N G 1985 Elimination of fast variables Phys. Rep. 124 69-160
    • (1985) Phys. Rep. , vol.124 , pp. 69-160
    • Van Kampen, N.G.1
  • 7
    • 0009139496 scopus 로고
    • Introduction to the asymptotic analysis of stochastic equations
    • ed R C DiPrima (Providence, RI: AMS)
    • Papanicolaou G C 1974 Introduction to the asymptotic analysis of stochastic equations Modern Modeling of Continuum Phenomena ed R C DiPrima (Providence, RI: AMS)
    • (1974) Modern Modeling of Continuum Phenomena
    • Papanicolaou, G.C.1
  • 9
    • 0009613618 scopus 로고
    • Problems in nonlinear transport theory
    • ed L Garrido (New York: Springer)
    • Zwanzig R 1980 Problems in nonlinear transport theory Systems Far from Equilibrium ed L Garrido (New York: Springer) pp 198-225
    • (1980) Systems Far from Equilibrium , pp. 198-225
    • Zwanzig, R.1
  • 11
    • 0000514837 scopus 로고
    • Transport, collective motion, and Brownian motion
    • Mori H 1965 Transport, collective motion, and Brownian motion Prog. Theor. Phys. 33 423-50
    • (1965) Prog. Theor. Phys. , vol.33 , pp. 423-450
    • Mori, H.1
  • 12
    • 18844402460 scopus 로고
    • Nonlinear generalized Langevin equations
    • Zwanzig R 1973 Nonlinear generalized Langevin equations J. Stat. Phys. 9 215-20
    • (1973) J. Stat. Phys. , vol.9 , pp. 215-220
    • Zwanzig, R.1
  • 15
    • 0032066219 scopus 로고    scopus 로고
    • Stochastic modelling of turbulence and anomalous transport in plasmas
    • Vanden-Eijnden E and Greco A 1998 Stochastic modelling of turbulence and anomalous transport in plasmas J. Plasma Phys. 59 683-94
    • (1998) J. Plasma Phys. , vol.59 , pp. 683-694
    • Vanden-Eijnden, E.1    Greco, A.2
  • 16
    • 0037234415 scopus 로고    scopus 로고
    • Testing approximate closures for turbulent diffusion on some model flows
    • Kramer P R, Majda A J and Vanden-Eijnden E 2003 Testing approximate closures for turbulent diffusion on some model flows J. Stat. Phys. 111 565-679
    • (2003) J. Stat. Phys. , vol.111 , pp. 565-679
    • Kramer, P.R.1    Majda, A.J.2    Vanden-Eijnden, E.3
  • 17
    • 0035918128 scopus 로고    scopus 로고
    • Stochastic modelling: Replacing fast degrees of freedom by noise
    • Just W, Kantz H, Rödenbeck C and Helm M 2001 Stochastic modelling: replacing fast degrees of freedom by noise J. Phys. A: Math. Gen. 34 3199-213
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 3199-3213
    • Just, W.1    Kantz, H.2    Rödenbeck, C.3    Helm, M.4
  • 18
    • 0038065263 scopus 로고    scopus 로고
    • Elimination of fast chaotic degrees of freedom: On the accuracy of the Born approximation
    • Just W, Gelfert K, Baba N, Riegert A and Kantz H 2003 Elimination of fast chaotic degrees of freedom: on the accuracy of the Born approximation J. Stat. Phys. 112 277-92
    • (2003) J. Stat. Phys. , vol.112 , pp. 277-292
    • Just, W.1    Gelfert, K.2    Baba, N.3    Riegert, A.4    Kantz, H.5
  • 20
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rossler O E 1976 An equation for continuous chaos Phys. Lett. 35a 397-8
    • (1976) Phys. Lett. , vol.35 A , pp. 397-398
    • Rossler, O.E.1
  • 25
    • 84971960661 scopus 로고
    • Problems with different time-scale s
    • Cambridge: Cambridge University Press
    • Kreiss H-O 1992 Problems with different time-scale s Acta Numer. (Cambridge: Cambridge University Press)
    • (1992) Acta Numer.
    • Kreiss, H.-O.1
  • 27
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • Providence, RI: AMS
    • Hale J K 1988 Asymptotic behavior of dissipative systems Mathematical Surveys and Monographs vol 25 (Providence, RI: AMS)
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 29
    • 84972564130 scopus 로고
    • Invariant manifolds of nonlinear operators
    • Wells J C 1976 Invariant manifolds of nonlinear operators Pac. J. Math. 62 285-93
    • (1976) Pac. J. Math. , vol.62 , pp. 285-293
    • Wells, J.C.1
  • 30
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel N 1971 Persistence and smoothness of invariant manifolds for flows Indiana Univ. Math. J. 193-226
    • (1971) Indiana Univ. Math. J. , pp. 193-226
    • Fenichel, N.1
  • 31
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel N 1979 Geometric singular perturbation theory for ordinary differential equations J. Diff. Eqns 31 53-98
    • (1979) J. Diff. Eqns , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 32
    • 0002339446 scopus 로고
    • Motion under a strong constraining force
    • Rubin H and Ungar P 1957 Motion under a strong constraining force Commun. Pure Appl. Math. 10 65-87
    • (1957) Commun. Pure Appl. Math. , vol.10 , pp. 65-87
    • Rubin, H.1    Ungar, P.2
  • 33
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • Neistadt A I 1984 The separation of motions in systems with rapidly rotating phase J. Appl. Math. Mech. 48 511-17
    • (1984) J. Appl. Math. Mech. , vol.48 , pp. 511-517
    • Neistadt, A.I.1
  • 34
    • 0011406472 scopus 로고
    • Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory: Part I
    • Bennetin G, Galgani L and Giorgilli A 1987 Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory: Part I Commun. Math. Phys. 113 87-103
    • (1987) Commun. Math. Phys. , vol.113 , pp. 87-103
    • Bennetin, G.1    Galgani, L.2    Giorgilli, A.3
  • 36
    • 0002658505 scopus 로고    scopus 로고
    • Homogenization of Hamiltonian systems with a strong constraining potential
    • Bornemann F A and Schütte Ch 1997 Homogenization of Hamiltonian systems with a strong constraining potential Physica D 102 57-77
    • (1997) Physica D , vol.102 , pp. 57-77
    • Bornemann, F.A.1    Schütte, Ch.2
  • 38
    • 0007015972 scopus 로고
    • Motion under the influence of a strong constraining force
    • Evanston, 1979 ed Z Nitecki and C Robinson (Berlin: Springer)
    • Takens F 1980 Motion under the influence of a strong constraining force Global Theory of Dynamical Systems (Evanston, 1979) ed Z Nitecki and C Robinson (Berlin: Springer)
    • (1980) Global Theory of Dynamical Systems
    • Takens, F.1
  • 42
    • 9644296375 scopus 로고    scopus 로고
    • Slow manifolds
    • ed T Dauxois et al (Singapore: World Scientific)
    • MacKay R S 2003 Slow manifolds Energy Localisation and Transfer ed T Dauxois et al (Singapore: World Scientific)
    • (2003) Energy Localisation and Transfer
    • MacKay, R.S.1
  • 43
    • 0009996169 scopus 로고
    • Some probabilistic problems and methods in singular perturbations
    • Papanicolaou G C 1976 Some probabilistic problems and methods in singular perturbations Rocky Mtn. J. Math. 6 653-73
    • (1976) Rocky Mtn. J. Math. , vol.6 , pp. 653-673
    • Papanicolaou, G.C.1
  • 44
    • 0012991938 scopus 로고
    • Averaging in dynamical systems and large deviations
    • Kifer Y 1992 Averaging in dynamical systems and large deviations Invent. Math. 110 337-70
    • (1992) Invent. Math. , vol.110 , pp. 337-370
    • Kifer, Y.1
  • 45
    • 84976088163 scopus 로고
    • Limit theorems for averaging in dynamical systems
    • Kifer Y 1995 Limit theorems for averaging in dynamical systems Ergod. Theory Dynam. Sys. 15 1143-72
    • (1995) Ergod. Theory Dynam. Sys. , vol.15 , pp. 1143-1172
    • Kifer, Y.1
  • 46
    • 2942629833 scopus 로고    scopus 로고
    • Averaging and climate models
    • Kifer Y 2001 Averaging and climate models Prog. Prob. 49 171-88
    • (2001) Prog. Prob. , vol.49 , pp. 171-188
    • Kifer, Y.1
  • 47
    • 0347544115 scopus 로고    scopus 로고
    • Stochastic versions of Anosov's and Neistadt's theorems on averaging
    • Kifer Y 2001 Stochastic versions of Anosov's and Neistadt's theorems on averaging Stochast. Dynam. 1 1-21
    • (2001) Stochast. Dynam. , vol.1 , pp. 1-21
    • Kifer, Y.1
  • 48
    • 9644282182 scopus 로고    scopus 로고
    • On singularly perturbed ordinary differential equations with measure-valued limits
    • Artstein Z 2002 On singularly perturbed ordinary differential equations with measure-valued limits Math. Bohem. 127 139-52
    • (2002) Math. Bohem. , vol.127 , pp. 139-152
    • Artstein, Z.1
  • 49
    • 0035917081 scopus 로고    scopus 로고
    • On singularly perturbed retarded functional differential equations
    • Artstein Z and Slemrod M 2001 On singularly perturbed retarded functional differential equations J. Diff. Eqns 171 88-109
    • (2001) J. Diff. Eqns , vol.171 , pp. 88-109
    • Artstein, Z.1    Slemrod, M.2
  • 50
    • 0012227045 scopus 로고    scopus 로고
    • Singularly perturbed ordinary differential equations with dynamic limits
    • Artstein Z and Vigodner A 1996 Singularly perturbed ordinary differential equations with dynamic limits Proc. R. Soc. Edinb. 126A 541-69
    • (1996) Proc. R. Soc. Edinb. , vol.126 A , pp. 541-569
    • Artstein, Z.1    Vigodner, A.2
  • 51
    • 0002546882 scopus 로고
    • A limit theorem for perturbed operator semigroups with applications to random evolutions
    • Kurtz T G 1973 A limit theorem for perturbed operator semigroups with applications to random evolutions J. Fund. Anal. 12 55-67
    • (1973) J. Fund. Anal. , vol.12 , pp. 55-67
    • Kurtz, T.G.1
  • 54
    • 84980152442 scopus 로고
    • Asymptotic theory of mixing stochastic ordinary differential equations
    • Papanicolaou G C and Kohler W 1974 Asymptotic theory of mixing stochastic ordinary differential equations Commun. Pure Appl. Math XXVII 641-68
    • (1974) Commun. Pure Appl. Math , vol.27 , pp. 641-668
    • Papanicolaou, G.C.1    Kohler, W.2
  • 56
    • 0033751055 scopus 로고    scopus 로고
    • Remarkable statistical behavior for truncated Burgers-Hopf dynamics
    • Majda A and Timofeyev I 2000 Remarkable statistical behavior for truncated Burgers-Hopf dynamics Proc. Natl Acad. Sci. USA 97 12413-17
    • (2000) Proc. Natl Acad. Sci. USA , vol.97 , pp. 12413-12417
    • Majda, A.1    Timofeyev, I.2
  • 57
    • 85128824735 scopus 로고    scopus 로고
    • Numerical techniques for multi-scale dynamical systems with stochastic effects
    • Vanden-Eijnden E 2003 Numerical techniques for multi-scale dynamical systems with stochastic effects Commun. Math. Sci. 1 377-84
    • (2003) Commun. Math. Sci. , vol.1 , pp. 377-384
    • Vanden-Eijnden, E.1
  • 59
    • 0043127074 scopus 로고    scopus 로고
    • Systematic strategies for stochastic mode reduction in climate
    • Majda A J, Timofeyev I and Vanden-Eijnden E 2003 Systematic strategies for stochastic mode reduction in climate J. Atmos. Sci. 60 1705-22
    • (2003) J. Atmos. Sci. , vol.60 , pp. 1705-1722
    • Majda, A.J.1    Timofeyev, I.2    Vanden-Eijnden, E.3
  • 60
    • 0001007175 scopus 로고
    • Brownian motion from deterministic dynamics
    • Beck C 1990 Brownian motion from deterministic dynamics Physica A 169 324-36
    • (1990) Physica A , vol.169 , pp. 324-336
    • Beck, C.1
  • 61
    • 0037105977 scopus 로고    scopus 로고
    • A priori tests of a stochastic mode reduction strategy
    • Majda A J, Timofeyev I and Vanden-Eijnden E 2002 A priori tests of a stochastic mode reduction strategy Physica D 170 206-52
    • (2002) Physica D , vol.170 , pp. 206-252
    • Majda, A.J.1    Timofeyev, I.2    Vanden-Eijnden, E.3
  • 62
    • 9644284959 scopus 로고    scopus 로고
    • White noise limits for discrete dynamical systems driven by fast deterministic dynamics
    • submitted
    • Givon D and Kupferman R 2003 White noise limits for discrete dynamical systems driven by fast deterministic dynamics Physica A submitted
    • (2003) Physica A
    • Givon, D.1    Kupferman, R.2
  • 63
    • 84980168193 scopus 로고
    • A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations
    • Papanicolaou G C and Varadhan S R S 1973 A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations Commun. Pure Appl. Math. XXVI 497-524
    • (1973) Commun. Pure Appl. Math. , vol.26 , pp. 497-524
    • Papanicolaou, G.C.1    Varadhan, S.R.S.2
  • 64
    • 0040152018 scopus 로고
    • Principle of averaging for parabolic and elliptic differential equations and for Markov processes with small diffusion
    • Khasminskii R Z 1963 Principle of averaging for parabolic and elliptic differential equations and for Markov processes with small diffusion Theory. Probab. Appl. 8 1-21
    • (1963) Theory. Probab. Appl. , vol.8 , pp. 1-21
    • Khasminskii, R.Z.1
  • 65
    • 0001761644 scopus 로고
    • A limit theorem for the solutions of differential equations with random right-handed sides
    • Khasminskii R Z 1966 A limit theorem for the solutions of differential equations with random right-handed sides Theory. Probab. Appl 11 390-406
    • (1966) Theory. Probab. Appl , vol.11 , pp. 390-406
    • Khasminskii, R.Z.1
  • 68
    • 0347975177 scopus 로고    scopus 로고
    • Long term behaviour of large mechanical systems with random initial data
    • Kupferman R, Stuart A M, Terry J R and Tupper P F 2002 Long term behaviour of large mechanical systems with random initial data Stochast. Dynam. 2 533-62
    • (2002) Stochast. Dynam. , vol.2 , pp. 533-562
    • Kupferman, R.1    Stuart, A.M.2    Terry, J.R.3    Tupper, P.F.4
  • 70
    • 0742328687 scopus 로고
    • Introduction to the theory of diffusion processes
    • Providence, RI: AMS
    • Krylov N V 1995 Introduction to the theory of diffusion processes AMS Translation of Monographs vol 142 (Providence, RI: AMS)
    • (1995) AMS Translation of Monographs , vol.142
    • Krylov, N.V.1
  • 72
    • 0000309970 scopus 로고
    • On the quantum Langevin equation
    • Ford G W and Kac M 1987 On the quantum Langevin equation J. Stat. Phys. 46 803-10
    • (1987) J. Stat. Phys. , vol.46 , pp. 803-810
    • Ford, G.W.1    Kac, M.2
  • 73
    • 6144273098 scopus 로고
    • Statistical mechanics of assemblies of coupled oscillators
    • Ford G W, Kac M and Mazur P 1965 Statistical mechanics of assemblies of coupled oscillators J. Math. Phys. 6504-15
    • (1965) J. Math. Phys. , pp. 6504-6515
    • Ford, G.W.1    Kac, M.2    Mazur, P.3
  • 74
    • 0033235604 scopus 로고    scopus 로고
    • Analysis and experiments for a computational model of a heat bath
    • Stuart A M and Warren J O 1999 Analysis and experiments for a computational model of a heat bath J. Stat. Phys. 97 687-723
    • (1999) J. Stat. Phys. , vol.97 , pp. 687-723
    • Stuart, A.M.1    Warren, J.O.2
  • 75
    • 0000996303 scopus 로고
    • Ergodic properties and quasideterministic properties of finite-dimensional stochastic systems
    • Tropper M M 1977 Ergodic properties and quasideterministic properties of finite-dimensional stochastic systems J. Stat. Phys. 17 491-509
    • (1977) J. Stat. Phys. , vol.17 , pp. 491-509
    • Tropper, M.M.1
  • 77
    • 0002011027 scopus 로고    scopus 로고
    • Ergodic properties of the non-Markovian Langevin equation
    • Jakšić V and Pillet C-A 1997 Ergodic properties of the non-Markovian Langevin equation Lett. Math. Phys. 41 49-57
    • (1997) Lett. Math. Phys. , vol.41 , pp. 49-57
    • Jakšić, V.1    Pillet, C.-A.2
  • 78
    • 0001724227 scopus 로고    scopus 로고
    • Linear response of Hamiltonian chaotic systems as a function of the number of degrees of freedom
    • Bianucci M and Mannella R 1996 Linear response of Hamiltonian chaotic systems as a function of the number of degrees of freedom Phys. Rev. Lett. 77 1258-61
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 1258-1261
    • Bianucci, M.1    Mannella, R.2
  • 79
    • 49149137092 scopus 로고
    • Dissipative contributions of internal multiplicative noise: I. Mechanical oscillator
    • Lindenberg K and Seshadri V 1981 Dissipative contributions of internal multiplicative noise: I. Mechanical oscillator Physica A 109 483-99
    • (1981) Physica A , vol.109 , pp. 483-499
    • Lindenberg, K.1    Seshadri, V.2
  • 80
    • 10644231733 scopus 로고    scopus 로고
    • Fitting SDE models to nonlinear Kac-Zwanzig heat bath models
    • in press
    • Kupferman R and Stuart A M 2004 Fitting SDE models to nonlinear Kac-Zwanzig heat bath models Physica D in press
    • (2004) Physica D
    • Kupferman, R.1    Stuart, A.M.2
  • 81
    • 0036112005 scopus 로고    scopus 로고
    • Asymptotic and numerical analyses for mechanical models of heat baths
    • Hald O H and Kupferman R 2002 Asymptotic and numerical analyses for mechanical models of heat baths J. Stat. Phys. 106 1121-84
    • (2002) J. Stat. Phys. , vol.106 , pp. 1121-1184
    • Hald, O.H.1    Kupferman, R.2
  • 82
    • 0347975171 scopus 로고    scopus 로고
    • Fractional kinetics in Kac-Zwanzig heat bath models
    • Kupferman R 2004 Fractional kinetics in Kac-Zwanzig heat bath models J. Stat. Phys. 114 291-326
    • (2004) J. Stat. Phys. , vol.114 , pp. 291-326
    • Kupferman, R.1
  • 83
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • Gillespie D T 1976 A general method for numerically simulating the stochastic time evolution of coupled chemical reactions J. Comput. Phys. 22 403-34
    • (1976) J. Comput. Phys. , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 84
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • Gillespie D T 1977 Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 2340-61
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 85
    • 0003010776 scopus 로고
    • Limit theorems and diffusion approximations for density dependent Markov chains
    • Kurtz T G 1976 Limit theorems and diffusion approximations for density dependent Markov chains Math. Prog. Stud. 5 67
    • (1976) Math. Prog. Stud. , vol.5 , pp. 67
    • Kurtz, T.G.1
  • 86
    • 0000660738 scopus 로고
    • Strong approximation theorems for density dependent Markov chains
    • Kurtz T G 1978 Strong approximation theorems for density dependent Markov chains Stochast. Proc. Appl. 6 223
    • (1978) Stochast. Proc. Appl. , vol.6 , pp. 223
    • Kurtz, T.G.1
  • 87
    • 22244490538 scopus 로고
    • Amplification of intrinsic fluctuations by chaotic dynamics in physical systems
    • Fox R F and Keizer J 1991 Amplification of intrinsic fluctuations by chaotic dynamics in physical systems Phys. Rev. A 43 1709-20
    • (1991) Phys. Rev. A , vol.43 , pp. 1709-1720
    • Fox, R.F.1    Keizer, J.2
  • 88
    • 0037131136 scopus 로고    scopus 로고
    • Fluctuations in the lattice gas for Burgers' equation
    • Haselwandter C and Vvedensky D 2002 Fluctuations in the lattice gas for Burgers' equation J. Phys. A: Math. Gen. 35 579-84
    • (2002) J. Phys. A: Math. Gen. , vol.35 , pp. 579-584
    • Haselwandter, C.1    Vvedensky, D.2
  • 91
    • 0030555032 scopus 로고    scopus 로고
    • Kinetic limits for a class of interacting particle systems
    • Rezakhanlou F 1996 Kinetic limits for a class of interacting particle systems Probab. Theory Rel. Fields 104 97-146
    • (1996) Probab. Theory Rel. Fields , vol.104 , pp. 97-146
    • Rezakhanlou, F.1
  • 93
    • 0034370539 scopus 로고    scopus 로고
    • Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains
    • Deuflhard P, Huisinga W, Fischer W and Schütte C 2000 Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains Linear Algebra Appl. 315 39-59
    • (2000) Linear Algebra Appl. , vol.315 , pp. 39-59
    • Deuflhard, P.1    Huisinga, W.2    Fischer, W.3    Schütte, C.4
  • 96
    • 21844517225 scopus 로고
    • Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type: I. RK methods
    • Nipp K and Stoffer D 1995 Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type: I. RK methods Numer. Math. 70 245-57
    • (1995) Numer. Math. , vol.70 , pp. 245-257
    • Nipp, K.1    Stoffer, D.2
  • 97
    • 0030516571 scopus 로고    scopus 로고
    • Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type: D. Linear multistep methods
    • Nipp K and Stoffer D 1996 Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type: D. Linear multistep methods Numer. Math. 74 305-23
    • (1996) Numer. Math. , vol.74 , pp. 305-323
    • Nipp, K.1    Stoffer, D.2
  • 98
    • 0040174368 scopus 로고
    • Attractive invariant manifolds for maps: Existence, smoothness and continuous dependence on the map
    • SAM, ETH, Zurich
    • Nipp K and Stoffer D 1992 Attractive invariant manifolds for maps: existence, smoothness and continuous dependence on the map Research Report 92-11, SAM, ETH, Zurich
    • (1992) Research Report 92-11 , vol.92 , Issue.11
    • Nipp, K.1    Stoffer, D.2
  • 103
    • 0041428215 scopus 로고    scopus 로고
    • Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum
    • Gear C W and Kevrekidis I G 2003 Projective methods for stiff differential equations: problems with gaps in their eigenvalue spectrum SIAM J. Sci. Comput. 24 1091-106
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1091-1106
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 104
    • 9644276018 scopus 로고    scopus 로고
    • Analysis of heterogeneous multiscale method for ordinary differential equations
    • at press
    • E W 2003 Analysis of heterogeneous multiscale method for ordinary differential equations Commun. Math. Sci. at press
    • (2003) Commun. Math. Sci.
    • W, E.1
  • 105
    • 9644282184 scopus 로고    scopus 로고
    • Analysis of numerical techniques for multiscale stochastic dynamical systems
    • at press
    • E W, Liu D and Vanden-Eijnden E 2004 Analysis of numerical techniques for multiscale stochastic dynamical systems Commun. Pure Appl. Math. at press
    • (2004) Commun. Pure Appl. Math.
    • W, E.1    Liu, D.2    Vanden-Eijnden, E.3
  • 106
    • 0028407615 scopus 로고
    • The csp method for simplifying kinetics
    • Lam S and Goussis D 1994 The csp method for simplifying kinetics Int. J. Chem. Kin. 26 461-86
    • (1994) Int. J. Chem. Kin. , vol.26 , pp. 461-486
    • Lam, S.1    Goussis, D.2
  • 107
    • 0026833045 scopus 로고
    • Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space
    • Maas U and Pope S B 1992 Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space Combust. Flame 88 239-64
    • (1992) Combust. Flame , vol.88 , pp. 239-264
    • Maas, U.1    Pope, S.B.2
  • 109
    • 34047228827 scopus 로고
    • Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
    • Kevrekidis I G, Jolly M S and Titi E S 1990 Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations Physica D 44 38-60
    • (1990) Physica D , vol.44 , pp. 38-60
    • Kevrekidis, I.G.1    Jolly, M.S.2    Titi, E.S.3
  • 110
    • 84968484137 scopus 로고
    • On the rate of convergence of the nonlinear Galerkin methods
    • Devulder C, Marion M and Titi E S 1993 On the rate of convergence of the nonlinear Galerkin methods Math. Comput. 60 495-514
    • (1993) Math. Comput. , vol.60 , pp. 495-514
    • Devulder, C.1    Marion, M.2    Titi, E.S.3
  • 111
    • 0036845619 scopus 로고    scopus 로고
    • Postprocessing Fourier spectral methods: The case of smooth solutions
    • Garcia-Archilla B, Novo J and Titi E S 2002 Postprocessing Fourier spectral methods: the case of smooth solutions Appl. Numer. Math. 43 191-209
    • (2002) Appl. Numer. Math. , vol.43 , pp. 191-209
    • Garcia-Archilla, B.1    Novo, J.2    Titi, E.S.3
  • 112
    • 85011452049 scopus 로고    scopus 로고
    • Numerical solution of highly oscillatory ordinary differential equations
    • Petzold L, Jay L O and Yen J 1997 Numerical solution of highly oscillatory ordinary differential equations Acta Numer. 6 437-83
    • (1997) Acta Numer. , vol.6 , pp. 437-483
    • Petzold, L.1    Jay, L.O.2    Yen, J.3
  • 113
    • 0032226405 scopus 로고    scopus 로고
    • Long-time-step methods for oscillatory differential equations
    • Archilla B Garcia, Serna J M Sanz and Skeel R D 1998 Long-time-step methods for oscillatory differential equations SIAM J. Sci. Comput. 20 930-63
    • (1998) SIAM J. Sci. Comput. , vol.20 , pp. 930-963
    • Garcia, A.B.1    Sanz, S.J.M.2    Skeel, R.D.3
  • 114
    • 0039585582 scopus 로고
    • On the application of invariant manifold theory, in particular to numerical analysis
    • Basel: Birkhauser
    • Kirchgraber U, Lasagni F, Nipp K and Stoffer D 1991 On the application of invariant manifold theory, in particular to numerical analysis Int. Ser. Numer. Math. vol 97 (Basel: Birkhauser) pp 189-97
    • (1991) Int. Ser. Numer. Math. , vol.97 , pp. 189-197
    • Kirchgraber, U.1    Lasagni, F.2    Nipp, K.3    Stoffer, D.4
  • 117
    • 9644292166 scopus 로고    scopus 로고
    • Ergodicity and numerical simulation
    • in press
    • Tupper P F 2004 Ergodicity and numerical simulation SIAM J. Numer. Anal. in press
    • (2004) SIAM J. Numer. Anal.
    • Tupper, P.F.1
  • 118
    • 85128805678 scopus 로고    scopus 로고
    • The heterogenous multiscale method
    • E W and Engquist B 2003 The heterogenous multiscale method Commun. Math. Sci. 1 87-132
    • (2003) Commun. Math. Sci. , vol.1 , pp. 87-132
    • W, E.1    Engquist, B.2
  • 119
    • 0033293798 scopus 로고    scopus 로고
    • The midpoint scheme and variants for Hamiltonian systems: Advantages and pitfalls
    • Ascher U and Reich S 1999 The midpoint scheme and variants for Hamiltonian systems: advantages and pitfalls SIAM J. Sci. Comput. 21 1045-65
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 1045-1065
    • Ascher, U.1    Reich, S.2
  • 120
  • 121
    • 0034612230 scopus 로고    scopus 로고
    • Optimal prediction of stiff oscillatory mechanics
    • Kast A P 2000 Optimal prediction of stiff oscillatory mechanics Proc. Natl Acad. Sci. USA 97 6253-7
    • (2000) Proc. Natl Acad. Sci. USA , vol.97 , pp. 6253-6257
    • Kast, A.P.1
  • 122
    • 25844453508 scopus 로고    scopus 로고
    • A test problem for molecular dynamics integrators
    • in press
    • Tupper P F 2004 A test problem for molecular dynamics integrators IMA J. Numer. Anal. in press
    • (2004) IMA J. Numer. Anal.
    • Tupper, P.F.1
  • 123
    • 0032764305 scopus 로고    scopus 로고
    • Data assimilation into nonlinear stochastic models
    • Miller R N, Carter E F and Blue S T 1999 Data assimilation into nonlinear stochastic models Tellus 51A 167-94
    • (1999) Tellus , vol.51 A , pp. 167-194
    • Miller, R.N.1    Carter, E.F.2    Blue, S.T.3
  • 124
    • 0000561678 scopus 로고
    • Molecular dynamics of conformational substates for a simplified protein model
    • Grubmüller H and Tavan P 1994 Molecular dynamics of conformational substates for a simplified protein model J. Chem. Phys. 101 5047-57
    • (1994) J. Chem. Phys. , vol.101 , pp. 5047-5057
    • Grubmüller, H.1    Tavan, P.2
  • 126
    • 9644277442 scopus 로고    scopus 로고
    • Parameter estimation for partially observed hypo-elliptic diffusions
    • submitted
    • Pokern Y, Stuart A M and Wiberg P 2003 Parameter estimation for partially observed hypo-elliptic diffusions J. R. Stat. Soc. Ser. B submitted
    • (2003) J. R. Stat. Soc. Ser. B
    • Pokern, Y.1    Stuart, A.M.2    Wiberg, P.3
  • 128
    • 0003159177 scopus 로고
    • Numerical Navier-Stokes solutions from gas kinetic theory
    • Xu K and Prendergast K H 1994 Numerical Navier-Stokes solutions from gas kinetic theory J. Comput. Phys. 114 9-17
    • (1994) J. Comput. Phys. , vol.114 , pp. 9-17
    • Xu, K.1    Prendergast, K.H.2
  • 130
    • 0000896840 scopus 로고    scopus 로고
    • Optimal prediction for Hamiltonian partial differential equations
    • Chorin A J, Kupferman R and Levy D 2000 Optimal prediction for Hamiltonian partial differential equations J. Comput. Phys. 162 267-97
    • (2000) J. Comput. Phys. , vol.162 , pp. 267-297
    • Chorin, A.J.1    Kupferman, R.2    Levy, D.3
  • 131
    • 0034724367 scopus 로고    scopus 로고
    • Optimal prediction and the Mori-Zwanzig representation of irreversible processes
    • Chorin A J, Hald O H and Kupferman R 2000 Optimal prediction and the Mori-Zwanzig representation of irreversible processes Proc. Natl Acad. Sci. USA 97 2968-73
    • (2000) Proc. Natl Acad. Sci. USA , vol.97 , pp. 2968-2973
    • Chorin, A.J.1    Hald, O.H.2    Kupferman, R.3
  • 132
    • 0033609018 scopus 로고    scopus 로고
    • Optimal prediction of the Klein-Cordon equation
    • Hald O H 1999 Optimal prediction of the Klein-Cordon equation Proc. Natl Acad. Sci. USA 96 4774-9
    • (1999) Proc. Natl Acad. Sci. USA , vol.96 , pp. 4774-4779
    • Hald, O.H.1
  • 133
    • 0009596680 scopus 로고    scopus 로고
    • Stochastic optimal prediction with application to averaged Euler equations
    • ed C A Lin Taiwan: Pingtung
    • Bell J, Chorin A J and Crutchfield W 2000 Stochastic optimal prediction with application to averaged Euler equations ed C A Lin Proc. 7th Natl Conf. on Computer Fluid Mech. (Taiwan: Pingtung) pp 1-13
    • (2000) Proc. 7th Natl Conf. on Computer Fluid Mech. , pp. 1-13
    • Bell, J.1    Chorin, A.J.2    Crutchfield, W.3
  • 134
    • 0037162264 scopus 로고    scopus 로고
    • 'Coarse' stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples
    • Makeev A, Maroudas D and Kevrekidis Y 2002 'Coarse' stability and bifurcation analysis using stochastic simulators: kinetic Monte Carlo examples J. Chem. Phys. 116 10083-91
    • (2002) J. Chem. Phys. , vol.116 , pp. 10083-10091
    • Makeev, A.1    Maroudas, D.2    Kevrekidis, Y.3
  • 136
    • 0029196548 scopus 로고
    • Topological feature maps with self-organized lateral connections: A population coded, one-layer model of associative memory
    • Hillermeier C, Kunstmann N, Rabus B and Tavan P 1994 Topological feature maps with self-organized lateral connections: a population coded, one-layer model of associative memory Biol. Cyber. 72 103-17
    • (1994) Biol. Cyber. , vol.72 , pp. 103-117
    • Hillermeier, C.1    Kunstmann, N.2    Rabus, B.3    Tavan, P.4
  • 137
    • 0034730149 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using timesteppers: A reaction diffusion example
    • Theodoropoulos K, Qian Y-H and Kevrekidis I G 2000 Coarse stability and bifurcation analysis using timesteppers: a reaction diffusion example Proc. Natl Acad. Sci. 97 9840-3
    • (2000) Proc. Natl Acad. Sci. , vol.97 , pp. 9840-9843
    • Theodoropoulos, K.1    Qian, Y.-H.2    Kevrekidis, I.G.3
  • 138
    • 0037044961 scopus 로고    scopus 로고
    • Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice gas model with lateral interactions
    • Makeev A G, Maroudas D, Panagiotopoulos A Z and Kevrekidis I G 2002 Coarse bifurcation analysis of kinetic Monte Carlo simulations: a lattice gas model with lateral interactions J. Chem. Phys. 117 8229-40
    • (2002) J. Chem. Phys. , vol.117 , pp. 8229-8240
    • Makeev, A.G.1    Maroudas, D.2    Panagiotopoulos, A.Z.3    Kevrekidis, I.G.4
  • 139
    • 9644288535 scopus 로고    scopus 로고
    • Coarse molecular dynamics of a peptide fragment: Free energy, kinetics and long time dynamics computations
    • submitted
    • Hummer G and Kevrekidis I G 2002 Coarse molecular dynamics of a peptide fragment: free energy, kinetics and long time dynamics computations J. Chem. Phys. submitted
    • (2002) J. Chem. Phys.
    • Hummer, G.1    Kevrekidis, I.G.2
  • 141
    • 0037104864 scopus 로고    scopus 로고
    • 'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods
    • Gear C W, Kevrekidis I G and Theodoropoulos C 2002 'Coarse' integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods Comput. Chem. Engng. 26 941-63
    • (2002) Comput. Chem. Engng. , vol.26 , pp. 941-963
    • Gear, C.W.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 142
    • 84905018295 scopus 로고    scopus 로고
    • An adaptive subdivision technique for the approximation of attractors and invariant measures
    • Dellnitz M and Junge O 1998 An adaptive subdivision technique for the approximation of attractors and invariant measures Comput. Vis. Sci. 1 63-8
    • (1998) Comput. Vis. Sci. , vol.1 , pp. 63-68
    • Dellnitz, M.1    Junge, O.2
  • 143
    • 0000371241 scopus 로고    scopus 로고
    • On the approximation of complicated dynamical behaviour
    • Dellnitz M and Junge O 1999 On the approximation of complicated dynamical behaviour SIAM J. Numer. Anal. 36 491-515
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 491-515
    • Dellnitz, M.1    Junge, O.2
  • 145
    • 0000573002 scopus 로고    scopus 로고
    • A direct approach to conformational dynamics based on hybrid Monte Carlo
    • Schütte C, Fischer A, Huisinga W and Deuflhard P 1999 A direct approach to conformational dynamics based on hybrid Monte Carlo J. Comput. Phys. 151 146-68
    • (1999) J. Comput. Phys. , vol.151 , pp. 146-168
    • Schütte, C.1    Fischer, A.2    Huisinga, W.3    Deuflhard, P.4
  • 146
    • 0035086606 scopus 로고    scopus 로고
    • A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamics parameterization in weather and climate prediction models
    • Palmer T N 2001 A nonlinear dynamical perspective on model error: a proposal for non-local stochastic-dynamics parameterization in weather and climate prediction models Quart. J. Met. Soc. 572 279-304
    • (2001) Quart. J. Met. Soc. , vol.572 , pp. 279-304
    • Palmer, T.N.1
  • 147
    • 0003851376 scopus 로고    scopus 로고
    • Coherent structures, dynamical systems and symmetry
    • Cambridge: Cambridge University Press
    • Berkooz G, Holmes P and Lumley J 1996 Coherent structures, dynamical systems and symmetry Cambridge Monograph on Mechanics (Cambridge: Cambridge University Press)
    • (1996) Cambridge Monograph on Mechanics
    • Berkooz, G.1    Holmes, P.2    Lumley, J.3
  • 148
    • 0001739371 scopus 로고
    • Low dimensional description of complicated phenomena, in connection between finite and infinity dimensional flows
    • Sirovich L and Sirovich C H 1989 Low dimensional description of complicated phenomena, in connection between finite and infinity dimensional flows Cont. Math. 99 277-305
    • (1989) Cont. Math. , vol.99 , pp. 277-305
    • Sirovich, L.1    Sirovich, C.H.2
  • 150
    • 9644259697 scopus 로고    scopus 로고
    • Computation of large scale quadratic forms and transfer functions using the theory of moments, quadrature and Pade approximation
    • ed A Bourlioux and M J Gander (Dordrecht: Kluwer)
    • Bai Z and Golub G 2002 Computation of large scale quadratic forms and transfer functions using the theory of moments, quadrature and Pade approximation Modern Methods in Scientific Computing and Applications (NATO Science Series) ed A Bourlioux and M J Gander (Dordrecht: Kluwer)
    • (2002) Modern Methods in Scientific Computing and Applications (NATO Science Series)
    • Bai, Z.1    Golub, G.2
  • 151
    • 0000658386 scopus 로고    scopus 로고
    • Reduced-order modelling techniques based on Krylov subspaces and their use in circuit simulation
    • Freund R W 1999 Reduced-order modelling techniques based on Krylov subspaces and their use in circuit simulation Appl. Comput. Control Signals Circuits 1 435-98
    • (1999) Appl. Comput. Control Signals Circuits , vol.1 , pp. 435-498
    • Freund, R.W.1
  • 152
    • 0010011201 scopus 로고    scopus 로고
    • A survey of model reduction methods for large scale systems
    • Providence, RI: AMS
    • Antoulas A C, Sorensen D C and Gugerrin S 2001 A survey of model reduction methods for large scale systems Contemp. Math. (Providence, RI: AMS)
    • (2001) Contemp. Math.
    • Antoulas, A.C.1    Sorensen, D.C.2    Gugerrin, S.3
  • 153
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods
    • Hughes T J R 1995 Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Eng. 127 387-401
    • (1995) Comput. Methods Appl. Mech. Eng. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 154
    • 0000713961 scopus 로고    scopus 로고
    • Convergence of a nonconformal multiscale finite element method
    • Efendiev Y R, Hou T Y and Wu X H 2000 Convergence of a nonconformal multiscale finite element method SIAM J. Numer. Anal. 37 888-910
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 888-910
    • Efendiev, Y.R.1    Hou, T.Y.2    Wu, X.H.3
  • 156
    • 0041691233 scopus 로고    scopus 로고
    • Averaging and renormalization for the KdV-Burgers equation
    • Chorin A J 2003 Averaging and renormalization for the KdV-Burgers equation Proc. Natl Acad. Sci. USA 100 9674-9
    • (2003) Proc. Natl Acad. Sci. USA , vol.100 , pp. 9674-9679
    • Chorin, A.J.1
  • 157
    • 21744452904 scopus 로고
    • Coupling of protein motion to electron transfer in a photosynthetic reaction center: Investigating the low temperature behaviour in the framework of the spin-boson model
    • Xu D and Schulten K 1994 Coupling of protein motion to electron transfer in a photosynthetic reaction center: investigating the low temperature behaviour in the framework of the spin-boson model Chem. Phys. 182 91-117
    • (1994) Chem. Phys. , vol.182 , pp. 91-117
    • Xu, D.1    Schulten, K.2
  • 158
    • 9644274562 scopus 로고
    • Curve crossing in a protein: Coupling of the elementary quantum process to motions of the protein
    • ed D Bicout and M J Field (Berlin: Springer)
    • Schulten K 1995 Curve crossing in a protein: coupling of the elementary quantum process to motions of the protein Proc. Ecole de Physique des Hauches ed D Bicout and M J Field (Berlin: Springer) pp 85-118
    • (1995) Proc. Ecole de Physique des Hauches , pp. 85-118
    • Schulten, K.1
  • 159
    • 41349092888 scopus 로고    scopus 로고
    • Excitons in a photosynthetic light-harvesting system: A combined molecular dynamics, quantum chemistry and polaron model study
    • Damjanovic A, Kosztin I, Kleinekathoefer U and Schulten K 2002 Excitons in a photosynthetic light-harvesting system: a combined molecular dynamics, quantum chemistry and polaron model study Phys. Rev. E 65 031919
    • (2002) Phys. Rev. E , vol.65 , pp. 031919
    • Damjanovic, A.1    Kosztin, I.2    Kleinekathoefer, U.3    Schulten, K.4
  • 161
    • 0016273821 scopus 로고
    • Classical statistical mechanics of constraints: A theorem and application to polymers
    • Fixman M 1974 Classical statistical mechanics of constraints: a theorem and application to polymers Proc. Natl Acad. Sci. USA 71 3050-3
    • (1974) Proc. Natl Acad. Sci. USA , vol.71 , pp. 3050-3053
    • Fixman, M.1
  • 162
    • 0001787214 scopus 로고
    • Smoothed dynamics of highly oscillatory Hamiltonian systems
    • Reich S 1995 Smoothed dynamics of highly oscillatory Hamiltonian systems Physica D 89 28-42
    • (1995) Physica D , vol.89 , pp. 28-42
    • Reich, S.1
  • 163
    • 0346057215 scopus 로고    scopus 로고
    • Smoothed Langevin dynamics of highly oscillatory systems
    • Reich S 2000 Smoothed Langevin dynamics of highly oscillatory systems Physica D 138 210-24
    • (2000) Physica D , vol.138 , pp. 210-224
    • Reich, S.1
  • 164
    • 0001259264 scopus 로고    scopus 로고
    • Coarse-grained molecular dynamics and the atomic limit of finite elements
    • Rudd R E and Broughton J Q 1998 Coarse-grained molecular dynamics and the atomic limit of finite elements Phys. Rev. B 58 R5893-6
    • (1998) Phys. Rev. B , vol.58
    • Rudd, R.E.1    Broughton, J.Q.2
  • 165
    • 42749099174 scopus 로고    scopus 로고
    • Matching conditions in atomistic-continuum modeling of materials
    • E W and Huang Z 2001 Matching conditions in atomistic-continuum modeling of materials Phys. Rev. Lett. 87
    • (2001) Phys. Rev. Lett. , vol.87
    • Huang, Z.1
  • 168
    • 0037086274 scopus 로고    scopus 로고
    • Theory of phase separation kinetics in polymer-liquid crystal systems
    • Muratov C and E W 2002 Theory of phase separation kinetics in polymer-liquid crystal systems J. Chem. Phys. 116 4723
    • (2002) J. Chem. Phys. , vol.116 , pp. 4723
    • Muratov, C.1    W, E.2
  • 170
    • 12144286593 scopus 로고    scopus 로고
    • Existence of solution for a micro-macro model of polymeric fluid: The FENE model
    • Le Bris C, Jourdain B and Lelievre T 2004 Existence of solution for a micro-macro model of polymeric fluid: the FENE model J. Funct. Anal. 209 162-93
    • (2004) J. Funct. Anal. , vol.209 , pp. 162-193
    • Le Bris, C.1    Jourdain, B.2    Lelievre, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.