메뉴 건너뛰기




Volumn 75, Issue 6, 2010, Pages 951-967

Asymptotic analysis of the Green-Kubo formula

Author keywords

Green Kubo formula; homogenization theory; Markov processes; self diffusion; Stieltjes integral representation formula

Indexed keywords

ANALYTIC CONTINUATION; ANTI-SYMMETRIC; ASYMPTOTIC LIMITS; DIFFUSION COEFFICIENTS; DIFFUSION TENSOR; EFFECTIVE DIFFUSIVITIES; EFFECTIVE PARAMETERS; GREEN-KUBO FORMULA; HETEROGENEOUS MEDIA; HOMOGENIZATION THEORY; INTEGRAL REPRESENTATION; LAMINAR AND TURBULENT FLOW; MARKOVIAN; MICROSCOPIC DYNAMICS; SELF-DIFFUSION; SELF-DIFFUSION COEFFICIENTS; STIELTJES INTEGRAL;

EID: 78649488426     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxq039     Document Type: Article
Times cited : (22)

References (36)
  • 1
    • 5244340276 scopus 로고
    • Mathematical models with exact renormalization for turbulent transport
    • AVELLANEDA, M. & MAJDA, A. J. (1990) Mathematical models with exact renormalization for turbulent transport. Commun. Pure Appl. Math., 131, 381-429.
    • (1990) Commun. Pure Appl. Math. , vol.131 , pp. 381-429
    • Avellaneda, M.1    Majda, A.J.2
  • 2
    • 0000705763 scopus 로고
    • An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows
    • AVELLANEDA, M. & MAJDA, A. J. (1991) An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows. Commun. Math. Phys., 138, 339-391.
    • (1991) Commun. Math. Phys. , vol.138 , pp. 339-391
    • Avellaneda, M.1    Majda, A.J.2
  • 3
    • 0001346893 scopus 로고
    • Stieltjes integral representation of effective diffusivities in timedependent flows
    • AVELLANEDA, M. & VERGASSOLA, M. (1995) Stieltjes integral representation of effective diffusivities in timedependent flows. Phys. Rev. E, 52, 3249-3251.
    • (1995) Phys. Rev. E , Issue.52 , pp. 3249-3251
    • Avellaneda, M.1    Vergassola, M.2
  • 6
    • 0001832511 scopus 로고
    • Asymptotics of solute dispersion in periodic porous media
    • BHATTACHARYA, R. N., GUPTA, V. K. & WALKER, H. F. (1989) Asymptotics of solute dispersion in periodic porous media. SIAM J. Appl. Math., 49, 86-98.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 86-98
    • Bhattacharya, R.N.1    Gupta, V.K.2    Walker, H.F.3
  • 7
    • 31144448217 scopus 로고    scopus 로고
    • Self-diffusion in granular gases: Green-kubo versus chapman-enskog
    • BRILLIANTOV, N. V. & PöSCHEL, T. (2005) Self-diffusion in granular gases: Green-Kubo versus Chapman- Enskog. Chaos, 15, 026108.
    • (2005) Chaos , vol.15 , pp. 026108
    • Brilliantov, N.V.1    Pöschel, T.2
  • 8
    • 33644646077 scopus 로고    scopus 로고
    • The green-kubo formula autocorrelation function and fluctuation spectrum for finite markov chains with continuous time
    • CHEN, Y., CHEN, X. & QIAN, M.-P. (2006) The Green-Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time. J. Phys. A, 39, 2539-2550.
    • (2006) J. Phys. A , vol.39 , pp. 2539-2550
    • Chen, Y.1    Chen, X.2    Qian, M.-P.3
  • 10
    • 33644641707 scopus 로고
    • On rigorous hydrodynamics self-diffusion and the green-kubo formulae
    • Stochastic Processes and their Applications in Mathematics and Physics Bielefeld 1985 S Albeverio, P. Blanchard & L. Streit eds Dordrecht The Netherlands Kluwer Academic Publisher
    • Dü RR, D., ZANGHì, N. & ZESSIN, H. (1990) On rigorous hydrodynamics, self-diffusion and the Green-Kubo formulae. Stochastic Processes and their Applications in Mathematics and Physics (Bielefeld, 1985) (S. Albeverio, P. Blanchard & L. Streit eds). Mathematics and Its Applications, vol. 61. Dordrecht, The Netherlands: Kluwer Academic Publisher, pp. 123-147.
    • (1990) Mathematics and Its Applications , vol.61 , pp. 123-147
    • Dürr, D.1    Zanghì, N.2    Zessin, H.3
  • 11
    • 84980153186 scopus 로고
    • Chapman-enskog-hilbert expansion for a markovian model of the boltzmann equation
    • ELLIS, R. S. (1973) Chapman-Enskog-Hilbert expansion for a Markovian model of the Boltzmann equation. Commun. Pure Appl. Math., 26, 327-359.
    • (1973) Commun. Pure Appl. Math. , vol.26 , pp. 327-359
    • Ellis, R.S.1
  • 12
    • 0003228130 scopus 로고    scopus 로고
    • Partial differential equations
    • RI American Mathematical Society
    • EVANS, L. C. (1998) Partial Differential Equations. Providence, RI: American Mathematical Society.
    • (1998) Providence
    • Evans, L.C.1
  • 13
    • 0042909264 scopus 로고    scopus 로고
    • On random perturbations of hamiltonian systems with many degrees of freedom
    • FREIDLIN, M. I. & WEBER, M. (2001) On random perturbations of Hamiltonian systems with many degrees of freedom. Stoch. Process. Appl., 94, 199-239.
    • (2001) Stoch. Process. Appl. , Issue.94 , pp. 199-239
    • Freidlin, M.I.1    Weber, M.2
  • 15
    • 0001611879 scopus 로고
    • Bounds for effective parameters of heterogeneous media by analytic continuation
    • GOLDEN, K. & PAPANICOLAOU, G. (1983) Bounds for effective parameters of heterogeneous media by analytic continuation. Commun. Math. Phys., 90, 473-491.
    • (1983) Commun. Math. Phys. , vol.90 , pp. 473-491
    • Golden, K.1    Papanicolaou, G.2
  • 16
    • 39749089200 scopus 로고    scopus 로고
    • From ballistic to diffusive behavior in periodic potentials
    • HAIRER, M. & PAVLIOTIS, G. A. (2008) From ballistic to diffusive behavior in periodic potentials. J. Stat. Phys., 131, 175-202.
    • (2008) J. Stat. Phys. , vol.131 , pp. 175-202
    • Hairer, M.1    Pavliotis, G.A.2
  • 17
    • 0142041467 scopus 로고    scopus 로고
    • The green-kubo formula and power spectrum of reversible markov processes
    • JIANG, D.-Q. & ZHANG, F.-X. (2003) The Green-Kubo formula and power spectrum of reversible Markov processes. J. Math. Phys., 44, 4681-4689.
    • (2003) J. Math. Phys. , vol.44 , pp. 4681-4689
    • Jiang, D.-Q.1    Zhang, F.-X.2
  • 18
    • 0013161462 scopus 로고    scopus 로고
    • On markov process generated by pseudodifferential operator of variable order
    • KIKUCHI, K. & NEGORO, A. (1997) On Markov process generated by pseudodifferential operator of variable order. Osaka J. Math., 34, 319-335.
    • (1997) Osaka J. Math. , vol.34 , pp. 319-335
    • Kikuchi, K.1    Negoro, A.2
  • 19
    • 34250130646 scopus 로고
    • Central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions
    • KIPNIS, C. & VARADHAN, S. R. S. (1986) Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Commun. Math. Phys., 104, 1-19.
    • (1986) Commun. Math. Phys. , vol.104 , pp. 1-19
    • Kipnis, C.1    Varadhan, S.R.S.2
  • 20
    • 0001495041 scopus 로고
    • The symmetry properties of the effective diffusivity tensor in anisotropic porous media
    • KOCH, D. L. & BRADY, J. F. (1988) The symmetry properties of the effective diffusivity tensor in anisotropic porous media. Phys. Fluids, 31, 965-973.
    • (1988) Phys. Fluids , vol.31 , pp. 965-973
    • Koch, D.L.1    Brady, J.F.2
  • 21
    • 0004138120 scopus 로고
    • II: Nonequilibrium Statistical Mechanics Springer Series in Solid-State Sciences 2nd edn. Berlin: Springer
    • KUBO, R., TODA, M. & HASHITSUME, N. (1991) Statistical Physics. II: Nonequilibrium Statistical Mechanics. Springer Series in Solid-State Sciences, vol. 31, 2nd edn. Berlin: Springer.
    • (1991) Statistical Physics , vol.31
    • Kubo, R.1    Toda, M.2    Hashitsume, N.3
  • 22
    • 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
  • 23
    • 78649462157 scopus 로고    scopus 로고
    • Central limit theorems for markov processes
    • LANDIM, C. & OLLA, S. (2005) Central Limit Theorems for Markov Processes. Lecture Notes.
    • (2005) Lecture Notes
    • Landim, C.1    Olla, S.2
  • 24
    • 21444456296 scopus 로고    scopus 로고
    • On the ornstein-uhlenbeck operator in L2 spaces with respect to invariant measures
    • LUNARDI, A. (1997) On the Ornstein-Uhlenbeck operator in L2 spaces with respect to invariant measures. Trans. Am. Math. Soc., 349, 155-169. (Pubitemid 127745289)
    • (1997) Transactions of the American Mathematical Society , vol.349 , Issue.1 , pp. 155-169
    • Lunardi, A.1
  • 25
    • 0347601794 scopus 로고    scopus 로고
    • Simplified models for turbulent diffusion: Theory numerical modeling and physical phenomena
    • MAJDA, A. J. & KRAMER, P. R. (1999) Simplified models for turbulent diffusion: theory, numerical modeling and physical phenomena. Phys. Rep., 314, 237-574.
    • (1999) Phys. Rep. , vol.314 , pp. 237-574
    • Majda, A.J.1    Kramer, P.R.2
  • 26
    • 0003004753 scopus 로고
    • The effect of mean flows on enhanced diffusivity in transport by incompressible periodic velocity fields
    • MAJDA, A. J. & MCLAUGHLIN, R. M. (1993) The effect of mean flows on enhanced diffusivity in transport by incompressible periodic velocity fields. Stud. Appl. Math., 89, 245-279.
    • (1993) Stud. Appl. Math. , Issue.89 , pp. 245-279
    • Majda, A.J.1    Mclaughlin, R.M.2
  • 27
    • 78649468646 scopus 로고    scopus 로고
    • Asymptotic analysis of the generalized langevin equation
    • OTTOBRE, M. & PAVLIOTIS, G. A. (2009) Asymptotic analysis of the generalized Langevin equation, Preprint.
    • (2009) Preprint
    • Ottobre, M.1    Pavliotis, G.A.2
  • 29
    • 77954205385 scopus 로고    scopus 로고
    • Multiscale methods: Averaging and homogenization
    • New York Springer
    • PAVLIOTIS, G. A. & STUART, A. M. (2008) Multiscale Methods: Averaging and Homogenization. Texts in Applied Mathematics, vol. 53. New York: Springer.
    • (2008) Texts in Applied Mathematics , vol.53
    • Pavliotis, G.A.1    Stuart, A.M.2
  • 30
    • 0033271169 scopus 로고    scopus 로고
    • Transport theory and collective modes I the case of moderately dense gases
    • PETROSKY, T. (1999a) Transport theory and collective modes. I. The case of moderately dense gases. Found. Phys., 29, 1417-1456.
    • (1999) Found. Phys. , vol.29 , pp. 1417-1456
    • Petrosky, T.1
  • 31
    • 0033276145 scopus 로고    scopus 로고
    • Transport theory and collective modes II long-time tail and green-kubo formalism
    • PETROSKY, T. (1999b) Transport theory and collective modes. II. Long-time tail and Green-Kubo formalism. Found. Phys., 29, 1581-1605.
    • (1999) Found. Phys. , vol.29 , pp. 1581-1605
    • Petrosky, T.1
  • 32
    • 0036243184 scopus 로고    scopus 로고
    • Thermodynamics of the general diffusion process: Time-reversibility and entropy production
    • QIAN, H., QIAN, M. & TANG, X. (2002) Thermodynamics of the general diffusion process: time-reversibility and entropy production. J. Stat. Phys., 107, 1129-1141.
    • (2002) J. Stat. Phys. , vol.107 , pp. 1129-1141
    • Qian, H.1    Qian, M.2    Tang, X.3
  • 33
    • 22244469053 scopus 로고
    • On the connection between the kinetic approach and the correlation-function method for thermal transport coefficients
    • Ré SIBOIS, P. (1964) On the connection between the kinetic approach and the correlation-function method for thermal transport coefficients. J. Chem. Phys., 41, 2979-2992.
    • (1964) J. Chem. Phys. , vol.41 , pp. 2979-2992
    • Résibois, P.1
  • 35
    • 0017675661 scopus 로고
    • The complete chapman-enskog procedure for the fokker-planck equation
    • SCHRö TER, J. (1977) The complete Chapman-Enskog procedure for the Fokker-Planck equation. Arch. Ration. Mech. Anal., 66, 183-199.
    • (1977) Arch. Ration. Mech. Anal. , vol.66 , pp. 183-199
    • Schröter, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.