메뉴 건너뛰기




Volumn 65, Issue 4, 1998, Pages 688-708

Epsilon-Ergodicity and the Success of Equilibrium Statistical Mechanics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0012524365     PISSN: 00318248     EISSN: None     Source Type: Journal    
DOI: 10.1086/392667     Document Type: Article
Times cited : (39)

References (72)
  • 1
    • 0001666873 scopus 로고
    • Equipartition and ergodicity in closed one-dimensional systems of hard spheres with different masses
    • Ackland, Graeme J. (1993), "Equipartition and ergodicity in closed one-dimensional systems of hard spheres with different masses". Physical Review E 47: 3268-3275.
    • (1993) Physical Review E , vol.47 , pp. 3268-3275
    • Ackland, G.J.1
  • 2
    • 0009597366 scopus 로고    scopus 로고
    • Why equilibrium statistical mechanics works: Universality and the renormalization group
    • Batterman, Robert W. (1998), "Why equilibrium statistical mechanics works: Universality and the renormalization group", Philosophy of Science 65: 183-208.
    • (1998) Philosophy of Science , vol.65 , pp. 183-208
    • Batterman, R.W.1
  • 3
    • 0000067643 scopus 로고
    • Effects of phase space discretization on the long-time behavior of dynamical systems
    • Beck, C. and G. Roepstorff (1987), "Effects of phase space discretization on the long-time behavior of dynamical systems", Physica D 25: 173-180.
    • (1987) Physica D , vol.25 , pp. 173-180
    • Beck, C.1    Roepstorff, G.2
  • 4
    • 0005299434 scopus 로고
    • Ergodicity and time-scales for statistical equilibrium in classical dynamical systems
    • Benettin, Giancarlo (1994), "Ergodicity and time-scales for statistical equilibrium in classical dynamical systems", Progress of Theoretical Physics Supplement 116: 207-234.
    • (1994) Progress of Theoretical Physics Supplement , vol.116 , pp. 207-234
    • Benettin, G.1
  • 5
    • 51249185427 scopus 로고
    • On the reliability of numerical studies of stochasticity. I: Existence of time averages
    • Benettin, Giancarlo, M. Casartelli, Luigi Galgani, Antonio Giorgilli, and Jean-Marie Strelcyn (1978), "On the reliability of numerical studies of stochasticity. I: Existence of time averages", Nuovo Cimento B 44: 183-195.
    • (1978) Nuovo Cimento B , vol.44 , pp. 183-195
    • Benettin, G.1    Casartelli, M.2    Galgani, L.3    Giorgilli, A.4    Strelcyn, J.-M.5
  • 6
    • 51249184688 scopus 로고
    • On the reliability of numerical studies of stochasticity. II: Identification of time averages
    • _. (1979), "On the reliability of numerical studies of stochasticity. II: Identification of time averages", Nuovo Cimento B 50: 211-232.
    • (1979) Nuovo Cimento B , vol.50 , pp. 211-232
  • 7
    • 0000277549 scopus 로고
    • Kolmogorov entropy of a dynamical system with an increasing number of degrees of freedom
    • Benettin, Giancarlo, C. Froeschlé, and J. P. Scheidecker (1979), "Kolmogorov entropy of a dynamical system with an increasing number of degrees of freedom", Physical Review A 19: 2454-2460.
    • (1979) Physical Review A , vol.19 , pp. 2454-2460
    • Benettin, G.1    Froeschlé, C.2    Scheidecker, J.P.3
  • 8
    • 35949037738 scopus 로고
    • Kolmogorov entropy and numerical experiments
    • Benettin, Giancarlo, Luigi Galgani, and Jean-Marie Strelcyn (1976), "Kolmogorov entropy and numerical experiments", Physical Review A 14: 2338-2345.
    • (1976) Physical Review A , vol.14 , pp. 2338-2345
    • Benettin, G.1    Galgani, L.2    Strelcyn, J.-M.3
  • 9
    • 0040539509 scopus 로고
    • Stochastic transition in two-dimensional Lennard-Jones systems
    • Benettin, Giancarlo, Guido Lo Vecchio, and Alexander Tenenbaum (1980), "Stochastic transition in two-dimensional Lennard-Jones systems", Physical Review A 22: 1709-1719.
    • (1980) Physical Review A , vol.22 , pp. 1709-1719
    • Benettin, G.1    Lo Vecchio, G.2    Tenenbaum, A.3
  • 10
    • 0039940278 scopus 로고
    • Statistical mechanics of Hénon-Heiles oscillators
    • Berdichevsky, V. L. and M. V. Alberti (1991), "Statistical mechanics of Hénon-Heiles oscillators", Physical Review A 44: 858-865.
    • (1991) Physical Review A , vol.44 , pp. 858-865
    • Berdichevsky, V.L.1    Alberti, M.V.2
  • 12
    • 0346927863 scopus 로고
    • On the significance of absolutely continuous invariant measures
    • Boyarsky, Abraham (1984), "On the significance of absolutely continuous invariant measures", Physica D 11: 130-146.
    • (1984) Physica D , vol.11 , pp. 130-146
    • Boyarsky, A.1
  • 13
    • 24844456363 scopus 로고
    • Discontinuity of physical measures
    • _. (1990), "Discontinuity of physical measures", Physics Letters A 149: 12-16.
    • (1990) Physics Letters A , vol.149 , pp. 12-16
  • 15
    • 0038633229 scopus 로고
    • Zero-point energy in classical nonlinear mechanics
    • Cercignani, C., Luigi Galgani, and A. Scotti (1972), "Zero-point energy in classical nonlinear mechanics", Physics Letters A 38: 403-404.
    • (1972) Physics Letters A , vol.38 , pp. 403-404
    • Cercignani, C.1    Galgani, L.2    Scotti, A.3
  • 16
    • 0012500963 scopus 로고
    • What good are numerical simulations of chaotic dynamical systems?
    • Corless, R. M. (1994), "What good are numerical simulations of chaotic dynamical systems?" Computers and Mathematics with Applications 28: 107-121.
    • (1994) Computers and Mathematics with Applications , vol.28 , pp. 107-121
    • Corless, R.M.1
  • 18
    • 0342792866 scopus 로고
    • Time scale to ergodicity in the Fermi-Pasta-Ulam system
    • De Luca, J., Allan J. Lichtenberg, and Michael A. Lieberman (1995), "Time scale to ergodicity in the Fermi-Pasta-Ulam system", Chaos 5: 283-297.
    • (1995) Chaos , vol.5 , pp. 283-297
    • De Luca, J.1    Lichtenberg, A.J.2    Lieberman, M.A.3
  • 19
    • 0007716335 scopus 로고
    • Energy transitions and time scales to equipartition in the Fermi-Pasta-Ulam oscillator chain
    • De Luca, J., Allan J. Lichtenberg, and Stefano Ruffo (1995), "Energy transitions and time scales to equipartition in the Fermi-Pasta-Ulam oscillator chain", Physical Review E 51: 2877-2885.
    • (1995) Physical Review E , vol.51 , pp. 2877-2885
    • De Luca, J.1    Lichtenberg, A.J.2    Ruffo, S.3
  • 21
    • 0002682492 scopus 로고    scopus 로고
    • Why ergodic theory does not explain the success of equilibrium statistical mechanics
    • Earman, John and Miklós Rédei (1996), "Why ergodic theory does not explain the success of equilibrium statistical mechanics", British Journal for the Philosophy of Science 47: 63-78.
    • (1996) British Journal for the Philosophy of Science , vol.47 , pp. 63-78
    • Earman, J.1    Rédei, M.2
  • 22
    • 0009043926 scopus 로고
    • Ergodic properties of high-dimensional symplectic maps
    • Falcioni, M., U. Marini Bettolo Marconi, and Angelo Vulpiani (1991), "Ergodic properties of high-dimensional symplectic maps", Physical Review A 44: 2263-2270.
    • (1991) Physical Review A , vol.44 , pp. 2263-2270
    • Falcioni, M.1    Marconi, U.M.B.2    Vulpiani, A.3
  • 24
    • 0000595654 scopus 로고
    • Studies of non linear problems
    • E. Segré (ed.), Chicago: University of Chicago Press, Original circulated 1955 as Document LA-1940
    • Fermi, Enrico, John Pasta, and S. Ulam (1965), "Studies of non linear problems", in E. Segré (ed.), Enrico Fermi: Collected papers, vol. II. Chicago: University of Chicago Press, pp. 978-988. [Original circulated 1955 as Document LA-1940.]
    • (1965) Enrico Fermi: Collected Papers , vol.2 , pp. 978-988
    • Fermi, E.1    Pasta, J.2    Ulam, S.3
  • 25
    • 0347371015 scopus 로고
    • The Fermi-Pasta-Ulam problem: Paradox turns discovery
    • Ford, Joseph (1992), "The Fermi-Pasta-Ulam problem: Paradox turns discovery", Physics Reports 213: 271-310.
    • (1992) Physics Reports , vol.213 , pp. 271-310
    • Ford, J.1
  • 26
    • 0347558924 scopus 로고
    • A partial vindication of ergodic theory
    • Friedman, K. S. (1976), "A partial vindication of ergodic theory", Philosophy of Science 43: 151-162.
    • (1976) Philosophy of Science , vol.43 , pp. 151-162
    • Friedman, K.S.1
  • 27
    • 0037679562 scopus 로고
    • Connectance of dynamical systems with increasing number of degrees of freedom
    • Froeschlé, C. (1978), "Connectance of dynamical systems with increasing number of degrees of freedom", Physical Review A 18: 277-281.
    • (1978) Physical Review A , vol.18 , pp. 277-281
    • Froeschlé, C.1
  • 28
    • 4243546454 scopus 로고
    • Stochasticity of dynamical systems with increasing number of degrees of freedom
    • Froeschlé, C. and J. P. Scheidecker (1975), "Stochasticity of dynamical systems with increasing number of degrees of freedom", Physical Review A 12: 2137-2143.
    • (1975) Physical Review A , vol.12 , pp. 2137-2143
    • Froeschlé, C.1    Scheidecker, J.P.2
  • 29
    • 0001276861 scopus 로고
    • On the problem of energy equipartition for large systems of the Fermi-Pasta-Ulam type: Analytical and numerical estimates
    • Galgani, Luigi, Antonio Giorgilli, Andrea Martinoli, and Stefano Vanzini (1992), "On the problem of energy equipartition for large systems of the Fermi-Pasta-Ulam type: Analytical and numerical estimates", Physica D 59: 334-348.
    • (1992) Physica D , vol.59 , pp. 334-348
    • Galgani, L.1    Giorgilli, A.2    Martinoli, A.3    Vanzini, S.4
  • 30
    • 51249180225 scopus 로고
    • Stochasticity thresholds for systems of coupled oscillators
    • Galgani, Luigi and Guido Lo Vecchio (1979), "Stochasticity thresholds for systems of coupled oscillators", Nuovo Cimento B 52: 1-14.
    • (1979) Nuovo Cimento B , vol.52 , pp. 1-14
    • Galgani, L.1    Lo Vecchio, G.2
  • 33
    • 22244459499 scopus 로고
    • Torus structure in higher-dimensional Hamiltonian systems
    • Györgyi, G., F. H. Ling, and G. Schmidt (1989), "Torus structure in higher-dimensional Hamiltonian systems", Physical Review A 40: 5311-5318.
    • (1989) Physical Review A , vol.40 , pp. 5311-5318
    • Györgyi, G.1    Ling, F.H.2    Schmidt, G.3
  • 34
    • 0038903941 scopus 로고
    • Numerical exploration of Hamiltonian systems
    • G. Iooss, R. H. G. Helleman, and R. Stora (eds.), New York: North-Holland
    • Hénon, Michel (1983), "Numerical exploration of Hamiltonian systems", in G. Iooss, R. H. G. Helleman, and R. Stora (eds.), Chaotic behaviour of deterministic systems. New York: North-Holland, pp. 53-170.
    • (1983) Chaotic Behaviour of Deterministic Systems , pp. 53-170
    • Hénon, M.1
  • 35
    • 0346297783 scopus 로고
    • On the tendency toward ergodicity with increasing number of degrees of freedom in Hamiltonian systems
    • J. Seimenis (ed.), New York: Plenum
    • Hurd, Lyman, Celso Grebogi, and Edward Ott (1994), "On the tendency toward ergodicity with increasing number of degrees of freedom in Hamiltonian systems", in J. Seimenis (ed.), Hamiltonian mechanics: Integrability and chaotic behavior. New York: Plenum, pp. 123-129.
    • (1994) Hamiltonian Mechanics: Integrability and Chaotic Behavior , pp. 123-129
    • Hurd, L.1    Grebogi, C.2    Ott, E.3
  • 36
    • 0013087334 scopus 로고
    • Vanishing stability thresholds in the thermodynamic limit of nonintegrable conservative systems
    • Kantz, Holger (1989), "Vanishing stability thresholds in the thermodynamic limit of nonintegrable conservative systems", Physica D 39: 322-335.
    • (1989) Physica D , vol.39 , pp. 322-335
    • Kantz, H.1
  • 37
    • 0347583689 scopus 로고
    • Equipartition thresholds in chains of anharmonic oscillators
    • Kantz, Holger, Roberto Livi, and Stefano Ruffo (1994), "Equipartition thresholds in chains of anharmonic oscillators", Journal of Statistical Physics 76: 627-643.
    • (1994) Journal of Statistical Physics , vol.76 , pp. 627-643
    • Kantz, H.1    Livi, R.2    Ruffo, S.3
  • 38
    • 0348188565 scopus 로고    scopus 로고
    • Hamiltonian systems with many degrees of freedom: Asymmetric motion and intensity of motion in phase space
    • Kazumasa, Shinjo and Sasada Tomohei (1996), "Hamiltonian systems with many degrees of freedom: Asymmetric motion and intensity of motion in phase space", Physical Review E 54: 4685-4700.
    • (1996) Physical Review E , vol.54 , pp. 4685-4700
    • Kazumasa, S.1    Tomohei, S.2
  • 41
    • 0001027451 scopus 로고
    • The K-property of four billiard balls
    • _. (1992), "The K-property of four billiard balls", Communications in Mathematical Physics 144: 107-148.
    • (1992) Communications in Mathematical Physics , vol.144 , pp. 107-148
  • 42
    • 0001864495 scopus 로고
    • Entropy and equilibrium states in classical statistical mechanics
    • A. Lenard (ed.), New York: Springer
    • Lanford, Oscar E., III (1973), "Entropy and equilibrium states in classical statistical mechanics", in A. Lenard (ed.), Statistical mechanics and mathematical problems. New York: Springer, pp. 1-113.
    • (1973) Statistical Mechanics and Mathematical Problems , pp. 1-113
    • Lanford O.E. III1
  • 43
    • 0038755990 scopus 로고
    • Introduction to the mathematical theory of dynamical systems
    • G. Iooss, R. H. G. Helleman, and R. Stora (eds.), New York: North-Holland
    • _. (1983), "Introduction to the mathematical theory of dynamical systems", in G. Iooss, R. H. G. Helleman, and R. Stora (eds.), Chaotic behaviour of deterministic systems. New York: North-Holland, pp. 3-51.
    • (1983) Chaotic Behaviour of Deterministic Systems , pp. 3-51
  • 44
    • 0041572688 scopus 로고
    • Malament and Zabell on Gibbs phase averaging
    • Leeds, Stephen (1989), ∑Malament and Zabell on Gibbs phase averaging", Philosophy of Science 56: 325-340.
    • (1989) Philosophy of Science , vol.56 , pp. 325-340
    • Leeds, S.1
  • 46
    • 33646652279 scopus 로고
    • Equipartition threshold in nonlinear large Hamiltonian systems: The FermiPasta-Ulam model
    • Livi, Roberto, Marco Pettini, Stefano Ruffo, Massimo Sparpaglione, and Angelo Vulpiani (1985a), "Equipartition threshold in nonlinear large Hamiltonian systems: The FermiPasta-Ulam model", Physical Review A 31: 1039-1045.
    • (1985) Physical Review A , vol.31 , pp. 1039-1045
    • Livi, R.1    Pettini, M.2    Ruffo, S.3    Sparpaglione, M.4    Vulpiani, A.5
  • 47
    • 0008981843 scopus 로고
    • Further results on the equipartition threshold in large nonlinear Hamiltonian systems
    • Livi, Roberto, Marco Pettini, Stefano Ruffo, and Angelo Vulpiani (1985b), "Further results on the equipartition threshold in large nonlinear Hamiltonian systems", Physical Review A 31: 2740-2742.
    • (1985) Physical Review A , vol.31 , pp. 2740-2742
    • Livi, R.1    Pettini, M.2    Ruffo, S.3    Vulpiani, A.4
  • 48
    • 33646976256 scopus 로고
    • Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics
    • _. (1987), "Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics", Journal of Statistical Physics 48: 539-559.
    • (1987) Journal of Statistical Physics , vol.48 , pp. 539-559
  • 49
    • 0001554670 scopus 로고
    • Why Gibbs phase averages work - The role of ergodic theory
    • Malament, David B. and Sandy L. Zabell (1980), "Why Gibbs phase averages work - The role of ergodic theory", Philosophy of Science 47: 339-349.
    • (1980) Philosophy of Science , vol.47 , pp. 339-349
    • Malament, D.B.1    Zabell, S.L.2
  • 50
  • 51
    • 0347558922 scopus 로고
    • Asymptotic form of the structure function for real systems
    • Mazur, P. and J. van der Linden (1963), "Asymptotic form of the structure function for real systems", Journal of Mathematical Physics 4: 271-277.
    • (1963) Journal of Mathematical Physics , vol.4 , pp. 271-277
    • Mazur, P.1    Van Der Linden, J.2
  • 52
    • 0001475851 scopus 로고
    • Shadowing by computable chaotic orbits
    • Palmore, Julian I. and Joseph L. McCauley (1987), "Shadowing by computable chaotic orbits", Physics Letters A 122: 399-402.
    • (1987) Physics Letters A , vol.122 , pp. 399-402
    • Palmore, J.I.1    McCauley, J.L.2
  • 53
    • 30344481019 scopus 로고
    • Strong stochasticity threshold in nonlinear large Hamiltonian systems: Effect on mixing times
    • Pettini, Marco and Monica Cerruti-Sola (1991), "Strong stochasticity threshold in nonlinear large Hamiltonian systems: Effect on mixing times", Physical Review A 44: 975-987.
    • (1991) Physical Review A , vol.44 , pp. 975-987
    • Pettini, M.1    Cerruti-Sola, M.2
  • 54
    • 0000569924 scopus 로고
    • Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics
    • Pettini, Marco and Marco Landolfi (1990), "Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics", Physical Review A 41: 768-783.
    • (1990) Physical Review A , vol.41 , pp. 768-783
    • Pettini, M.1    Landolfi, M.2
  • 55
    • 0346297785 scopus 로고
    • A philosophical explanation of the explanatory functions of ergodic theory
    • Quay, Paul M. (1978), "A philosophical explanation of the explanatory functions of ergodic theory", Philosophy of Science 45: 47-59.
    • (1978) Philosophy of Science , vol.45 , pp. 47-59
    • Quay, P.M.1
  • 57
    • 4243727882 scopus 로고
    • Gravity in one dimension: Stability of periodic orbits
    • Reidl, Charles J., Jr. and Bruce N. Miller (1992), "Gravity in one dimension: Stability of periodic orbits", Physical Review A 46: 837-843.
    • (1992) Physical Review A , vol.46 , pp. 837-843
    • Reidl C.J., Jr.1    Miller, B.N.2
  • 58
    • 0000846473 scopus 로고
    • Gravity in one dimension: The critical population
    • _. (1993), "Gravity in one dimension: The critical population", Physical Review A 48: 4250-4256.
    • (1993) Physical Review A , vol.48 , pp. 4250-4256
  • 60
    • 0000616278 scopus 로고
    • The K-property of N billiard balls I
    • Simányi, Nándor (1992a), "The K-property of N billiard balls I", Inventiones Mathematicae 108: 521-548.
    • (1992) Inventiones Mathematicae , vol.108 , pp. 521-548
    • Simányi, N.1
  • 61
    • 0000944602 scopus 로고
    • The K-property of N billiard balls II. Computation of neutral linear spaces
    • _. (1992b), "The K-property of N billiard balls II. Computation of neutral linear spaces", Inventiones Mathematicae 110: 151-172.
    • (1992) Inventiones Mathematicae , vol.110 , pp. 151-172
  • 62
    • 21844504054 scopus 로고
    • The K-property of 4D billiards with nonorthogonal cylindric scatterers
    • Simányi, Nándor and Domokos Szász (1994), "The K-property of 4D billiards with nonorthogonal cylindric scatterers", Journal of Statistical Physics 76: 587-604.
    • (1994) Journal of Statistical Physics , vol.76 , pp. 587-604
    • Simányi, N.1    Szász, D.2
  • 63
    • 84927896522 scopus 로고
    • Dynamical systems with elastic reflections
    • Sinai, Yakov G. (1970), "Dynamical systems with elastic reflections", Russian Mathematical Surveys 25: 137-189.
    • (1970) Russian Mathematical Surveys , vol.25 , pp. 137-189
    • Sinai, Y.G.1
  • 64
    • 84956132011 scopus 로고
    • Ergodic properties of certain systems of two-dimensional disks and three-dimensional balls
    • Sinai, Yakov G. and N. I. Chernov (1987), "Ergodic properties of certain systems of two-dimensional disks and three-dimensional balls", Russian Mathematical Surveys 42: 181-207.
    • (1987) Russian Mathematical Surveys , vol.42 , pp. 181-207
    • Sinai, Y.G.1    Chernov, N.I.2
  • 65
    • 85055959122 scopus 로고
    • Statistical explanation and ergodic theory
    • Sklar, Lawrence (1973), "Statistical explanation and ergodic theory", Philosophy of Science 40: 194-212.
    • (1973) Philosophy of Science , vol.40 , pp. 194-212
    • Sklar, L.1
  • 66
    • 0348188564 scopus 로고
    • Comments
    • P. D. Asquith and I. Hacking (eds.), East Lansing, MI: Philosophy of Science Association
    • _. (1978), "Comments", in P. D. Asquith and I. Hacking (eds.), PSA 1978, vol. 2. East Lansing, MI: Philosophy of Science Association, pp. 186-193.
    • (1978) PSA 1978 , vol.2 , pp. 186-193
  • 68
    • 4243720275 scopus 로고
    • Numerical experiments on the stochastic behavior of a Lennard-Jones gas system
    • Stoddard, Spotswood D. and Joseph Ford (1973), "Numerical experiments on the stochastic behavior of a Lennard-Jones gas system", Physical Review A 8: 1504-1512.
    • (1973) Physical Review A , vol.8 , pp. 1504-1512
    • Stoddard, S.D.1    Ford, J.2
  • 69
    • 1542574947 scopus 로고    scopus 로고
    • Boltzmann's ergodic hypothesis, a conjecture for centuries?
    • Szász, Domokos (1996), "Boltzmann's ergodic hypothesis, a conjecture for centuries?" Studia Scientiarum Mathematicarum Hungarica 31: 299-322.
    • (1996) Studia Scientiarum Mathematicarum Hungarica , vol.31 , pp. 299-322
    • Szász, D.1
  • 70
    • 0042574856 scopus 로고
    • Regular and chaotic motions in dynamical systems: Introduction to the problems
    • G. Velo and A. S. Wightman (eds.), New York: Plenum
    • Wightman, A. S. (1985), "Regular and chaotic motions in dynamical systems: Introduction to the problems", in G. Velo and A. S. Wightman (eds.), Regular and chaotic motion in dynamical systems. New York: Plenum, pp. 1-26.
    • (1985) Regular and Chaotic Motion in Dynamical Systems , pp. 1-26
    • Wightman, A.S.1
  • 71
    • 0344454308 scopus 로고
    • Gravity in one dimension: A dynamical and statistical study
    • Wright, H. L. and Bruce N. Miller (1984), "Gravity in one dimension: A dynamical and statistical study", Physical Review A 29: 1411-1418.
    • (1984) Physical Review A , vol.29 , pp. 1411-1418
    • Wright, H.L.1    Miller, B.N.2
  • 72
    • 0000148628 scopus 로고    scopus 로고
    • Ergodicity in hard-ball systems and Boltzmann's entropy
    • Zheng, Zhigang, Gang Hu, and Juyuan Zhang (1996), "Ergodicity in hard-ball systems and Boltzmann's entropy", Physical Review E 53: 3246-3252.
    • (1996) Physical Review E , vol.53 , pp. 3246-3252
    • Zheng, Z.1    Hu, G.2    Zhang, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.