메뉴 건너뛰기




Volumn 138, Issue 1, 2010, Pages 270-290

Dynamical aspects of mean field plane rotators and the Kuramoto model

Author keywords

(Ir)reversibility; Kuramoto model; Mean field Spin XY model; Spectral gap inequality; Synchronization

Indexed keywords


EID: 77249132487     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9908-9     Document Type: Article
Times cited : (85)

References (26)
  • 2
    • 0000377165 scopus 로고
    • Non-negative solutions of linear parabolic equations
    • Aronson, D. G.: Non-negative solutions of linear parabolic equations. Ann. Scuola Norm. Sup. Pisa 22(3), 607-694 (1968).
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , Issue.3 , pp. 607-694
    • Aronson, D.G.1
  • 3
    • 0032264667 scopus 로고    scopus 로고
    • Metastability for the exclusion process with mean field interactions
    • Asselah, A., Giacomin, G.: Metastability for the exclusion process with mean field interactions. J. Stat. Phys. 93, 1051-1110 (1998).
    • (1998) J. Stat. Phys. , vol.93 , pp. 1051-1110
    • Asselah, A.1    Giacomin, G.2
  • 6
    • 0033070782 scopus 로고    scopus 로고
    • Hydrodynamic limit of Brownian particles Interacting with short and long range forces
    • Buttà, P., Lebowitz, J. L.: Hydrodynamic limit of Brownian particles Interacting with short and long range forces. J. Stat. Phys. 94, 653-694 (1999).
    • (1999) J. Stat. Phys. , vol.94 , pp. 653-694
    • Buttà, P.1    Lebowitz, J.L.2
  • 7
    • 0000122907 scopus 로고
    • Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators
    • Daido, H.: Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators. Prog. Theor. Phys. 88, 1213-1218 (1992).
    • (1992) Prog. Theor. Phys. , vol.88 , pp. 1213-1218
    • Daido, H.1
  • 8
    • 0030210666 scopus 로고    scopus 로고
    • McKean-Vlasov limit for interacting random processes in random media
    • Dai Pra, P., den Hollander, F.: McKean-Vlasov limit for interacting random processes in random media. J. Stat. Phys. 84, 735-772 (1996).
    • (1996) J. Stat. Phys. , vol.84 , pp. 735-772
    • Dai Pra, P.1    den Hollander, F.2
  • 9
    • 84985400388 scopus 로고
    • On McKean-Vlasov limit for interacting diffusions
    • Gärtner, J.: On McKean-Vlasov limit for interacting diffusions. Math. Nachr. 137, 197-248 (1988).
    • (1988) Math. Nachr. , vol.137 , pp. 197-248
    • Gärtner, J.1
  • 10
    • 0031116136 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions I: Macroscopic limits
    • Giacomin, G., Lebowitz, J. L.: Phase segregation dynamics in particle systems with long range interactions I: macroscopic limits. J. Stat. Phys. 87, 37-61 (1997).
    • (1997) J. Stat. Phys. , vol.87 , pp. 37-61
    • Giacomin, G.1    Lebowitz, J.L.2
  • 11
    • 0032291814 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions II: Interface motion
    • Giacomin, G., Lebowitz, J. L.: Phase segregation dynamics in particle systems with long range interactions II: interface motion. SIAM J. Appl. Math. 58, 1707-1729 (1998).
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1707-1729
    • Giacomin, G.1    Lebowitz, J.L.2
  • 12
    • 0004261516 scopus 로고    scopus 로고
    • Fields Institute Monographs, Providence: American Mathematical Society
    • den Hollander, F.: Large Deviations. Fields Institute Monographs. American Mathematical Society, Providence (2000).
    • (2000) Large Deviations
    • den Hollander, F.1
  • 13
    • 0042693799 scopus 로고
    • Some inequalities of Bessel and modified Bessel functions
    • Joshi, C. M., Bissu, S. K.: Some inequalities of Bessel and modified Bessel functions. J. Aust. Math. Soc. Ser. A 50, 333-342 (1991).
    • (1991) J. Aust. Math. Soc. Ser. A , vol.50 , pp. 333-342
    • Joshi, C.M.1    Bissu, S.K.2
  • 14
    • 0003862232 scopus 로고
    • 2nd edn., Grundlehren der Mathematischen Wissenschaften, Berlin: Springer
    • Kato, T.: Perturbation Theory for Linear Operators, 2nd edn. Grundlehren der Mathematischen Wissenschaften, vol. 132. Springer, Berlin (1976).
    • (1976) Perturbation Theory for Linear Operators , vol.132
    • Kato, T.1
  • 17
    • 0040554658 scopus 로고
    • A martingale approach to the law of large numbers for weakly interacting stochastic processes
    • Oelschläger, K.: A martingale approach to the law of large numbers for weakly interacting stochastic processes. Ann. Probab. 12, 458-479 (1984).
    • (1984) Ann. Probab. , vol.12 , pp. 458-479
    • Oelschläger, K.1
  • 18
    • 0142013256 scopus 로고
    • Mean-field bounds on the magnetization for ferromagnetic spin models
    • Pearce, P. A.: Mean-field bounds on the magnetization for ferromagnetic spin models. J. Stat. Phys. 25, 309-320 (1981).
    • (1981) J. Stat. Phys. , vol.25 , pp. 309-320
    • Pearce, P.A.1
  • 21
    • 0002192231 scopus 로고
    • Cooperative phenomena in coupled oscillator systems under external fields
    • Sakaguchi, H.: Cooperative phenomena in coupled oscillator systems under external fields. Prog. Theor. Phys. 79, 39-46 (1988).
    • (1988) Prog. Theor. Phys. , vol.79 , pp. 39-46
    • Sakaguchi, H.1
  • 24
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • Strogatz, S. H.: From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1-20 (2000).
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 25
    • 1542499302 scopus 로고
    • Stability of incoherence in a population of coupled oscillators
    • Strogatz, S. H., Mirollo, R. E.: Stability of incoherence in a population of coupled oscillators. J. Stat. Phys. 63, 613-635 (1991).
    • (1991) J. Stat. Phys. , vol.63 , pp. 613-635
    • Strogatz, S.H.1    Mirollo, R.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.