메뉴 건너뛰기




Volumn 377, Issue 2, 2007, Pages 469-486

Kinetic theory with angle-action variables

Author keywords

Fokker Planck equations; Kinetic theory; Long range interactions

Indexed keywords

ENTROPY; LINEAR EQUATIONS; RELAXATION PROCESSES; STATISTICAL MECHANICS; THERMODYNAMICS;

EID: 33846674201     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.11.078     Document Type: Article
Times cited : (43)

References (39)
  • 1
    • 33846651795 scopus 로고    scopus 로고
    • T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens (Eds.), Dynamics and Thermodynamics of Systems with Long Range Interactions, Lecture Notes in Physics, vol. 602, Springer, Berlin, 2002.
  • 23
    • 33846688852 scopus 로고    scopus 로고
    • B [f] at fixed mass M [f] and energy E [f]; see Ref. [2] for more details and references.
  • 25
    • 33846686348 scopus 로고    scopus 로고
    • J. Binney, S. Tremaine, Galactic Dynamics, Princeton Series in Astrophysics, 1987.
  • 29
    • 33846694993 scopus 로고    scopus 로고
    • It is easy to show that if the distribution function f = f (ε{lunate}, t) depends only on the energy, then the condition of hydrostatic equilibrium ∇ p + ρ ∇ Φ = 0 holds at any time; see, e.g., Eq. (33) in Ref. [30].
  • 31
    • 33846673160 scopus 로고    scopus 로고
    • c [12,14]. In any case, in the N → + ∞ limit, there will be a time-scale separation between the decorrelation time of the fluctuations and the evolution of the smooth meanfield distribution which justifies the decomposition made in this paper.
  • 35
    • 33846701517 scopus 로고    scopus 로고
    • 0 to t = ∞ (the conventional Laplace transform uses - s in place of - i ω in the integrand); see Lifshitz and Pitaevskii [26] and Binney and Tremaine [25], Appendix 5.A for more details on these technical issues.
  • 36
    • 33846706025 scopus 로고    scopus 로고
    • The same approximation is made by Pichon [37] to investigate the linear dynamical stability of a steady solution of the Vlasov equation (7).
  • 37
    • 33846662826 scopus 로고    scopus 로고
    • C. Pichon, Ph.D. Thesis, Cambridge, 1994.
  • 38
    • 33846665167 scopus 로고    scopus 로고
    • P.H. Chavanis, M. Lemou, in preparation.
  • 39
    • 33846662516 scopus 로고    scopus 로고
    • The Fokker-Planck structure of this equation where the first term in brackets represents a diffusion and the second term a drift (friction) is clear from the discussion of Ref. [2], Section 2.8. This will also be shown in Section 9.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.