Breakdown of hot-spot model in determining convective amplification in large homogeneous systems

Physical Review Letters

Volumn 93, Issue 18, 2004, Pages

  Mounaix, Philippe ^a   Divol, Laurent ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AMPLIFICATION; BENCHMARKING; ELECTRIC FIELDS; LARGE SCALE SYSTEMS; LASER BEAMS; MATHEMATICAL MODELS; RANDOM PROCESSES;

CONVECTIVE AMPLIFICATION; LARGE HOMOGENEOUS SYSTEMS (HS); SCATTERING INSTABILITIES;

AMPLIFIERS (ELECTRONIC);

EID: 19744381960     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.185003     Document Type: Article

References (19)

1. G. Lavai et al., Phys. Fluids 20, 2049 (1977); E. A. Williams, J. R. Albritton, and M. N. Rosenbluth, Phys. Fluids 22, 139 (1979); and references therein.
2. G. Lavai et al., Phys. Fluids 20, 2049 (1977); E. A. Williams, J. R. Albritton, and M. N. Rosenbluth, Phys. Fluids 22, 139 (1979); and references therein.
3. H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994).
4. Ph. Mounaix et al., Phys. Rev. Lett. 85, 4526 (2000).
5. H.A. Rose and D. F. DuBois, Phys. Fluids B 5, 590 (1993); J. Garnier, Phys. Plasmas 6, 1601 (1999); and references therein.
6. H.A. Rose and D. F. DuBois, Phys. Fluids B 5, 590 (1993); J. Garnier, Phys. Plasmas 6, 1601 (1999); and references therein.
7. Ph. Mounaix, Phys. Rev. Lett 87, 085006 (2001).
8. J. Adler, The Geometry of Random Fields (Wiley, New York, 1981).
9. Use, e.g., Eq. (1.10) of P. Cartier and C. DeWitt-Morette, J. Math. Phys. (N.Y.) 36, 2237 (1995).
10. Ph. Mounaix and L. Divol, Phys. Rev. Lett. 89, 165005 (2002).
11. If this expansion does not exist, (1) does not admit any well defined HS model.
12. N. Kaiser, Astrophys. J. 284, L9 (1984); J.M. Bardeen et al., Astrophys. J. 304, 15 (1986).
13. N. Kaiser, Astrophys. J. 284, L9 (1984); J.M. Bardeen et al., Astrophys. J. 304, 15 (1986).
14. 2.
15. The proof consists in showing that the conditional probability distributions P(Δu\Lu ≥ r) and P(δ\Lu ≥ r) do not depend on r as r →+∞.
16. 2 convergence to pointwise convergence is allowed since all the stochastic fields in play are continuous with probability 1.
17. 1, which does not possess any well defined deterministic profile.
18. 2D is a 2D top-hat random-phase-plate field; Y. Kato et al., Phys. Rev. Lett. 53, 1057 (1984).
19. Temporal smoothing and departure from strongly damped regime bring about an intricate space-time behavior, which makes the situation unclear.