Logarithmically slow expansion of hot bubbles in gases

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 1403-1406

  Meerson, Baruch ^a   Sasorov, Pavel V ^a   Sekimoto, Ken ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPACT SUPPORT; DYNAMIC SCALING; LOGARITHMIC CORRECTIONS; MATCHED ASYMPTOTIC EXPANSION; MODEL PROBLEMS; TEMPERATURE PROFILES;

EXPANSION;

EID: 0000316279     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.1403     Document Type: Article

References (18)

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10. Alternatively, one obtains a nonlinear diffusion equation for the gas density, (Formula presented), with the effective diffusion coefficient decreasing with (Formula presented). This equation appeared in a number of nonlinear diffusion problems where (Formula presented) decays at (Formula presented) 17. In the hot bubble problem (Formula presented) at (Formula presented), and this difference results in quite a different dynamics.
11. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
12. The heat flux (Formula presented) should be continuous. For (Formula presented) it implies (Formula presented).
13. Shrinking is possible when a cold “cloud” is heated by a hot and underdense peripheral gas. A problem mathematically equivalent to this one was considered in Ref. 17.
14. In reality, the temperature should approach a finite value at large distances. Correspondingly, the solution we are interested in represents an intermediate asymptotics 2.
15. If (Formula presented) is a solution of Eq. (3), then (Formula presented) is also a solution for any (Formula presented). This property enables one to restore the k dependence in the final results.
16. S. Wolfram, The Mathematica Book, 3rd ed. (Cambridge University Press, Cambridge, England, 1996).
17. Y. Kurzweil, E. Livne, and B. Meerson (unpublished).
18. P. Rosenau, Phys. Rev. Lett. 74, 1056 (1995).