Computer Science – Sound
Scientific paper
Dec 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000head....5.4417b&link_type=abstract
American Astronomical Society, HEAD Meeting #5, #44.17; Bulletin of the American Astronomical Society, Vol. 32, p.1653
Computer Science
Sound
Scientific paper
In the two-fluid model for the diffusive acceleration of cosmic rays in supernova shock waves, 1, 2, or 3 distinct solutions for the flow structure can be found depending on the upstream parameters. The available solutions can include both smooth and discontinuous transitions. However, the precise nature of the critical conditions delineating the number and character of possible shock transitions has remained unclear, mainly due to the inappropriate choice of parameters used in the determination of the upstream boundary conditions. In this talk, we derive the exact critical conditions by reformulating the upstream boundary conditions in terms of two individual Mach numbers defined with respect to the cosmic-ray and gas sound speeds. We assume that the gas and cosmic-ray adiabatic indices have constant values. Our results provide for the first time a complete, analytical classification of the parameter space of shock transitions in the two-fluid model. In addition to classifying the parameter space, we have also examined the question of stability when multiple solutions are available. We show that the Boltzmann entropy of the combined gas/particle system can be used to discriminate between the various solutions. Once the entropy is calculated, application of the second law of thermodynamics allows indentification of the most stable configuration.
Becker Peter A.
Kazanas Demos
Le Truong
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