Other
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phdt........12c&link_type=abstract
Thesis (PhD). COLUMBIA UNIVERSITY, Source DAI-B 61/04, p. 1989, Oct 2000, 176 pages.
Other
7
Scientific paper
The traditional singular perturbation method is modified by constraining the solvability condition to be used on the partial sum of the perturbative series rather than on each term. The procedure is applied to the study of kinetic equations and transport theories. When applied to the relaxation model of the classical Boltzmann equation, the new procedure leads to a set of transport equations different from the traditional Navier-Stokes formulism. With these equations, a new mechanism of producing bulk viscosity is uncovered. This bulk viscosity is independent of the structure of the particles and it is a universal feature of nonequilibrium. It is also found that the gradient of temperature has a contribution to the transport of momentum and the fluid acceleration has a contribution to the heat current. These transport equations are applied to ultrasonic oscillations and shock structures and produce a significant improvement over other macroscopic theories. In extending the often-used Eddington approximation in radiation transfer, a resummation procedure is developed and used to derive a closure relation which works well even in the optically thin limit to produce a nonlocal shear tensor. The transport coefficients are uniquely determined through the calculation of the comoving entropy generation. When scattering is included, it is found that the bulk viscosity can be much larger than the other transport coefficients when the Thompson electron scattering dominates the absorption. This may have significant effects on estimates of the entropy generation of the early universe. The application of the method to a one-component relativistic fluid results in a first-order relativistic hydrodynamics, which is free from the causality problem inherent in the standard first-order relativistic hydrodynamics by Eckart and Landau-Lifshitz. The simplest application of the formalism to a model expanding universe shows that the bulk viscosity due to the nonequilibrium process is capable of driving or sustaining an inflationary stage and generating the right amount of the comoving entropy during the inflation.
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