The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state （endowed some deviation from the conventionally assumed cosmic perfect fluid model）....The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state （endowed some deviation from the conventionally assumed cosmic perfect fluid model）. We assume the bulk viscosityis a linear combination of two terms： one is constant, and the other is proportional to the scalar expansion 0 = 3a/a. The equation of state is described as p = （γ - 1）p ＋ po, where po is a parameter. In this framework we demonstrate that this model can be used to explain the dark energy dominated universe, and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolution： no future singularity, big rip, or Type-Ⅲ singularity as presented in IS. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71 （2005） 063004].展开更多
The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic com...The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic compatibility and mechanical ana- logue have not yet been properly considered. In the present study, by discussing both these issues, we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct. Based on this generalized Jeffreys fluid, a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.展开更多
基金The project partly supported by National Natural Science Foundation of China under Grant No. 10675062 and the Doctoral Foundation of China We thank Profs. I. Brevik, S.D. 0dintsov, and Lewis H. Ryder for lots of interesting discussions.
文摘The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state （endowed some deviation from the conventionally assumed cosmic perfect fluid model）. We assume the bulk viscosityis a linear combination of two terms： one is constant, and the other is proportional to the scalar expansion 0 = 3a/a. The equation of state is described as p = （γ - 1）p ＋ po, where po is a parameter. In this framework we demonstrate that this model can be used to explain the dark energy dominated universe, and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolution： no future singularity, big rip, or Type-Ⅲ singularity as presented in IS. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71 （2005） 063004].
基金supported by the National Natural Science Foundation of China(Grant No. 10972117)
文摘The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic compatibility and mechanical ana- logue have not yet been properly considered. In the present study, by discussing both these issues, we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct. Based on this generalized Jeffreys fluid, a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.
