论文期刊

The quantitative catastrophe model of non-equilibrium phase transform process by the catastrophe theory




作者: Xiao Liang, Jiu Hui Wu, H. B. Zhong
发表/完成日期: 2017-08-03
期刊名称: Physics of Fluidics
期卷: Vol.29, No.8
相关文章: The quantitative catastrophe model of non-equilibrium phase transform process by the catastrophe theory.pdf    An enhanced catastrophe theory that explains turbulence.pdf.pdf   
论文简介
Catastrophe theory is a highly generalized mathematical theory that summarizes the rules of nonequilibrium phase transition by several catastrophe models. This paper investigates the general nonequilibrium phase transition process quantitatively using catastrophe theory for the first time, to our
knowledge. First, a new approach is proposed by combining the catastrophe theory with dimensionless
analysis. Second, the new approach is applied to two classic examples: one is the turbulent phase
transition and the other is the bottleneck effect of particle flow. For the turbulence phase transition
process, the quantitative relationships are obtained. Comparing with Kolmogorov’s turbulent theory,
the new method proposed in this paper is able to evaluate not only the complete turbulence condition
but also the development of turbulence, and Kolmogorov’s turbulent theory is only a special case
of our results by this new approach. For the particle flow bottleneck effect, the results obtained by
this new method correspond with the empirical formulated results. Therefore, the proposed method
can solve non-equilibrium phase transition process problems and has the potential to extend to fluid,
aerodynamics, and so forth.