Quantitative analysis of non-equilibrium phase transition process by the catastrophe theory

Abstract

Catastrophe theory is a highly generalized mathematical theory that summarizes the rules of non-equilibrium phase transition by several catastrophe models. This paper investigates the general non-equilibrium 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.