A Demonstration Bench for Representing the Character of Phase Transitions of the First and Second Kind

Abstract

The paper presents the description of a demonstration bench, which includes a mathematical model and analysis tools for understanding the features of phase transitions of the first and second kind. The advantage of this demonstration bench is the rejection of all phenomenology and the obvious limitation of the application of various approximations and hypotheses. The description is formed on the well-known equations of hydrodynamics, which are well-tested and are a reliable basis for the construction of realistic models. The Proctor-Sivashinsky model, which was used to describe the process of convection development in a thin layer of liquid with poorly conductive heat boundaries, is the basis for the demonstration bench. Exactly this model allows to observe phase transitions of the first and second kind. The feature of the model is that it allocates one spatial scale of interaction, leaving for the evolution of the system the possibility to choose the nature of symmetry. All spatial disturbances of the same size but of different orientation interact with each other. This allows us not to distract from the main task of this work, which is to demonstrate the process of structure formation as a result of a cascade of phase transitions. The mechanism of phase transitions associated with the presence of minimums of the interaction coefficients of modes of the spectrum of the instability. There are a large number of structural defects, which appear as attributes of phase transition. The instability spectrum modes interference is the reason of the high rate of correlations in the propagation of a new phase.