On the Stochastic Modeling of Phase Transitions and the Behavior Analysis by Simulations

Phase transition phenomena are often observed in various kinds of fields of engineering, including chemical, biological and fluid engineering. To construct precise models of phase transitions and their analysis are one of very important problems in engineering. Usually, phase transition phenomena are modeled by the order parameter, which is classified into the conserved and nonconserved type. In this paper, using two types of the order parameter, we propose models of two kinds of phase transitions. One is the model of phase separation phenomena and the other is the model of the orderdisorder transitions. Thermal fluctuation and disturbance such as impurities in chemical substances play an important role in phase transitions, so in this paper, we propose stochastic models of phase transitions and analyse behavior and influence of the disturbance on the phase transition through simulations.