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Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.

The frequency and extent of debris flows have increased tremendously due to the extreme weather and the Wenchuan earthquake on May 12, 2008. Previous studies focused on the debris flow from gullies damming the mountain streams. In this paper, an equation for the run-out distance of debris flow in the main river is proposed based on the dynamic equation of debris flow at different slopes given by Takahashi. By undertaking field investigations and flume experiments, a new calculation method of the volume of debris flow damming large river is obtained. Using the percolation theory and the renormalization group theory it was deduced that the large particles should comprise more than 50% for forming a stable debris flow dam. Hence, the criteria of damming large river by debris flow is presented in terms of run-out distance and grain composition which was then validated through the event of damming river by debris flow at Gaojia gully, the upper reaches of the Minjiang River, Sichuan, China, on July 3, 2011.