Simple extension of Suzuki's scaling approach to the onset time of an unstable state: Application to supercooled liquid

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Abstract
Motivated by the experimental findings of the onset time of a supercooled liquid, we extend Suzuki's scaling method to include the case of a time-dependent externally controlled growth rate. The simple application of this modified nonlinear-time-scale transformation leads to the following predictions: the deeper one quenches the sample, or the longer one waits before heating the sample, or the more the heating of the sample, the shorter the onset time of the freezing process. Its inadequacy to explain the quench-rate dependence of the onset time suggests that a similar examination of a two-mode theory may be the key to the behavior of the fusion phenomenon of supercooled liquid.