体温计模型的临界行为

CRITICAL BEHAVIORS OF A CLINICAL THERMOMETER MODEL

提出一个可用离散朗之万方程描述的体温计模型.该体温计的特点是其温度示数只能随外界温度的升高而上升,当外界温度降低时,其示数却不能下降.根据体温计示数这种只升不降的特点,定义了“停顿”事件.用随机行走的理论解析地推导了停顿时间分布函数数值模拟和解析结果都显示这种分布函数呈幂律形式D(S)∝s^(-ε),揭示出在这一过程中所表现出的临界性.

A clinical thermometer model is proposed, which can be described by discrete Langevin equation. The characteristic of the clinical thermometer is that its reading can only increase with the increasing of its temperature, but cannot fall even when its temperature decreases. 'Pause' events are defined according to the non-decreasing character of the reading. Using the random walk thoery, we derive analitically the distribution of the duration of the pause events. Both numerical and analytical results show that the distribution function has the form of a power law D(s)∝s-ξ, indicting the critical behavior in this process.