标题： 信息论方法在流变学中松弛时间分布的研究：对数正态松弛谱模型 显示英文标题

标题： Information-Theoretical Approach to Relaxation Time Distribution in Rheology: Log-Normal Relaxation Spectrum Model

摘要： 粘弹性流体的松弛模量可以分解为多个麦克斯韦模型，并通过松弛时间的松弛谱进行表征。 经验上已知对数松弛时间有助于表达松弛谱。 我们使用信息几何来分析松弛模量，并表明对数松弛时间是松弛谱最自然的变量。 然后我们使用信息论来估计松弛谱最可能的函数形式。 我们证明对数正态分布是信息理论上最可能的松弛谱。 我们分析了对数正态松弛谱模型的特性，并将其与分数阶麦克斯韦模型进行比较。 具有小幂律指数的分数阶麦克斯韦模型可以近似为具有大标准差的对数正态松弛谱模型。 我们还将对数正态松弛谱模型与高密度聚乙烯在熔融状态和固态下的实验线性粘弹性数据进行了比较。 显示英文摘要

摘要： The relaxation modulus of a viscoelastic fluid can be decomposed into multiple Maxwell models and characterized by the relaxation spectrum for the relaxation time. It is empirically known that the logarithmic relaxation time is useful to express the relaxation spectrum. We use information geometry to analyze the relaxation modulus and shown that the logarithmic relaxation time is the most natural variable for the relaxation spectrum. Then we use information theory to estimate the most probable functional form for the relaxation spectrum. We show that the log-normal distribution is the information-theoretically most probable relaxation spectrum. We analyze the properties of the log-normal relaxation spectrum model and compare it with the fractional Maxwell model. The fractional Maxwell model with a small power-law exponent can be approximated as the log-normal relaxation spectrum model with a large standard deviation. We also compare the log-normal relaxation spectrum model with experimental linear viscoelasticity data for a high-density polyethylene, both at melt and solid states.