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首页> 外文期刊>Applied Mathematical Modelling >Macroscopic and microscopic anomalous diffusion in comb model with fractional dual-phase-lag model
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Macroscopic and microscopic anomalous diffusion in comb model with fractional dual-phase-lag model

机译：分数双相滞后模型的梳形模型的宏观和微观异常扩散

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摘要

A novel constitutive equation which considers the macroscopic and microscopic relaxation characteristics and the memory and nonlocal characteristics is proposed to describe the anomalous diffusion in comb model. Formulated governing equation with the fractional derivative of order 1 + αcorresponds to a diffusion-wave one and solutions are obtained analytically with the Laplace and Fourier transforms. As the solutions show, the existence of macroscopic relaxation parameter makes the expression of mean square displacement contain an integral form and the specific value for the microscopic relaxation parameter and macroscopic one changes the coefficient of fractional integral. The particle distribution and mean square displacement of Fick's model and the dual-phase-lag model are same at the short and long time behaviors and the special case of equal macroscopic and microscopic relaxation parameters. The particle distributions and mean square displacement with the effects of different parameters are presented graphically. Results show that the wave characteristic becomes stronger for a largerα, a largerτqor a smallerτP. For mean square displacement, the magnitude is larger at the short time behavior and smaller at the long time behavior for a smallerα. Besides, for a smallerτqor a largerτP, the magnitude is larger.
机译：提出了一种考虑宏观和微观弛豫特性以及记忆和非局部特性的本构方程，用于描述梳形模型中的反常扩散。用阶导数为1 +derivativeα的分数导数制定的控制方程与一个扩散波一对应，并通过拉普拉斯和傅立叶变换解析地获得了解。如解所示，宏观弛豫参数的存在使均方位移的表达式包含一个积分形式，微观弛豫参数和宏观变量的特定值改变了分数积分的系数。在短期和长期行为以及宏观和微观弛豫参数相等的特殊情况下，Fick模型和双相滞后模型的粒子分布和均方位移均相同。图形显示了在不同参数作用下的颗粒分布和均方位移。结果表明，对于较大的α，较大的τq或较小的τP，波动特性变得更强。对于均方位移，对于较小的α，其大小在短期行为中较大，而在长期行为中较小。另外，对于较小的τq或较大的τP，幅度较大。

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