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Fractional anomalous diffusion with Cattaneo-Christov flux effects in a comb-like structure

机译：梳状结构中具有Cattaneo-Christov通量效应的分数异常扩散

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摘要

This paper investigates the fractional anomalous transport of particles in a comb-like structure. The higher spatial gradients are introduced in the constitutive relationship between the flux and the particles distribution and the effects of Cattaneo-Christov flux are taken into account. Formulated fractional governing equation displays a parabolic character for α in (0, 0.5) and the coexisting characteristics of the parabolic and hyperbolic for α→1 with relaxing parameter effect When the relaxing parameter equals to zero, the equation reduces a parabolic equation which is derived from the classical Fick's first law of diffusion. Solutions are obtained numerically by using L1 - and L2-approximations for fractional derivative. The effects of the involved parameters on particles distribution behavior are shown graphically and analyzed. Results indicate that the anomalous transport of particles possesses both diffusion and wave characteristics with the existence of relaxing time and for α → 1. Meanwhile, the formation of cusps has been discussed in detail.
机译：本文研究了梳状结构中颗粒的分数异常输送。在通量和颗粒分布之间的本构关系中引入了较高的空间梯度，并考虑到Cattaneo-Christov通量的影响。公式化的分数控制方程具有（0，0.5）中的α的抛物线特性，以及具有松弛参数效应的α→1的抛物线和双曲线的共存特性当松弛参数等于0时，该方程式简化了导出的抛物线方程来自古典菲克的第一扩散定律。通过使用分数导数的L1-和L2-逼近来数值求解。图形显示并分析了所涉及参数对颗粒分布行为的影响。结果表明，随着弛豫时间的存在和α→1的存在，颗粒的反常输运具有扩散和波动的特征。同时，对尖峰的形成也进行了详细的讨论。

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  • 来源
    《Applied Mathematical Modelling》 |2016年第14期|6663-6675|共13页
  • 作者

    Lin Liu; Liancun Zheng; Xinxin Zhang;

  • 作者单位

    School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China,School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;

    School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;

    School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Comb structure; Cattaneo-Christov flux model; Anomalous diffusion; Time fractional derivative;

    机译：梳状结构Cattaneo-Christov通量模型;异常扩散;时间分数导数;

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