摘要翻译：
本文介绍了具有异常亚扩散的化学趋化的介观和宏观模型方程，用于模拟生物在变化的化学环境中的化学定向迁移，扩散受到陷阱或大分子拥挤的阻碍。细观模型采用连续时间随机游动主方程，宏观模型采用分数阶微分方程。根据趋化强迫的时间不同，提出了不同的模型。本文还导出了包括线性反应动力学的模型的推广。最后介绍了一种模拟具有趋化性的反常子扩散的Monte Carlo方法，并将模拟结果与模型方程的数值解进行了比较。本文所建立的模型方程可以用来代替被陷阱、大分子拥挤或其他障碍阻碍运输的生物系统中的Keller-Segel型方程。
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英文标题：
《Fractional Chemotaxis Diffusion Equations》
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作者：
T.A.M. Langlands, B.I. Henry
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Dynamical Systems        动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
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PDF链接：
https://arxiv.org/pdf/1003.1548