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摘要翻译：
污染物颗粒在裂隙岩石或多孔沉积物等复杂环境中的运动往往具有反常扩散的特征：由于存在阻碍颗粒迁移的障碍物，污染物运移量的扩散在时间上很早就长大了。这些系统的渐近行为通常用分数阶扩散很好地描述，它为反常输运的建模提供了一个优雅而统一的框架。我们表明，对分数扩散的预渐近修正可能会变得相关，这取决于粒子的微观动力学。为了考虑这些影响，我们推导了一个修正的输运方程，并通过蒙特卡罗模拟验证了它的有效性。
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英文标题：
《Pre-asymptotic corrections to fractional diffusion equations》
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作者：
M. Marseguerra, A. Zoia
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最新提交年份：
2008
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分类信息：
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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英文摘要：
The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to the presence of obstacles which hinder particle migration. The asymptotic behavior of these systems is usually well described by fractional diffusion, which provides an elegant and unified framework for modeling anomalous transport. We show that pre-asymptotic corrections to fractional diffusion might become relevant, depending on the microscopic dynamics of the particles. To incorporate these effects, we derive a modified transport equation and validate its effectiveness by a Monte Carlo simulation.
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PDF链接：
https://arxiv.org/pdf/711.1947
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