摘要翻译：
我们提出了一个在非均匀环境中的异常迁移模型，如裂隙岩石，其中颗粒只沿着预先存在的自相似曲线（裂隙）移动。利用随机Loewner方程可以有效地生成分形维数为d_f$的可调曲线。我们用数值方法计算了从半无限平面边缘的一点到半径$R$的半圆上任意一点的首次通过概率（长度或时间）。标度概率分布的方差随d_f$增加，偏度非单调，尾部衰减快于简单指数分布。后者与基于分数动力学的预测形成鲜明对比，并为我们的模型提供了一个实验标志。
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英文标题：
《First passage times and distances along critical curves》
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作者：
A. Zoia, Y. Kantor, M. Kardar
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最新提交年份：
2007
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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：
  We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate such curves with tunable fractal dimension $d_f$. We numerically compute the probability of first passage (in length or time) from one point on the edge of the semi-infinite plane to any point on the semi-circle of radius $R$. The scaled probability distributions have a variance which increases with $d_f$, a non-monotonic skewness, and tails that decay faster than a simple exponential. The latter is in sharp contrast to predictions based on fractional dynamics and provides an experimental signature for our model.
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PDF链接：
https://arxiv.org/pdf/705.1474