Abstract

An asymptotic theory of impurity transport has been developed for the simplest regularly inhomogeneous medium (Dykhne model, demonstrating subdiffusive transport regime) with parameters obeying large-scale spatial dependences. The results for concentration at distances from impurity source greatly exceeding the size of main impurity localization region are expressed in terms of linear integrals along concentration-signal trajectories. The latter are obtained from the variational principle, which is an analogue of the Fermat principle in geometric optics. Integrals along trajectories are analogues of optical path length. The form of these integrals depends on transport regime, and the trajectories may be either 2D and 3D curves (depending on the regime).

中文翻译：

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具有坐标相关参数的 Dykhne 模型中的非经典杂质传输。费马原理

摘要

已经为最简单的规则非均匀介质（Dykhne 模型，展示了亚扩散传输机制）开发了杂质传输的渐近理论，其参数服从大尺度空间依赖性。距离杂质源远超过主要杂质定位区域尺寸的浓度结果用沿浓度信号轨迹的线性积分表示。后者是从变分原理中获得的，它是几何光学中费马原理的类似物。沿轨迹的积分类似于光路长度。这些积分的形式取决于传输状态，并且轨迹可以是 2D 和 3D 曲线（取决于状态）。