Abstract

An asymptotic theory of classical anisotropic diffusion in inhomogeneous media has been developed based on the differential geometry formalism taken from the general theory of relativity. A simple analytical formula is obtained for concentration; the elements of this formula are linear integrals along the geodesic (concentration signal trajectory). The trajectory follows from the variational principle (to which the exponential factor in the expression for concentration obeys) and is determined from the first-order ordinary differential equation for the vector tangent to the geodesic. The theory is valid for distances from the impurity source that exceed significantly the size of the main localization region of impurity.

中文翻译：

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非均匀介质中各向异性经典扩散的渐近理论

摘要

非均匀介质中经典各向异性扩散的渐近理论已经基于广义相对论的微分几何形式主义发展起来。得到一个简单的浓度分析公式；该公式的元素是沿测地线（浓度信号轨迹）的线性积分。轨迹遵循变分原理（浓度表达式中的指数因子遵循该原理），并由测地线的向量切线的一阶常微分方程确定。该理论对于距杂质源的距离明显超过杂质主要定位区域的尺寸是有效的。