论文标题
分数对流扩散 - 空气对称方程
Fractional advection-diffusion-asymmetry equation
论文作者
论文摘要
分数动力学方程利用非全能计算来模拟许多系统中的异常松弛和扩散。尽管对这种方法进行了充分的探索，但到目前为止，它未能描述无序系统中重要的运输类别。在地质形成中污染物扩散的工作中，我们提出并研究了描述偏见扩散数据包的分数对流扩散方程。虽然通常通过扩散和漂移来描述通常的运输，但我们发现了一个描述对称性破坏的第三项，该术语无处不在，用于无序系统中的运输。我们的工作基于连续时间随机步行，并具有有限的平均等待时间和不同的差异，而这种情况一方面很普遍，另一方面是分数方程的万花筒文献中缺少的情况。分数太空衍生物源于较长的捕获时间，而以前它们是由于空间L {é} Vy飞行而被解释的。
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems. Motivated by work on contaminant spreading in geological formations we propose and investigate a fractional advection-diffusion equation describing the biased spreading packet. While usual transport is described by diffusion and drift, we find a third term describing symmetry breaking which is omnipresent for transport in disordered systems. Our work is based on continuous time random walks with a finite mean waiting time and a diverging variance, a case that on the one hand is very common and on the other was missing in the kaleidoscope literature of fractional equations. The fractional space derivatives stem from long trapping times while previously they were interpreted as a consequence of spatial L{é}vy flights.
