分数阶对流扩散不对称方程
Fractional advection-diffusion-asymmetry equation
摘要：
分数阶动力学方程采用非整数微积分来模拟许多系统中的反常弛豫和扩散。虽然这种方法被很好地探索，但到目前为止，它未能描述无序系统中的一类重要的输运。受地质构造中污染物扩散研究工作的启发，我们提出并研究了描述有偏扩散包的分数阶对流扩散方程。虽然通常的运输所描述的扩散和漂移，我们发现第三项描述对称性破缺是无所不在的运输无序系统。我们的工作是基于连续时间随机游走有限的平均等待时间和发散方差，这种情况下，一方面是非常常见的，另一方面是失踪的万花筒文学的分数方程。分数空间导数源于长捕获时间，而以前它们被解释为空间L{é}vy飞行的结果。
英文摘要：
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.
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