Rukolaine S A, Samsonov A M
The Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 26 Polytekhnicheskaya, St. Petersburg 194021, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062116. doi: 10.1103/PhysRevE.88.062116. Epub 2013 Dec 10.
We consider the Jeffreys-type equation as the foundation in three different models of mass transfer, namely, the Jeffreys-type and two-phase models and the D(1) approximation to the linear Boltzmann equation. We study two classic (1+1)-dimensional problems in the framework of each model. The first problem is the transfer of a substance initially confined at a point. The second problem is the transfer of a substance from a stationary point source. We calculate the mean-square displacement (MSD) for the solutions of the first problem. The temporal behavior of the MSD in the framework of the first and third models is found to be the same as that in the Brownian motion described by the standard Langevin equation. In addition, we find a remarkable phenomenon when a portion of the substance does not move.
我们将杰弗里斯型方程视为三种不同传质模型的基础，即杰弗里斯型和两相模型以及线性玻尔兹曼方程的D(1)近似。我们在每个模型的框架内研究两个经典的(1 + 1)维问题。第一个问题是最初局限于一点的物质的转移。第二个问题是物质从静止点源的转移。我们计算了第一个问题解的均方位移(MSD)。发现在第一个和第三个模型框架内MSD的时间行为与标准朗之万方程描述的布朗运动中的相同。此外，当一部分物质不移动时，我们发现了一个显著的现象。
