Masoliver Jaume, Lindenberg Katja
Department of Condensed Matter Physics and Institute of Complex Systems (UBICS), University of Barcelona, 08028 Catalonia, Spain.
Department of Chemistry and Biochemistry and BioCircuits Institute, University of California, San Diego 92093-0340, USA.
Phys Rev E. 2020 Jan;101(1-1):012137. doi: 10.1103/PhysRevE.101.012137.
We study the planar motion of telegraphic processes. We derive the two-dimensional telegrapher's equation for isotropic and uniform motions starting from a random walk model which is the two-dimensional version of the multistate random walk with a continuum number of states representing the spatial directions. We generalize the isotropic model and the telegrapher's equation to include planar fractional motions. Earlier, we worked with the one-dimensional version [Masoliver, Phys. Rev. E 93, 052107 (2016)PREHBM2470-004510.1103/PhysRevE.93.052107] and derived the three-dimensional version [Masoliver, Phys. Rev. E 96, 022101 (2017)PREHBM2470-004510.1103/PhysRevE.96.022101]. An important lesson is that we cannot obtain the two-dimensional version from the three-dimensional or the one-dimensional one from the two-dimensional result. Each dimension must be approached starting from an appropriate random walk model for that dimension.
我们研究电报过程的平面运动。我们从一个随机游走模型出发，推导了各向同性和均匀运动的二维电报方程，该随机游走模型是多态随机游走的二维版本，其中具有连续数量的状态来表示空间方向。我们将各向同性模型和电报方程推广到包括平面分数运动。此前，我们研究了一维版本[马索利弗，《物理评论E》93，052107(2016年)PREHBM2470 - 004510.1103/PhysRevE.93.052107]并推导了三维版本[马索利弗，《物理评论E》96，022101(2017年)PREHBM2470 - 004510.1103/PhysRevE.96.022101]。一个重要的教训是，我们不能从三维版本得到二维版本，也不能从二维结果得到一维版本。每个维度都必须从适用于该维度的适当随机游走模型开始进行研究。
