论文标题
广义扩散方程与时空非局部性。内存功能建模
Generalized diffusion equation with nonlocality of space-time. Memory function modelling
论文作者
论文摘要
我们提出了一种通用方法，用于通过将liouville方程与分数衍生物一起用于经典粒子系统和Zubarev的非平衡统计运算符（NSO）方法，以获取具有分数衍生物的广义传输方程。 在空间异质环境中，具有分形结构和广义的Cattaneo-Maxwell扩散方程的新的非马克维亚扩散方程，并考虑了时空非局部性。 发现Cattaneo-Maxwell扩散方程的分散关系，并考虑到分数衍生物的时空非局部性。 计算频谱，相位和组速度。 结果表明，它具有不连续性的波浪行为， 这也体现在相速度的行为中。
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium statistical operator (NSO) method within Gibbs statistics. The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo-Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations are found for the Cattaneo-Maxwell diffusion equation with taking into account the space-time nonlocality in fractional derivatives. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behaviour with discontinuities, which are also manifested in the behaviour of the phase velocity.
