Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7377952 | Physica A: Statistical Mechanics and its Applications | 2016 | 17 Pages |
Abstract
We analyze the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, and specifically how they modify the Poissonian switching-time statistics. After addressing simple cases such as diffusion in a channel, and the switching statistics in the presence of a polarization potential, we thoroughly study Poisson-Kac diffusion in fractal domains. Diffusion in fractal spaces highlights neatly how the modification in the switching-time statistics associated with reflections against a complex and fractal boundary induces new emergent features of Poisson-Kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli,