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arXiv · 1507.08851

On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes

Massimiliano Giona·Antonio Brasiello·Silvestro Crescitelli
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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.

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Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli. 2015-07-31. On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes. https://doi.org/10.1016/j.physa.2015.12.142

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