English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We disclose the origin of anisotropic percolation perimeters in terms of theStochastic Loewner Evolution (SLE) process. Precisely, our results fromextensive numerical simulations indicate that the perimeters of multi-layeredand directed percolation clusters at criticality are the scaling limits of theLoewner evolution of an anomalous Brownian motion, being subdiffusive andsuperdiffusive, respectively. The connection between anomalous diffusion andfractal anisotropy is further tested by using long-range power-law correlatedtime series (fractional Brownian motion) as driving functions in the evolutionprocess. The fact that the resulting traces are distinctively anisotropiccorroborates our hypothesis. Under the conceptual framework of SLE, our studytherefore reveals new perspectives for mathematical and physicalinterpretations of non-Markovian processes in terms of anisotropic paths atcriticality and vice-versa.

Stochastic Loewner Evolution Relates Anomalous Diffusion and Anisotropic Percolation