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

A combined dynamics consisting of Brownian motion and L\'evy flights isexhibited by a variety of biological systems performing search processes.Assessing the search reliability of ever locating the target and the searchefficiency of doing so economically of such dynamics thus poses an importantproblem. Here we model this dynamics by a one-dimensional fractionalFokker-Planck equation combining unbiased Brownian motion and L\'evy flights.By solving this equation both analytically and numerically we show that thesuperposition of recurrent Brownian motion and L\'evy flights with stableexponent $\alpha<1$, by itself implying zero probability of hitting a point ona line, lead to transient motion with finite probability of hitting any pointon the line. We present results for the exact dependence of the values of boththe search reliability and the search efficiency on the distance between thestarting and target positions as well as the choice of the scaling exponent$\alpha$ of the L\'evy flight component.

Search reliability and search efficiency of combined L\'evy-Brownian motion: long relocations mingled with thorough local exploration