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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We analyze \emph{fractional Brownian motion} and \emph{scaled Brownianmotion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that theintrinsic long time correlations that characterize fractional Brownian motioncollude with the specific dynamics (\emph{navigation strategies}) carried outon the surface giving rise to rich transport properties. We focus our study ontwo classes of navigation strategies: one induced by a specific set ofcoordinates chosen for $\mathbb{S}^2$ (we have chosen the spherical ones in thepresent analysis), for which we find that contrary to what occurs in theabsence of such long-time correlations, \emph{non-equilibrium stationarydistributions} are attained. These results resemble those reported in confinedflat spaces in one and two dimensions [Guggenberger {\it et al.} New J. Phys.21 022002 (2019), Vojta {\it et al.} Phys. Rev. E 102, 032108 (2020)], howeverin the case analyzed here, there are no boundaries that affects the motion onthe sphere. In contrast, when the navigation strategy chosen corresponds to aframe of reference moving with the particle (a Frenet-Serret reference system),then the \emph{equilibrium} \emph{distribution} on the sphere is recovered inthe long-time limit. For both navigation strategies, the relaxation timestowards the stationary distribution depend on the particular value of the Hurstparameter. We also show that on $\mathbb{S}^{2}$, scaled Brownian motion,distinguished by a time-dependent diffusion coefficient with a power-scaling,is independent of the navigation strategy finding a good agreement between theanalytical calculations obtained from the solution of a time-dependentdiffusion equation on $\mathbb{S}^{2}$, and the numerical results obtained fromour numerical method to generate ensemble of trajectories.

Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies