论文标题
在球体上的分数和缩放的布朗运动：长期相关对导航策略的影响
Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies
论文作者
论文摘要
我们在二维球上分析\ emph {分数布朗运动}和\ emph {scaled brownian运动} $ \ mathbb {s}^{2} $。我们发现，固有的长时间相关性表征了分数布朗运动与在表面上进行的特定动力学（\ emph {导航策略}）相关的，从而产生了丰富的运输特性。我们将研究重点放在两类的导航策略上：一种是由一组特定的坐标诱导的，以$ \ mathbb {s}^2 $（我们在当前分析中选择了球形），为此，我们发现与这种长期相关性的情况相反，\ emph {non-equilibiribiul atnections}是相反的。这些结果类似于在一个和二维中的密闭平面中报告的结果[Guggenberger {\ it等} New J. Phys。 21 022002（2019），vojta {\ it等人}物理。 Rev. E 102，032108（2020）]，但是在此处分析的情况下，没有任何边界会影响球体上的运动。相反，当选择的导航策略对应于用粒子（Frenet-Serret参考系统）移动的参考框架时，则在长期限制中恢复了球体上的\ emph {emph {equilibrium} \ emph {Distribution}。对于两种导航策略，固定分布的放松时间取决于赫斯特参数的特定值。 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 the analytical calculations obtained from the solution of a time-dependent diffusion equation on $\mathbb{S}^{2}$, and the numerical results obtained from our numerical生成轨迹合奏的方法。
We analyze \emph{fractional Brownian motion} and \emph{scaled Brownian motion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that the intrinsic long time correlations that characterize fractional Brownian motion collude with the specific dynamics (\emph{navigation strategies}) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for $\mathbb{S}^2$ (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, \emph{non-equilibrium stationary distributions} are attained. These results resemble those reported in confined flat 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)], however in the case analyzed here, there are no boundaries that affects the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the \emph{equilibrium} \emph{distribution} on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times towards the stationary distribution depend on the particular value of the Hurst parameter. 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 the analytical calculations obtained from the solution of a time-dependent diffusion equation on $\mathbb{S}^{2}$, and the numerical results obtained from our numerical method to generate ensemble of trajectories.
