Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated non-monotonous behavior, which results in transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to superballistic one and turns at still later times into subdiffusion; eventually normal diffusion is achieved. Our theory agrees very well with the MD results, although extreme computational costs prevented to detect the final diffusion regime. Qualitatively, the reported intermediate diffusion regimes are generic for granular gases with any realistic dependence of the restitution coefficient on the impact velocity.
Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
Path integral formulation of fractional Brownian motion for general Hurst exponent
在J.Phys.A：Math.Gen.28，4305（1995），K. L. Sebastian给出了次扩散分数布朗运动（fBm）传播子的路径积分计算，即fBm具有Hurst或自相似指数$H\in(0,1/2)$ .塞巴斯蒂安的计算扩展到超扩散，$H\in(1/2,1]$，然而，变得相当复杂，由于外观上的分数阶导数的path.In本文中，我们解决了建设的路径积分表示在一个不同的方式，它允许处理subdiffusion和superdiffusion在平等的基础上。然后，以整洁和统一的方式进行一般赫斯特指数的fBm的传播子的推导。
Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation
研究了在周期势场中运动的惯性布朗粒子的远平衡输运。如最近对于SQUID棘轮动力学（Spiechowicz J. & Luczka J. Phys. Rev. E 91，062104（2015））所检测到的，粒子位置与其平均值的均方差可能涉及三个不同的中间扩散机制，尽管是扩展的扩散机制：最初是超扩散，然后是亚扩散，最后是渐近长时间限制中的正常扩散。尽管这些异常是瞬态效应，但它们的寿命可能比设置的特征时间尺度长很多很多个数量级，并且对温度或潜在不对称性等系统参数非常敏感。在本文中，我们揭示了与系统的遍历性，对称性破缺的周期势和超低松弛的粒子速度向其稳定状态的扩散异常的机制。类似的扩散行为序列可以在各种系统中检测到，包括，除其他外，在随机电位的胶体颗粒，玻璃形成液体和粒状气体。
Maximum likelihood, neural networks and posterior mean for inferring fractional Brownian motion parameters
School of Mathematics and Statistics, University of New South Wales（新南威尔士大学数学与统计学院）；School of Mathematical Sciences, Queensland University of Technology (QUT)（昆士兰科技大学数理科学学院）；ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems, QUT（昆士兰科技大学ARC细胞系统数学分析卓越中心）
