A time fractional model to represent rainfall process

This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.

A 3-DOF piezoelectric robot with continuous walking gait aiming at cross-scale smooth motion

Piezoelectric robots play important roles in the field of micromanipulation, but it is difficult for them to generate steady precision motion at any moment. In order to eliminate the changing inertial force and improve the motion smoothness, this work proposes a piezoelectric robot with continuous walking gait inspired by ants. The idea is verified with theoretical models and numerical simulation, and the performances are evaluated with experiments. The robot is proven to have the ability to generate 3-DOF(dgeree of freedom) continuous smooth motions with constant speeds. The maximum and minimum smooth velocities have a difference of six orders of magnitude, realizing cross-scale velocity control. Besides, the motion resolution reaches several nanometers with the unlimited workspace, so the cross-scale displacement control can be also obtained. Furthermore, with great robustness against varying loads, the stable actuation capability of the robot is more than 22 times of the self-weight. To sum up,the proposed robot generates cross-scale smooth motion in both aspects of displacement and velocity, so it has good prospects in the applications requiring steady precision motion. The design philosophy and research methods in this work can be valuable references for further advances of micromanipulation robots.

Environment-dependent continuous time random walk

A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are replaced by two new ones： the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement （x^2（t）） - t^a is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0 〈 a 〈 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.

Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk

The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.

Chung-type Law of the Iterated Logarithm for Continuous Time Random Walk

A continuous time random walk is a random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper, we establish a Chung-type law of the iterated logarithm for continuous time random walk with jumps and waiting times in the domains of attraction of stable laws.