Mechanisms of Avalanche Dynamics in a Stochastic Four-State Sandpile Model

We study the stochastic four-state sandpile model on the square lattice. The static and dynamical properties of the model are investigated and compared with the deterministic sandpile model of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59 (1987) 381]. The numerical results show that the stochastic model defines a new universality class with respect to the deterministic sandpile. We also find that the waves in an avalanche are uncorrelated in the stochastic model (in the BTW model, the waves in an avalanche are correlated). The physical origin of the critical behaviour of the stochastic model being different from that of the BTW model is ascribed to the ordering and deterministic property of the toppling law in the BTW model.     

Multi-Scale Gaussian Processes： a Novel Model for Chaotic Time Series Prediction

Based on the classical Gaussian process （GP） model, we propose a multi-scale Gaussian process （MGP） model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine. Moreover, the scaling function with its different dilations and translations can form a set of complete bases, resulting in the fact that the MGP can acquire better prediction performance than the GP. The experiments can lead to the following conclusions： （i） The MGP gives a relatively better prediction performance in comparison with the classical GP model. （ii） The prediction performance of the MGP is competitive with support vector machine （SVM）. They give better performance as compared to the radial basis function networks.     

Analytic Solutions of Three-Level Dressed-Atom Model

On the basis of the dressed-atom model, the general analytic expressions for the eigenenergies, eigenstates and their optical potentials of the A-configuration three-level atom system are derived and analysed. From the calculation of dipole matrix element of different dressed states, we obtain the spontaneous-emission rates in the dressed-atom picture. We find that our general expressions of optical potentials for the three-level dressed atom can be reduced to the same as ones in previous references under the approximation of a small saturation parameter. We also analyse the dependences of the optical potentials of a three-level ^85Rb atom on the laser detuning and the dependences of spontaneous-emission rates on the radial position in the dark hollow beam, and discuss the probability (population) evolutions of dressed-atomic eigenstates in three levels in the hollow beam.