PTPT Symmetric Real Dirac Fermions and Semimetals

Recently Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the $PT$ symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, $2$D sub topological insulators and Fermi arcs, are studied in the $PT$ symmetric Dirac semimetals, and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about $PT$ symmetric Dirac nodal line semimetals.Comment: 7.5 pages, 5 figures. Accepted by Phys. Rev. Let

The identification of coupled map lattice models for autonomous cellular neural network patterns

The identification problem for spatiotemporal patterns which are generated by autonomous Cellular Neural Networks (CNN) is investigated in this paper. The application of traditional identification algorithms to these special spatiotemporal systems can produce poor models due to the inherent piecewise nonlinear structure of CNN. To solve this problem, a new type of Coupled Map Lattice model with output constraints and corresponding identification algorithms are proposed in the present study. Numerical examples show that the identified CML models have good prediction capabilities even over the long term and the main dynamics of the original patterns appears to be well represented

The identification of cellular automata

Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced