Topological Classification and Stability of Fermi Surfaces

In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.Comment: 5 pages, published version in PR

A simple scalar coupled map lattice model for excitable media

A simple scalar coupled map lattice model for excitable media is intensively analysed in this paper. This model is used to explain the excitability of excitable media, and a Hopf-like bifurcation is employed to study the different spatio-temporal patterns produced by the model. Several basic rules for the construction of these kinds of models are proposed. Illustrative examples demonstrate that the sCML model is capable of generating complex spatiotemporal patterns

A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood

An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap- propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed and the parameters of the model are investigated

Synthetic vision and emotion calculation in intelligent virtual human modeling

The virtual human technique already can provide vivid and believable human behaviour in more and more scenarios. Virtual humans are expected to replace real humans in hazardous situations to undertake tests and feed back valuable information. This paper will introduce a virtual human with a novel collision-based synthetic vision, short-term memory model and a capability to implement the emotion calculation and decision making. The virtual character based on this model can ‘see’ what is in his field of view (FOV) and remember those objects. After that, a group of affective computing equations have been introduced. These equations have been implemented into a proposed emotion calculation process to enlighten emotion for virtual intelligent huma

Kinetic Alfv\'{e}n turbulence below and above ion-cyclotron frequency

Alfv\'{e}nic turbulent cascade perpendicular and parallel to the background magnetic field is studied accounting for anisotropic dispersive effects and turbulent intermittency. The perpendicular dispersion and intermittency make the perpendicular-wavenumber magnetic spectra steeper and speed up production of high ion-cyclotron frequencies by the turbulent cascade. On the contrary, the parallel dispersion makes the spectra flatter and decelerate the frequency cascade above the ion-cyclotron frequency. Competition of the above factors results in spectral indices distributed in the interval [-2,-3], where -2 is the index of high-frequency space-filling turbulence, and -3 is the index of low-frequency intermittent turbulence formed by tube-like fluctuations. Spectra of fully intermittent turbulence fill a narrower range of spectral indices [-7/3,-3], which almost coincides with the range of indexes measured in the solar wind. This suggests that the kinetic-scale turbulent spectra are shaped mainly by dispersion and intermittency. A small mismatch with measured indexes of about 0.1 can be associated with damping effects not studied here.Comment: 9 Pages, 3 Figures, and 2 Table

Identification of excitable media using a scalar coupled map lattice model

The identification problem for excitable media is investigated in this paper. A new scalar coupled map lattice (SCML) model is introduced and the orthogonal least squares algorithm is employed to determinate the structure of the SCML model and to estimate the associated parameters. A simulated pattern and a pattern observed directly from a real Belousov-Zhabotinsky reaction are identified. The identified SCML models are shown to possess almost the same local dynamics as the original systems and are able to provide good long term predictions

General response theory of topologically stable Fermi points and its implications for disordered cases

We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective non-linear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge `2' are respectively illustrated for the classes A and AIII. We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the non-linear sigma models, based on the one-to-one classification correspondence.Comment: 8 pages and 2 figures, revised version with appendi