107,030 research outputs found
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
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
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
Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
A topology-intrinsic connection between the stabilities of Fermi surfaces
(FSs) and topological insulators/superconductors (TIs/TSCs) is revealed. In
particular, a one-to-one relation between the topological types of FSs and
TIs/TSCs is rigorously derived; combining it with a well-established
topological theory of FSs, we produce a complete table illustrating precisely
topological types of all TIs/TSCs, while a valid part of it was postulated
before. Moreover, we propose and prove a general index theorem that relates the
topological charge of FSs on the natural boundary of a strong TI/TSC to its
bulk topological number. Implications of the general index theorem on the
boundary quasi-particles are also addressed.Comment: 5 pages with Supplemental Material, more content is adde
Kernel Regression For Determining Photometric Redshifts From Sloan Broadband Photometry
We present a new approach, kernel regression, to determine photometric
redshifts for 399,929 galaxies in the Fifth Data Release of the Sloan Digital
Sky Survey (SDSS). In our case, kernel regression is a weighted average of
spectral redshifts of the neighbors for a query point, where higher weights are
associated with points that are closer to the query point. One important design
decision when using kernel regression is the choice of the bandwidth. We apply
10-fold cross-validation to choose the optimal bandwidth, which is obtained as
the cross-validation error approaches the minimum. The experiments show that
the optimal bandwidth is different for diverse input patterns, the least rms
error of photometric redshift estimation arrives at 0.019 using color+eClass as
the inputs, the less rms error amounts to 0.020 using ugriz+eClass as the
inputs. Here eClass is a galaxy spectra type. Then the little rms scatter is
0.021 with color+r as the inputs.Comment: 6 pages,2 figures, accepted for publication in MNRA
Time Delay Compensation and Stability Analysis of Networked Predictive Control Systems Based on Hammerstein Model
A novel approach is proposed for a networked control system with random delays containing a nonlinear process based on a Hammerstein model. The method uses a time delay two step generalized predictive control (TDTSGPC), which consists of two parts, one is to deal with the input nonlinearity of the Hammerstein model and the other is to compensate the network induced delays in the networked control system. Theoretical results using the Popov theorem are presented for the closed-loop stability of the system in the case of a constant delay. Simulation examples illustrating the validity of the approach are presented
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
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