A note of pointwise estimates on Shishkin meshes

We propose the estimates of the discrete Green function for the stream- line diffusion finite element method (SDFEM) on Shishkin meshes.Comment: 10pages, 1 figur

Some notes on the paper "The mean value of a new arithmetical function"

In reference [2], we used the elementary method to study the mean value prop- erties of a new arithmetical function, and obtained two mean value formulae for it, but there exist some errors in that paper. The main purpose of this paper is to correct the errors in reference [2], and give two correct conclusions

Shape, orientation and magnitude of the curl quantum flux, the coherence and the statistical correlations in energy transport at nonequilibrium steady state

We provide a quantitative description of the nonequilibriumness based on the model of coupled oscillators interacting with multiple energy sources. This can be applied to the study of vibrational energy transport in molecules. The curl quantum flux quantifying the nonequilibriumness and time-irreversibility is quantified in the coherent representation and we find the geometric description of the shape and polarization of the flux which provides the connection between the microscopic description of quantum nonequilibriumness and the macroscopic observables, i.e., correlation function. We use the Wilson loop integral to quantify the magnitude of curl flux, which is shown to be correlated to the correlation function as well. Coherence contribution is explicitly demonstrated to be non-trivial and to considerably promote the heat transport quantified by heat current and efficiency. This comes from the fact that coherence effect is microscopically reflected by the geometric description of the flux. To uncover the effect of vibron-phonon coupling between the vibrational modes of molecular stretching (vibron) and the molecular chain (phonon), we further explore the influences of localization, which leads to the coherent and incoherent regimes that are characterised by the current-current correlations.Comment: 21 pages, 6 figure

A tight-binding model for the excitonic band structure of a one-dimensional molecular chain: UV-Vis spectra, Zak phase and topological properties

Recently organic optics becomes a hot topic due to the rapid development of organic light-emitting diodes, organic solar cells, and organic photon detectors. The optical spectra of the molecular semiconductors are difficult to solve an model from first-principles because (i) the very large number of atoms in a unit cell and (ii) the accurate theoretical excited state is still under development. Here we present a tight-binding model of an exciton band structure in a molecular chain. We take into account the intra-molecule and charge-transfer excitation within a molecular dimer in a unit cell, then we apply the tight-binding model by including the coupling between two types of excitations. We not only found that our calculations can explain a body of UV-Vis optical spectra of transition-metal phthalocyanines, but also a one-dimensional excitonic topological band structure if we fine-tune the couplings in a dimerized molecular chain. We have found a large space to obtain the topological Zak phase in the parameter space, in which there is a simple linear relationship between the hopping integrals between cells and within cell.Comment: 5 pages, 5 figure

Intranight optical variability of radio-quiet BL Lacertae objects

Aims: Intranight variation (or microvariation) is a common phenomenon of radio-loud BL Lac objects. However, it is not clear whether the recently found radio-quiet BL Lac objects have the same properties. The occurrence rate of intranight variation is helpful in distinguishing the mechanism of the continuum of radio-quiet BL Lac objects. Methods: We conducted a photometric monitoring of 8 radio-quiet BL Lac objects by the Xinglong 2.16m and Lijiang 2.4m telescopes. The differential light curves are calculated between each target and two comparison stars. To quantify the variation, the significance of variation is examined by a scaled $F$-test. Results: No significant variation is found in the 11 sessions of light curves of 8 radio-quiet BL Lac objects (one galactic source is excluded). The lack of microvariation in radio-quiet BL Lac objects is consistent with the detection rate of microvariation in normal radio-quiet AGNs, but much lower than for radio-loud AGNs. This result indicates that the continua of the radio-quiet BL Lac objects are not dominated by jets that will induce frequent microvariations.Comment: Accepted for publication in Astronomy and Astrophysics; 7 pages, 1 figure, 3 table