Comparing holographic dark energy models with statefinder

We apply the statefinder diagnostic to the holographic dark energy models, including the original holographic dark energy (HDE) model, the new holographic dark energy model, the new agegraphic dark energy (NADE) model, and the Ricci dark energy model. In the low-redshift region the holographic dark energy models are degenerate with each other and with the $\Lambda$CDM model in the $H(z)$ and $q(z)$ evolutions. In particular, the HDE model is highly degenerate with the $\Lambda$CDM model, and in the HDE model the cases with different parameter values are also in strong degeneracy. Since the observational data are mainly within the low-redshift region, it is very important to break this low-redshift degeneracy in the $H(z)$ and $q(z)$ diagnostics by using some quantities with higher order derivatives of the scale factor. It is shown that the statefinder diagnostic $r(z)$ is very useful in breaking the low-redshift degeneracies. By employing the statefinder diagnostic the holographic dark energy models can be differentiated efficiently in the low-redshift region. The degeneracy between the holographic dark energy models and the $\Lambda$CDM model can also be broken by this method. Especially for the HDE model, all the previous strong degeneracies appearing in the $H(z)$ and $q(z)$ diagnostics are broken effectively. But for the NADE model, the degeneracy between the cases with different parameter values cannot be broken, even though the statefinder diagnostic is used. A direct comparison of the holographic dark energy models in the $r$--$s$ plane is also made, in which the separations between the models (including the $\Lambda$CDM model) can be directly measured in the light of the current values $\{r_0,s_0\}$ of the models.Comment: 8 pages, 8 figures; accepted by European Physical Journal C; matching the publication versio

Statefinder hierarchy exploration of the extended Ricci dark energy

We apply the statefinder hierarchy plus the fractional growth parameter to explore the extended Ricci dark energy (ERDE) model, in which there are two independent coefficients $\alpha$ and $\beta$. By adjusting them, we plot evolution trajectories of some typical parameters, including Hubble expansion rate $E$, deceleration parameter $q$, the third and fourth order hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ and fractional growth parameter $\epsilon$, respectively, as well as several combinations of them. For the case of variable $\alpha$ and constant $\beta$, in the low-redshift region the evolution trajectories of $E$ are in high degeneracy and that of $q$ separate somewhat. However, the $\Lambda$CDM model is confounded with ERDE in both of these two cases. $S_3^{(1)}$ and $S_4^{(1)}$, especially the former, perform much better. They can differentiate well only varieties of cases within ERDE except $\Lambda$CDM in the low-redshift region. For high-redshift region, combinations $\{S_n^{(1)},\epsilon\}$ can break the degeneracy. Both of $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ have the ability to discriminate ERDE with $\alpha=1$ from $\Lambda$CDM, of which the degeneracy cannot be broken by all the before-mentioned parameters. For the case of variable $\beta$ and constant $\alpha$, $S_3^{(1)}(z)$ and $S_4^{(1)}(z)$ can only discriminate ERDE from $\Lambda$CDM. Nothing but pairs $\{S_3^{(1)},\epsilon\}$ and $\{S_4^{(1)},\epsilon\}$ can discriminate not only within ERDE but also ERDE from $\Lambda$CDM. Finally we find that $S_3^{(1)}$ is surprisingly a better choice to discriminate within ERDE itself, and ERDE from $\Lambda$CDM as well, rather than $S_4^{(1)}$.Comment: 8 pages, 14 figures; published versio

No evidence for the evolution of mass density power-law index γ\gamma from strong gravitational lensing observation

In this paper, we consider the singular isothermal sphere lensing model that has a spherically symmetric power-law mass distribution $\rho_{tot}(r)\sim r^{-\gamma}$. We investigate whether the mass density power-law index $\gamma$ is cosmologically evolutionary by using the strong gravitational lensing (SGL) observation, in combination with other cosmological observations. We also check whether the constraint result of $\gamma$ is affected by the cosmological model, by considering several simple dynamical dark energy models. We find that the constraint on $\gamma$ is mainly decided by the SGL observation and independent of the cosmological model, and we find no evidence for the evolution of $\gamma$ from the SGL observation.Comment: 7 pages, 3 figure

Revisiting the holographic dark energy in a non-flat universe: alternative model and cosmological parameter constraints

We propose an alternative model for the holographic dark energy in a non-flat universe. This new model differs from the previous one in that the IR length cutoff $L$ is taken to be exactly the event horizon size in a non-flat universe, which is more natural and theoretically/conceptually concordant with the model of holographic dark energy in a flat universe. We constrain the model using the recent observational data including the type Ia supernova data from SNLS3, the baryon acoustic oscillation data from 6dF, SDSS-DR7, BOSS-DR11, and WiggleZ, the cosmic microwave background data from Planck, and the Hubble constant measurement from HST. In particular, since some previous studies have shown that the color-luminosity parameter $\beta$ of supernovae is likely to vary during the cosmic evolution, we also consider such a case that $\beta$ in SNLS3 is time-varying in our data fitting. Compared to the constant $\beta$ case, the time-varying $\beta$ case reduces the value of $\chi^2$ by about 35 and results in that $\beta$ deviates from a constant at about 5$\sigma$ level, well consistent with the previous studies. For the parameter $c$ of the holographic dark energy, the constant $\beta$ fit gives $c=0.65\pm 0.05$ and the time-varying $\beta$ fit yields $c=0.72\pm 0.06$. In addition, an open universe is favored (at about 2$\sigma$) for the model by the current data.Comment: 8 pages, 4 figure

A closer look at interacting dark energy with statefinder hierarchy and growth rate of structure

We investigate the interacting dark energy models by using the diagnostics of statefinder hierarchy and growth rate of structure. We wish to explore the deviations from $\Lambda$CDM and to differentiate possible degeneracies in the interacting dark energy models with the geometrical and structure growth diagnostics. We consider two interacting forms for the models, i.e., $Q_1=\beta H\rho_c$ and $Q_2=\beta H\rho_{de}$, with $\beta$ being the dimensionless coupling parameter. Our focus is the I$\Lambda$CDM model that is a one-parameter extension to $\Lambda$CDM by considering a direct coupling between the vacuum energy ($\Lambda$) and cold dark matter (CDM), with the only additional parameter $\beta$. But we begin with a more general case by considering the I$w$CDM model in which dark energy has a constant $w$ (equation-of-state parameter). For calculating the growth rate of structure, we employ the "parametrized post-Friedmann" theoretical framework for interacting dark energy to numerically obtain the $\epsilon(z)$ values for the models. We show that in both geometrical and structural diagnostics the impact of $w$ is much stronger than that of $\beta$ in the I$w$CDM model. We thus wish to have a closer look at the I$\Lambda$CDM model by combining the geometrical and structural diagnostics. We find that the evolutionary trajectories in the $S^{(1)}_3$--$\epsilon$ plane exhibit distinctive features and the departures from $\Lambda$CDM could be well evaluated, theoretically, indicating that the composite null diagnostic $\{S^{(1)}_3, \epsilon\}$ is a promising tool for investigating the interacting dark energy models.Comment: 17 pages, 4 figures; accepted for publication in JCA

A Method Based on Multi-Sensor Data Fusion for Fault Detection of Planetary Gearboxes

Studies on fault detection and diagnosis of planetary gearboxes are quite limited compared with those of fixed-axis gearboxes. Different from fixed-axis gearboxes, planetary gearboxes exhibit unique behaviors, which invalidate fault diagnosis methods that work well for fixed-axis gearboxes. It is a fact that for systems as complex as planetary gearboxes, multiple sensors mounted on different locations provide complementary information on the health condition of the systems. On this basis, a fault detection method based on multi-sensor data fusion is introduced in this paper. In this method, two features developed for planetary gearboxes are used to characterize the gear health conditions, and an adaptive neuro-fuzzy inference system (ANFIS) is utilized to fuse all features from different sensors. In order to demonstrate the effectiveness of the proposed method, experiments are carried out on a planetary gearbox test rig, on which multiple accelerometers are mounted for data collection. The comparisons between the proposed method and the methods based on individual sensors show that the former achieves much higher accuracies in detecting planetary gearbox faults

Path Analysis of Work Family Conflict, Job Salary and Promotion Satisfaction, Work Engagement to Subjective Well-being of the Primary and Middle School Principals

Objective: To investigate the path analysis of work family conflict, job salary and promotion satisfaction、work engagement to subjective well-being of the primary and middle school principals, and provide advice for enhancing their well-being. Methods: Using convenient sampling, totally 300 primary and middle school principals completed the WFC、JSPSS、UWES and GWB. Results: There were four significant paths influencing the well-being：(1) work family conflict could influence subjective well-being directly, the direct effect was -0.275(P<0.001); but the indirect effect through work engagement wasn’t significant. (2) work engagement could influence subjective well-being directly, the direct effect was 0.388(P<0.001); (3) job salary and promotion satisfaction could influence subjective well-being directly, the direct effect was 0.137(P<0.05); (4) job salary and promotion satisfaction could influence subjective well-being through work engagement, the indirect effect was 0.096, the total effect was 0.233; work engagement partially mediated the relation between them. Conclusion: We can enhance the subjective well-being of the primary and middle school principals through balancing work family conflict, improving work engagement, raising incomes and providing development opportunities