Magnetic impact on heat and mass transfer utilizing nonofluid in an annulus between a superellipse obstacle and a cavity with periodic side-wall temperature and concentration

The magnetic impacts upon the transport of heat and mass of an electrically conducting nanofluid within an annulus among an inner rhombus with convex and outer cavity with periodic temperature/concentration profiles on its left wall are assessed by the ISPH method. The right wall has ${T}_{c}$ and ${C}_{c},$ flat walls are adiabatic, and the temperature and concentration of the left wall are altered sinusoidally with time. The features of the heat and mass transfer and fluid flow through an annulus are assessed across a wide scale of Hartmann number $Ha,$ Soret number $Sr,$ oscillation amplitude $A,$ Dufour number $Du,$ nanoparticles parameter $\phi ,$ oscillation frequency $f,$ Rayleigh number $Ra,$ and radius of a superellipse $a$ at Lewis number $Le=20,$ magnetic field's angle $\gamma =45^\circ ,$ Prandtl number ${\Pr }=6.2,$ a superellipse coefficient $n=3/2,$ and buoyancy parameter $N=1.$ The results reveal that the velocity's maximum reduces by $70.93 \% $ as $Ha$ boosts from 0 to 50, and by $66.24 \% $ as coefficient $a$ boosts from $0.1$ to $0.4.$ Whilst the velocity's maximum augments by $83.04 \% $ as $Sr$ increases from 0.6 to 2 plus a decrease in $Du$ from 1 to 0.03. The oscillation amplitude $A,$ and frequency $f$ are significantly affecting the nanofluid speed, and heat and mass transfer inside an annulus. Increasing the parameters $A$ and $f$ is augmenting the values of mean Nusselt number $\overline{Nu}$ and mean Sherwood number $\overline{Sh}.$ Increasing the radius of a superellipse $a$ enhances the values of $\overline{Nu}$ and $\overline{Sh}.$     

Core structure and Peierls stress of the 90° dislocation and the 60° dislocation in aluminum investigated by the fully discrete Peierls model

The core structure, Peierls stress and core energy, etc. are comprehensively investigated for the $90^\circ$ dislocation and the $60^\circ$ dislocation in metal aluminum using the fully discrete Peierls model, and in particular thermal effects are included for temperature range $0\leq T \leq 900$ K. For the $90^\circ$ dislocation, the core clearly dissociates into two partial dislocations with the separating distance $D\sim 12$ Å, and the Peierls stress is very small $\sigma_{\rm p}<1$ kPa. The nearly vanishing Peierls stress results from the large characteristic width and a small step length of the $90^\circ$ dislocation. The $60^\circ$ dislocation dissociates into $30^\circ$ and $90^\circ$ partial dislocations with the separating distance $D\sim 11$ Å. The Peierls stress of the $60^\circ$ dislocation grows up from $1$ MPa to $2$ MPa as the temperature increases from $0$ K to $900$ K. Temperature influence on the core structures is weak for both the $90^\circ$ dislocation and the $60^\circ$ dislocation. The core structures theoretically predicted at $T=0$ K are also confirmed by the first principle simulations.     

A new transition metal diphosphide α-MoP2 synthesized by a high-temperature and high-pressure technique

Monoclinic $\alpha $-MoP$_{2}$, with the OsGe$_{2}$-type structure (space group $C2/m$, $Z = 4$) and lattice parameters $a = 8.7248(11) $ Å, $b = 3.2322(4) $ Å, $c = 7.4724(9) $ Å, and $\beta =119.263^\circ $, was synthesized under a pressure of 4 GPa at a temperature between 1100 ${^\circ}$C and 1200 ${^\circ}$C. The structure of $\alpha $-MoP$_{2}$ and its relationship to other transition metal diphosphides are discussed. Surprisingly, the ambient pressure phase orthorhombic $\beta $-MoP$_{2}$ (space group Cmc2$_{1}$) is denser in structure than $\alpha $-MoP$_{2}$. Room-temperature high-pressure x-ray diffraction studies exclude the possibility of phase transition from $\beta $-MoP$_{2}$ to $\alpha $-MoP$_{2}$, suggesting that $\alpha $-MoP$_{2}$ is a stable phase at ambient conditions; this is also supported by the total energy and phonon calculations.     

The rehybridization of electronic orbitals in carbon nanotubes

Rehybridization of electronic orbitals in carbon nanotubes contains tilting angles of π orbital, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, etc. In this paper, we have obtained analytical formulas of tilting angle of π orbital relative to tube surface, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, separately, as well as the numerical results.     

Impurity effects of the Λhyperon in the hypernuclear systems ${}_{{\rm{\Lambda }}}^{25}\mathrm{Mg}$ and ${}_{{\rm{\Lambda }}}^{29}\mathrm{Si}$

Based on the beyond-mean-field Skyrme–Hartree–Fock model, impurity effects of the Λhyperon in the hypernuclear systems ${}_{\,{\rm{\Lambda }}}^{25}$ Mg and ${}_{\,{\rm{\Lambda }}}^{29}$ Si are investigated, respectively. Four cases, in which the Λhyperon occupies the single-particle orbitals ${\rm{\Lambda }}$[000]${\tfrac{1}{2}}^{+}$, ${\rm{\Lambda }}$[110]${\tfrac{1}{2}}^{-}$, ${\rm{\Lambda }}$[101]${\tfrac{3}{2}}^{-}$ and ${\rm{\Lambda }}$[101]${\tfrac{1}{2}}^{-}$, are focused. In each case, the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of the Λhyperon on the nuclear core. Beside the shrinkage effect that is induced by the Λhyperon occupying the s_Λ orbital, it is found that the Λhyperon on the p_Λ orbital, ${\rm{\Lambda }}$[110]${\tfrac{1}{2}}^{-}$, drives the nuclear core toward a prolate shape, while the ones on the other two p_Λ orbitals, ${\rm{\Lambda }}$[101]${\tfrac{3}{2}}^{-}$ and ${\rm{\Lambda }}$[101]${\tfrac{1}{2}}^{-}$, drive the nuclear core toward an oblate shape. The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.     

Spin polarization effect for molecule Ta2

Density functional theory （DFT） （B3p86） has been used to optimize the structure of the molecule Ta2. The result shows that the ground state of molecule Ta2 is a 7-multiple state and its electronic configuration is ^7∑u^＋, which shows the spin polarization effect for molecule Ta2 of transition metal elements for the first time. Meanwhile, spin pollution has not been found because the wavefunction of the ground state does not mix with those of higher states. So, the fact that the ground state of molecule Ta2 is a 7-multiple state indicates a spin polarization effect of molecule Ta2 of the transition metal elements, i.e. there exist 6 parallel spin electrons and the non-conjugated electrons are greatest in number. These electrons occupy different space orbitals so that the energy of molecule Ta2 is minimized. It can be concluded that the effect of parallel spin of the molecule Ta2 is larger than the effect of the conjugated molecule, which is obviously related to the effect of d-electron delocalization. In addition, the Murrell-Sorbie potential functions with parameters for the ground state ^7∑u^＋ and other states of the molecule Ta2 are derived. The dissociation energy De, equilibrium bond length Re and vibration frequency we for the ground state of molecule Ta2 are 4.5513eV, 0.2433nm and 173.06cm^-1, respectively. Its force constants f2, f3 and f4 are 1.5965×10^2aJ.nm^-2, -6.4722×10^3aJ·nm^-3 and 29.4851×10^4aJ·nm^-4, respectively. Other spectroscopic data we xe, Be and αe for the ground state of Ta2 are 0.2078cm^-1, 0.0315 cm^-1 and 0.7858×10^-4 cm^-1, respectively.     

Spin polarization effect for Os2 molecule

Density functional Theory （DFT） （B3p86） of Gaussian03 has been used to optimize the structure of Os2 molecule. The result shows that the ground state for Os2 molecule is 9-multiple state and its electronic configuration is ^9∑^＋g, which shows spin polarization effect of Os2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, the fact that the ground state for Os2 molecule is a 9-multiple state is indicative of spin polarization effect of Os2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Os2 molecule is minimized. It can be concluded that the effect of parallel spin of Os2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state ^9∑^＋g and other states of Os2 molecule are derived. Dissociation energy De for the ground state of Os2 molecule is 3.3971eV, equilibrium bond length Re is 0.2403nm, vibration frequency ωe is 235.32cm^-1. Its force constants f2, f3, and f4 are 3.1032×10^2aJ·nm^-2, -14.3425×10^3aJ·nm^-3 and 50.5792×10^4aJ·nm^-4 respectively. The other spectroscopic data for the ground state of Os2 molecule ωexe, Be and ae are 0.4277cm^- 1, 0.0307cm^- 1 and 0.6491 × 10^-4cm^-1 respectively.     

Spin polarization effect for Co2 molecule

The density functional theory (DFT)(b3p86) of Gaussian 03 has been used to optimize the structure of the Co$_{2}$ molecule, a transition metal element molecule. The result shows that the ground state for the Co$_{2}$ molecule is a 7-multiple state, indicating a spin polarization effect in the Co$_{2}$ molecule. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state is not mingled with wavefunctions of higher-energy states. So for the ground state of Co$_{2}$ molecule to be a 7-multiple state is the indicative of spin polarization effect of the Co$_{2}$ molecule, that is, there exist 6 parallel spin electrons in a Co$_{2}$ molecule. The number of non-conjugated electrons is the greatest. These electrons occupy different spacial orbitals so that the energy of the Co$_{2}$ molecule is minimized. It can be concluded that the effect of parallel spin in the Co$_{2}$ molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state and the other states of the Co$_{2}$ molecule are derived. The dissociation energy $De$ for the ground state of Co$_{2}$ molecule is 4.0489eV, equilibrium bond length $R_{\rm e}$ is 0.2061~nm, and vibration frequency $\omega _\e $ is 378.13~cm$^{ - 1}$. Its diatomic molecule force constants $f_2$, $f_3$, and $f_4$ are 2.4824~aJ$\cdot$nm$^{ - 2}$, -7.3451~aJ$\cdot$nm$^{ - 3}$, and 11.2222~aJ$\cdot$nm$^{ - 4 }$respectively(1~aJ=$10^{-18}$~J). The other spectroscopic data for the ground state of Co$_{2}$ molecule $\omega_{\e}\chi _{\e}$, $B_{\e}$, and $\alpha_{\e}$ are 0.7202~cm$^{-1}$, 0.1347~cm$^{-1 }$, and 2.9120$\times $ 10$^{-1}$~cm$^{-1}$ respectively. And $\omega_{\e}\chi _{\e}$ is the non-syntonic part of frequency, $B_{\e}$ is the rotational constant, $\alpha_{\e}$ is revised constant of rotational constant for non-rigid part of Co$_2$ molecule.     

Relativistic calculations on the transition electric dipole moments and radiative lifetimes of the spin-forbidden transitions in the antimony hydride molecule

Calculations on the spectroscopic constants and transition properties of the first three states (${\rm a}^{1}\Delta $, ${\rm b}^{1}\Sigma^{+}$, and X$^{3}\Sigma^-$) of the SbH molecule were performed under the relativistic framework using the exact two-component Hamiltonian (X2C). The potential energy curves in the Franck-Condon region were computed and compared with the previous values. Furthermore, the transition dipole moments for the weak spin-forbidden transitions (${\rm b}0^{+}$-X$_{1}0^{+}$, ${\rm b}0^{+}$-X$_{2}$1, X$_{1}0^{+}$-X$_{2}$1, and X$_{2}$1-${\rm a}$2) were reported. The spontaneous radiative lifetime of the ${\rm b}^{1}\Sigma^{+}$ ($\upsilon '=0$) state was calculated as 163.5 $\pm$ 7.5 μs, which is in reasonable agreement with the latest experimental value of 173 $\pm$ 3 μs. The spontaneous radiative lifetimes of the X$_{2}$1 ($\upsilon '=0$) state and the ${\rm a}$2 ($\upsilon '=0$) state were calculated to be 48.6 s and $\sim 8 $ ms, respectively. Our study is expected to be a benchmark transition property computation for comparison with other theoretical and experimental results. The datasets presented in this paper, including the transition dipole moments, are openly available at https://dx.doi.org/10.11922/sciencedb.j00113.00018.     

Analysis of thermal conductivity in tree-like branched networks

Asymmetric tree-like branched networks are explored by geometric algorithms. Based on the network, an analysis of the thermal conductivity is presented. The relationship between effective thermal conductivity and geometric structures is obtained by using the thermal-electrical analogy technique. In all studied cases, a clear behaviour is observed, where angle (δ ,θ ) among parent branching extended lines, branches and parameter of the geometric structures have stronger effects on the effective thermal conductivity. When the angle δ is fixed, the optical diameter ratio β^* is dependent on angle θ . Moreover, γ and m are not related to β ^* . The longer the branch is, the smaller the effective thermal conductivity will be. It is also found that when the angle θ < δ / 2, the higher the iteration m is, the lower the thermal conductivity will be and it tends to zero, otherwise, it is bigger than zero. When the diameter ratio β ₁< 0.707 and angle δ is bigger, the optimal k of the perfect ratio increases with the increase of the angle δ ; when β ₁> 0.707, the optimal k decreases. In addition, the effective thermal conductivity is always less than that of single channel material. The present results also show that the effective thermal conductivity of the asymmetric tree-like branched networks does not obey Murray's law.     

百兆电子伏特/核子原子核诱发乳胶核反应靶核反冲质子多重数涨落分析(英文)

利用标度阶乘矩方法对290 A MeV $^{12}$C-AgBr, 400 A MeV $^{12}$C-AgBr, 400 A MeV $^{20}$Ne-AgBr及500 A MeV $^{56}$Fe-AgBr 作用靶核反冲质子在二维正常相空间及累积变量空间发射过程中的多重数涨落分别进行了分析。实验结果表明:在正常相空间,对于秩数q较小时标度阶乘矩（$ln$）随相空间的分割数的增加而增加,而对于秩数较大时标度阶乘矩（$ln$）随相空间的分割数的增加表现出先增加后趋于饱和或减小的趋势;在累积变量空间,标度阶乘矩（$ln$）随相空间的分割数的增加而减小,这表明对于我们所研究的核作用体系靶核反冲质子发射过程中不存在非统计涨落。Multiplicity fluctuation of the target recoil protons emitted in $290$\,A MeV $^{12}$C-AgBr, $400$\,A MeV $^{12}$C-AgBr, $400$\,A MeV $^{20}$Ne-AgBr and $500$\,A MeV $^{56}$Fe-AgBr interactions are studied using the scaled factorial moment (SFM) method in two-dimensional normal phase space and cumulative variable space, respectively. It is found that in normal phase space the SFM ($\ln$) increases linearly with the increase of the divided number of phase space ($\ln{M}$) for lower q-values and increases linearly and then becomes saturation or decrease with the increase of $\ln{M}$ for higher q-values, and in cumulative variable space $\ln$ decreases linearly with the increase of $\ln{M}$, which indicates that no evidence of non-statistical multiplicity fluctuation is observed in our data sets.     

Hopf Bifurcations,Drops in the Lid-Driven Square Cavity Flow

The lid-driven square cavity flow is investigated by numerical experiments. It is found that from $ \mathrm{Re} $$=$ $5,000 $ to $ \mathrm{Re} $$=$$ 7,307.75 $ the solution is stationary, but at $ \mathrm{Re}$$=$$7,308 $ the solution is time periodic. So the critical Reynolds number for the first Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 7,307.75 $ and $ \mathrm{Re} $$=$$ 7,308 $. Time periodical behavior begins smoothly, imperceptibly at the bottom left corner at a tiny tertiary vortex; all other vortices stay still, and then it spreads to the three relevant corners of the square cavity so that all small vortices at all levels move periodically. The primary vortex stays still. At $ \mathrm{Re} $$=$$ 13,393.5 $ the solution is time periodic; the long-term integration carried out past $ t_{\infty} $$=$$ 126,562.5 $ and the fluctuations of the kinetic energy look periodic except slight defects. However, at $ \mathrm{Re} $$=$$ 13,393.75 $ the solution is not time periodic anymore: losing unambiguously, abruptly time periodicity, it becomes chaotic. So the critical Reynolds number for the second Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 13,393.5 $ and $ \mathrm{Re} $$=$$ 13,393.75 $. At high Reynolds numbers $ \mathrm{Re} $$=$$ 20,000 $ until $ \mathrm{Re} $$=$$ 30,000 $ the solution becomes chaotic. The long-term integration is carried out past the long time $ t_{\infty} $$=$$ 150,000 $, expecting the time asymptotic regime of the flow has been reached. The distinctive feature of the flow is then the appearance of drops: tiny portions of fluid produced by splitting of a secondary vortex, becoming loose and then fading away or being absorbed by another secondary vortex promptly. At $ \mathrm{Re} $$=$$ 30,000 $ another phenomenon arises—the abrupt appearance at the bottom left corner of a tiny secondary vortex, not produced by splitting of a secondary vortex.     

Magnetocrystalline anisotropy and dynamic spin reorientation of half-doped Nd_(0.5)Pr_(0.5)FeO_3 single crystal

The single crystals of Nd_(0.5)Pr_(0.5)FeO_3 were successfully grown by optical floating zone method.Room temperature x-ray diffraction and Laue photograph declared the homogeneity and high quality of the crystal.The significant magnetic anisotropy and multiple magnetic transitions illustrate the complex magnetic structure.At high temperatures(T 66 K),it shows the typical characteristics of Γ_4(G_x,A_y,F_z) state.With the decrease of the temperature,it undergoes a first-order spin reorientation transition from Γ_4(G_x,A_y,F_z) to Γ_2(F_x,C_y,G_z) state in the temperature window of 45-66 K under an applied magnetic field of 0.01 T.As the temperature drops to ～17 K,a new magnetic interaction mechanism works,which results in a further enhancement of magnetization.The T-H phase diagram of Nd_(0.5)Pr_(0.5)FeO_3 single crystal was finally constructed.     

Effect of local structure on electron paramagnetic resonance spectra for trigonal [Cr(H2O)6]3+coordination complex in the sulfate alums series: a ligand field theory study

A simple theoretical method is introduced for studying the interrelation between electronic and molecular structures.By diagonalizing the 120 × 120 complete energy matrices,the relationships between zero-field splitting(ZFS) parameter D and local distortion parameter △θ for Cr 3+ ions doped,separately,in α-and β-alums are investigated.Our results indicate that there exists an approximately linear relationship between D and △θ in a temperature range 4.2-297 K and the signs of D and △θ are opposite to each other.Moreover,in order to understand the contribution of spin-orbit coupling coefficient ζ to ZFS parameter D,the relation between D and ζ is also discussed.     

Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ～ N α , with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τ p and follows a falling exponential function for duration time τ > τ p . For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.     

Central black hole mass determination for blazars

In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of $0.16-2.09(\lambda=1.0)$ or $0.24-2.86\ (\lambda=0.1)$; the angle (${\it\Phi}$) in the range of $9.53^{\circ}-73.85^{\circ}\ (\lambda=1.0)$ or $7.36^{\circ}-68.89^{\circ}\ (\lambda=0.1)$; and the distance ($d/R_{\rm g}$) in the range of $22.39-609.36\ (\lambda=1.0)$ or $17.54-541.88\ (\lambda=0.1)$.     

The first-principles study of ferroelectric behaviours of PbTiO3/SrTiO3 and BaTiOn/SrTiO3 superlattices

We have performed the first-principles calculation to investigate the origins of ferroelectricities and different po- larization behaviours of superlattices BaTiO3/SrTiO3 and PbTiO3/SrTiO3. The density of state （DOS） and electronic charge profiles show that there are strong hybridizations between atoms Ti and O and between atoms Pb and O which play very important roles in producing the ferroelectricities of superlattices BaTiO3/SrTiO3 and PbTiO3/SrTiO3. Ow- ing to the decline of internal electric field in SrTiO3 （ST） layer, the tetragonality and polarizations of superlattices decrease with increasing the fraction of SrTiO3 in the superlattices. We find that the polarization of PbTiO3/SrTiO3 is largerthan that of BaTiO3/SrTiO3 at the same ratio of components, because the polarization mismatch between PbTiO3 and SrTiO3 is larger than that between BaTiO3 and SrTiO3. The polarization and tetragonality are en- hanced with respect to those of bulk tetragonal BaTiO3 in the superlattices BaTiO3/SrTiO3, while the polarization and tetragonality are reduced with respect to those of bulk tetragonal PbTiO3 in superlattices PbTiO3/SrTiO3.     

Comparison Between $\chi^2$ and Bayesian Statistics with Considering the Redshift Dependence of Stretch and Color from JLA Data

In this work, we compare the impacts given by $\chi^2$ statistics and Bayesian statistics. Bayesian statistics is a new statistical method proposed by [C. Ma, P. S. Corasaniti, and B. A. Bassett, arXiv:1603.08519[astro-ph.CO](2016)] recently, which gives a fully account for the standard-candle parameter dependence of the data covariance matrix. For this two statistical methods, we explore the possible redshift-dependence of stretch-luminosity parameter $\alpha$ and color-luminosity parameter $\beta$ by using redshift tomography. By constraining the $\Lambda$CDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the linear parametrization to explore the possible evolution of $\alpha$ and $\beta$ and the deceleration parameter $q(z)$ for CPL, JBP, BA and Wang models. We find that: (i) Using the full JLA data, at high redshift $\alpha$ has a trend of decreasing at more than $1.5\sigma$ confidence level (CL), and $\beta$ has a significant trend of decreasing at more than $19\sigma$ CL. (ii) Compared with $\chi^2$ statistics (constant $\alpha$, $\beta$) and Bayesian statistics (constant $\alpha$, $\beta$), Bayesian statistics (linear $\alpha$ and $\beta$) yields a larger best-fit value of fractional matter density $\Omega_{m0}$ from JLA+CMB+GC data, which is much closer to slightly deviates from the best-fit result given by other cosmological observations. (iii) The figure of merit (FoM) given by JLA+CMB+GC data from Bayesian statistics is also larger than the FoM from $\chi^2$ statistics, which indicates that former statistics has a better accuracy. (iv) $q(z)$ given by both statistical methods favor an eternal cosmic acceleration at 1$\sigma$ CL.