Gravity/Fluid Correspondence and Its Application on Bulk Gravity with U(1)U(1) Gauge Field

As the long wavelength limit of the AdS/CFT correspondence, the gravity/fluid correspondence has been shown to be a useful tool for extracting properties of the fluid on the boundary dual to the gravity in the bulk. In this paper, after briefly reviewing the algorithm of gravity/fluid correspondence, we discuss the results of its application on bulk gravity with a $U(1)$ gauge field. In the presence of a $U(1)$ gauge field, the dual fluid possesses more interesting properties such as its charge current. Furthermore, an external field $A_\mu^{ext}$ could affect the charge current, and the $U(1)$ Chern-Simons term also reinduces extra structures to the dual current giving anomalous transport coefficients.Comment: 14 pages, no figure, version publishe

Generalized Vaidya Solutions and Misner-Sharp mass for nn-dimensional massive gravity

Dynamical solutions are always of interest to people in gravity theories. We derive a series of generalized Vaidya solutions in the $n$-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric. Similar to the case of the Einstein gravity, the generalized Vaidya solution can describe shining/absorbing stars. Moreover, we also find a more general Vaidya-like solution by introducing a more generic matter field than the pure radiation in the original Vaidya spacetime. As a result, the above generalized Vaidya solution is naturally included in this Vaidya-like solution as a special case. We investigate the thermodynamics for this Vaidya-like spacetime by using the unified first law, and present the generalized Misner-Sharp mass. Our results show that the generalized Minser-Sharp mass does exist in this spacetime. In addition, the usual Clausius relation $\delta Q= TdS$ holds on the apparent horizon, which implicates that the massive gravity is in a thermodynamic equilibrium state. We find that the work density vanishes for the generalized Vaidya solution, while it appears in the more general Vaidya-like solution. Furthermore, the covariant generalized Minser-Sharp mass in the $n$-dimensional de Rham-Gabadadze-Tolley massive gravity is also derived by taking a general metric ansatz into account.Comment: 10 pages, no figure, version published in PR

SUSY SU(5) ×S4\times S_{4} GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large θ13PMNS\theta^{PMNS}_{13}

We propose an $S_{4}$ flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of \textbf{10} dimensional representations in SU(5) are all assigned to be $1_{1}$ of $S_{4}$. The second generation of \textbf{10} is to be $1_{2}$ of $S_{4}$. Right-handed neutrinos of singlet \textbf{1} and three generations of $\bar{\textbf{5}}$ are all assigned to be $3_{1}$ of $S_{4}$. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is $\langle\Phi^{\nu}\rangle \sim \lambda_{c}\langle\Phi^{e}\rangle$. Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification $m_{\tau}=m_{b}$ and the popular Georgi-Jarlskog relation $m_{\mu}=3m_{s}$ as well as a new mass relation $m_{e}=\frac{8}{27}m_{d}$ in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field $H_{24}$. The GUT relation leads to a sizable mixing angle $\theta^{e}_{12} \sim \theta_{c}$ and the correct quark mixing matrix $V_{CKM}$ can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing $\theta^{\nu}_{13}$ in TBM mixing to a large $\theta^{PMNS}_{13}\simeq\theta_{c}/\sqrt{2}$, in excellent agreement with experimental results. A Dirac CP violation phase $\phi_{12}\simeq\pm\pi/2$ is required to make the deviation from $\theta^{\nu}_{12}$ small. We also present some phenomenological numerical results predicted by the model.Comment: 36 pages, 12 figures, major revison to the previous editio

Thermodynamics of Black Holes in Massive Gravity

We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -\mu^2/4 +c_2 m^2$ in the four dimensional case, where $\mu$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 \ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.Comment: Latex 19 pages with 8 figure

VPM/CFD-Based Research on Rotor Performance and Loads of Individual Blade Control Rotor System

This paper aims to explore the effect of individual blade control (IBC) on aerodynamic performance of helicopter rotor and explain its formation mechanism. For this purpose, the vortex particle method (VPM)-computational fluid dynamics (CFD) coupling method was proposed to calculate rotor aerodynamic performance under open-loop IBC active control. Specifically, the near-blade flow field was calculated by the CFD method, while the far-field flow field was solved by the VPM method. In this way, the entire flow field was computed through the information interaction between the two calculated fields. Then, the UH-60A rotor was selected as an example to verify the established VPM/CFD method. First, the proposed method was proved valid; then, the effect of control frequency and phase on the helicopter performance was analysed under different forward flight conditions; finally, the mechanism of IBC control was examined by comparing the lift coefficient distribution and the induced inflows of the optimal control and the worst control. The results showed that proper IBC control parameters can lower the required power of the rotor to some extent, but the optimal control parameters vary with flight states. Comparatively, the lift distribution is more even and the induced flows are less fluctuating under optimal control than under worst control

Lifshitz Scaling Effects on Holographic Superconductors

Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent $z$ on holographic superconductors are studied in some detail, including $s$ wave and $p$ wave models. Working in the probe limit, we find that the behaviors of holographic models indeed depend on concrete value of $z$. We obtain the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with general $z$. For both $s$ wave and $p$ wave models in the black hole backgrounds, as $z$ increases, the phase transition becomes more difficult and the growth of conductivity is suppressed. For the Lifshitz soliton backgrounds, when $z$ increases ($z=1,~2,~3$), the critical chemical potential decreases in the $s$ wave cases but increases in the $p$ wave cases. For $p$ wave models in both Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when $z$ increases. The analytical results uphold the numerical results.Comment: Typos corrected; Footnote added; References added; To be published in Nuclear Physics