Application of a three-dimensional viscous transonic inverse method to NASA rotor 67

The development and application of a three-dimensional inverse methodology in which the blade geometry is computed on the basis of the specification of static pressure loading distribution is presented. The methodology is based on the intensive use of computational fluid dynamics (CFD) to account for three-dimensional subsonic and transonic viscous flows. In the design computation, the necessary blade changes are determined directly by the discrepancies between the target and initial values, and the calculation converges to give the final blade geometry and the corresponding steady state flow solution. The application of the method is explored using a transonic test case, NASA rotor 67. Based on observations, it is conclusive that the shock formation and its intensity in such a high-speed turbomachinery flow are well defined on the loading distributions. Pressure loading is therefore as effective a design parameter as conventional inverse design quantities such as static pressure. Hence, from an understanding of the dynamics of the flow in the fan in relation to its pressure loading distributions, simple guidelines can be developed for the inverse method in order to weaken the shock formation. A qualitative improvement in performance is achieved in the redesigned fan. The final flowfield result is confirmed by a well-established commercial CFD package

Thermodynamics of charged rotating dilaton black branes with power-law Maxwell field

In this paper, we construct a new class of charged rotating dilaton black brane solutions, with complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both canonical and grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of Maxwell field on the thermal stability of the solutions. We find that for $\alpha \leq 1$, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For $\alpha>1$, the solutions can encounter an unstable phase depending on the metric parameters.Comment: 15 pages, 14 figures. We have revised the text to remove the overlap

Counterterms for Static Lovelock Solutions

In this paper, we introduce the counterterms that remove the non-logarithmic divergences of the action in third order Lovelock gravity for static spacetimes. We do this by defining the cosmological constant in such a way that the asymptotic form of the metric have the same form in Lovelock and Einstein gravities. Thus, we employ the counterterms of Einstein gravity and show that the power law divergences of the action of Lovelock gravity for static spacetimes can be removed by suitable choice of coefficients. We find that the dependence of these coefficients on the dimension in Lovelock gravity is the same as in Einstein gravity. We also introduce the finite energy-momentum tensor and employ these counterterms to calculate the finite action and mass of static black hole solutions of third order Lovelock gravity. Next, we calculate the thermodynamic quantities and show that the entropy calculated through the use of Gibbs-Duhem relation is consistent with the obtained entropy by Wald's formula. Furthermore, we find that in contrast to Einstein gravity in which there exists no uncharged extreme black hole, third order Lovelock gravity can have these kind of black holes. Finally, we investigate the stability of static charged black holes of Lovelock gravity in canonical ensemble and find that small black holes show a phase transition between very small and small black holes, while the large ones are stable.Comment: arXiv admin note: text overlap with arXiv:1008.0102 by other author

Holographic Conductivity for Logarithmic Charged Dilaton-Lifshitz Solutions

We disclose the effects of the logarithmic nonlinear electrodynamics on the holographic conductivity of Lifshitz dilaton black holes/branes. We analyze thermodynamics of these solutions as a necessary requirement for applying gauge/gravity duality, by calculating conserved and thermodynamic quantities such as the temperature, entropy, electric potential and mass of the black holes/branes. We calculate the holographic conductivity for a $(2+1)$-dimensional brane boundary and study its behavior in terms of the frequency per temperature. Interestingly enough, we find out that, in contrast to the Lifshitz-Maxwell-dilaton black branes which has conductivity for all $z$, here in the presence of nonlinear gauge field, the holographic conductivity do exist provided $z\leq3$ and vanishes for $z>3$. It is shown that independent of the nonlinear parameter $\beta$, the real part of the conductivity is the same for a specific value of frequency per temperature in both AdS and Lifshitz cases. Besides, the behavior of real part of conductivity for large frequencies has a positive slope with respect to large frequencies for a system with Lifshitz symmetry whereas it tends to a constant for a system with AdS symmetry. This behavior may be interpreted as existence of an additional charge carrier rather than the AdS case, and is due to the presence of the scalar dilaton field in model. Similar behavior for optical conductivity of single-layer graphene induced by mild oxygen plasma exposure has been reported.Comment: V1: 12 pages, 5 figures (each one includes 2 subfigres) V2: 13 pages, Some references added, Conductivity calculations improved, Accepted for publication in PL

Holographic conductivity in the massive gravity with power-law Maxwell field

We obtain a new class of topological black hole solutions in $(n+1)$-dimensional massive gravity in the presence of the power-Maxwell electrodynamics. We calculate the conserved and thermodynamic quantities of the system and show that the first law of thermodynamics is satisfied on the horizon. Then, we investigate the holographic conductivity for the four and five dimensional black brane solutions. For completeness, we study the holographic conductivity for both massless ($m=0$) and massive ($m \neq 0$) gravities with power-Maxwell field. The massless gravity enjoys translational symmetry whereas the massive gravity violates it. For massless gravity, we observe that the real part of conductivity, $\mathrm{Re}[\sigma]$, decreases as charge $q$ increases when frequency $\omega$ tends to zero, while the imaginary part of conductivity, $\mathrm{Im}[\sigma ]$, diverges as $\omega \rightarrow 0$. For the massive gravity, we find that $\mathrm{Im}[\sigma ]$ is zero at $\omega =0$ and becomes larger as $q$\ increases (temperature decreases), which is in contrast to the massless gravity. Interestingly, we observe that in contrast to the massless case, $\mathrm{Re}[\sigma ]$ has a maximum value at $\omega =0$ (known as the Drude peak) for $p=\left( n+1\right) /4$ (conformally invariant electrodynamics) where $p$ is the power parameter of the power-law Maxwell field and this maximum increases with increasing $q$. Finally, we show that for high frequencies, the real part of the holographic conductivity have the power law behavior in terms of frequency, $\omega ^{a}$ where $a \propto (n+1-4p)$. Some similar behaviors for high frequencies in possible dual CFT systems have been reported in experimental observations.Comment: V2: 15 pages, 5 figures (each one includes \geq 3 subfigures), Some Refs added, Some discussions regarding i) the power-law Maxwell electrodynamics and ii) the relation between our results and experimental observations presented, A suggestion for future extensions give