On AdS2AdS_2 holography from redux, renormalization group flows and cc-functions

Extremal black branes upon compactification in the near horizon throat region are known to give rise to $AdS_2$ dilaton-gravity-matter theories. Away from the throat region, the background has nontrivial profile. We interpret this as holographic renormalization group flow in the 2-dim dilaton-gravity-matter theories arising from dimensional reduction of the higher dimensional theories here. The null energy conditions allow us to formulate a holographic c-function in terms of the 2-dim dilaton for which we argue a c-theorem subject to appropriate boundary conditions which amount to restrictions on the ultraviolet theories containing these extremal branes. At the infrared $AdS_2$ fixed point, the c-function becomes the extremal black brane entropy. We discuss the behaviour of this inherited c-function in various explicit examples, in particular compactified nonconformal branes, and compare it with other discussions of holographic c-functions. We also adapt the holographic renormalization group formulated in terms of radial Hamiltonian flow to 2-dim dilaton-gravity-scalar theories, which while not Wilsonian, gives qualitative insight into the flow equations and $\beta$-functions.Comment: Latex, 40pgs incl appendices; v2: minor tweaks, figure added; v3: minor clarifications added, matches version to be publishe

Mean field dynamo action in renovating shearing flows

We study mean field dynamo action in renovating flows with finite and non zero correlation time ($\tau$) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and non helical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly non helical, then such mean field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval $\tau$. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the $\alpha^2 \Omega$ dynamo, in the small $\tau$ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.Comment: 16 pages, 1 figur

Hyperscaling violation and the shear diffusion constant

We consider holographic theories in bulk $(d+1)$-dimensions with Lifshitz and hyperscaling violating exponents $z,\theta$ at finite temperature. By studying shear gravitational modes in the near-horizon region given certain self-consistent approximations, we obtain the corresponding shear diffusion constant on an appropriately defined stretched horizon, adapting the analysis of Kovtun, Son and Starinets. For generic exponents with $d-z-\theta>-1$, we find that the diffusion constant has power law scaling with the temperature, motivating us to guess a universal relation for the viscosity bound. When the exponents satisfy $d-z-\theta=-1$, we find logarithmic behaviour. This relation is equivalent to $z=2+d_{eff}$ where $d_{eff}=d_i-\theta$ is the effective boundary spatial dimension (and $d_i=d-1$ the actual spatial dimension). It is satisfied by the exponents in hyperscaling violating theories arising from null reductions of highly boosted black branes, and we comment on the corresponding analysis in that context.Comment: Latex, 17pgs, v3: clarifications added on z<2+d_{eff} and standard quantization, to be publishe

Dynamic Interaction of a Marine Hydrokinetic Turbine with Its Surrounding Environment

A marine hydrokinetic turbine (MHkT) operating in its natural environment is subjected to dynamic effects due to variations in its operating conditions. Though the flow velocity and direction are predictable and do not undergo drastic variations as in wind turbines (wind gusts and changes in wind direction), a denser working medium due to placement in water imposes higher structural loading on turbine blades. Furthermore, a variation in water depth alters the turbine depth of immersion during operation. These dynamic conditions change the ratio between the turbine rotation disc (area) and channel area that affects blockage and hence the performance characteristics. Furthermore, variations in blade tip clearance from free surface is hypothesized to affect flow-field and performance characteristics of a marine hydrokinetic turbine, especially those operating in a shallow channel. Significant flow acceleration occurs in and around the turbine rotation plane; the magnitude of which depends on size of the turbine relative to the channel cross-section and is commonly referred to as solid blockage. In addition, the wake behind the turbine creates a restriction to the flow called wake blockage. Understanding the effects of solid and wake blockages in presence of free surface proximity on performance of MHkT is crucial for deployment and efficient operation of individual turbines. In addition, since the free surface is deformable, it is expected to modify both near and far-wake characteristics behind a turbine which must be accounted for in order to develop efficient models of MHkT farms where an array of such devices are deployed in the river bed.In this dissertation, the dynamic interaction of a stall regulated, fixed pitch, horizontal axis MHkT with its environment is addressed through closely coupled experimental, computational and analytical studies. The analytical model was developed based on blade element momentum theory to investigate effect of rotational speed, flow speed, blade pitch, chord length, twist angle on hydrodynamic and structural performance of turbine. The model was further extended to perform one way fluid-structure interaction analysis and a multi-objective optimization (with Genetic Algorithm) study for improving hydrodynamic and structural performance of river-turbine-prototype. To validate the results of analytical model, a three dimensional coupled- computational fluid dynamics-finite element analysis scheme was developed in ANSYS Workbench. In addition, a coupled experimental and computational study was carried out with the objective of unraveling the influence of boundary proximity and blockage effects on the turbine performance. Experimental efforts consisted of performance measurements with a lab-scale prototype in a water channel at various flow velocities, rotational speeds, and depths of immersions to understand effects of free surface proximity, Reynolds number, and Froude number on power and thrust developed by the turbine. The experimental measurements were complimented by a steady state and transient CFD analysis for flow-field characterization behind the turbine. Further, to quantify the influence of free surface proximity on blockage effects, two different models were developed: first for a closed-top channel, and second an open surface water channel (free surface proximity environment). The blockage effects were quantified in terms of percentage change in flow velocity, power coefficient, and thrust coefficient compared to an unblocked, non-free surface environment. In addition, to understand the mechanism responsible for variation of power coefficient with rotational speed and free surface proximity, stereoscopic particle image velocimetry measurements were carried out in the near-wake region of turbine at various rotational speeds and blade tip-free surface clearances. Time averaged measurements were carried out to determine the ensemble-averaged statistics of flow quantities such as mean velocity, strain rates, Reynolds stresses, and turbulence parameters at various turbine operating conditions. In addition to free-run PIV, a phase locked PIV measurements were carried out in the wake region to study transient phenomena like wake development and propagation process, tip and hub vortices formation and propagation.A reduction in tip-depth of immersion was observed to improve the turbine performance until it reached an optimum depth beyond which a reduction in performance was observed due to free surface interaction with wake and bypass region. For low tip clearance ratios, a significant drop (up to 5 to 10% of channel depth) in free surface was observed (from both experimental investigations and transient CFD analysis) behind the turbine with complex three dimensional flow structures that lead to a skewed wake affecting its expansion and restoration process. The percent change in power coefficient (with respect to unblocked, non-free surface environment) was found to be dependent on flow velocity, rotation speed and free surface to blade tip clearance. Flow field visualization, based on SPIV, showed presence of slower wake at higher rotational velocities and increased asymmetry in wake at high free surface proximity. In addition, significant difference in flow structures was observed between upper and lower bypass regions

Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity

We study quasi-stationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase-theorem in a wider class of gravitational theories.Comment: 5 pages, no figur

Effect of Cooling Conditions, Retrofitting on Strength of Concrete Subjected to Elevated Temperature

Concrete has a high degree of fire resistance at moderate temperatures. High temperatures, however, cause concrete to lose its stiffness and strength. The effects of cooling techniques and retrofitting on the strength of concrete exposed to high temperatures have not been synchronized in previous studies. This experimental research aims to evaluate the effect of cooling conditions and the effectiveness of retrofitting concrete subjected to elevated temperatures. Four types of concrete: M 20 normal concrete (NC); M 20 metakaolin concrete (MC); M 40 standard concrete (SC); and M 40 self-compacting concrete (SCC) are considered in this study. A total of 864 samples consisting of cube, beam, and cylinder specimens are subjected to sustained elevated temperatures of 400oC, 600oC, and 800oC for 2 hours rating. The weight and strength of half of the heat-damaged samples are assessed following natural air cooling (NAC) and water jet cooling (WJC). The remaining 50% of samples retrofitted with carbon fiber reinforced polymer (CFRP) are tested to evaluate the upgraded strength. The experimental findings demonstrate that water jet cooling (WJC) causes more strength degradation, and CFRP proves to be effective in restoring the strength of heat-deteriorated specimens. Overall, self-compacting concrete (SCC) has shown high resistance to elevated temperatures. Doi: 10.28991/CEJ-2023-09-07-013 Full Text: PD