Mode decomposition and renormalization in semiclassical gravity

We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being closely connected with models used in the literature, we show how to completely reconcile the results obtained in the context of stochastic semiclassical gravity when using mode decomposition with those obtained by other standard functional techniques.Comment: 4 pages, RevTeX, no figure

On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira

The classical theorems of Taylor, Lagrange, Laurent and Teixeira, are extended from the representation of a complex function F(z), to its derivative F(ν)(z) of complex order ν, understood as either a Liouville (1832) or a Rieman (1847) differintegration (Campos 1984, 1985); these results are distinct from, and alternative to, other extensions of Taylor's series using differintegrations (Osler 1972, Lavoie & Osler & Tremblay 1976). We consider a complex function F(z), which is analytic (has an isolated singularity) at ζ, and expand its derivative of complex order F(ν)(z), in an ascending (ascending-descending) series of powers of an auxiliary function f(z), yielding the generalized Teixeira (Lagrange) series, which includes, for f(z)=z−ζ, the generalized Taylor (Laurent) series. The generalized series involve non-integral powers and/or coefficients evaluated by fractional derivatives or integrals, except in the case ν=0, when the classical theorems of Taylor (1715), Lagrange (1770), Laurent (1843) and Teixeira (1900) are regained. As an application, these generalized series can be used to generate special functions with complex parameters (Campos 1986), e.g., the Hermite and Bessel types

Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes

The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum nature of spacetime. It reflects the low and medium energy (referring to Planck energy as high energy) behavior of any viable theory of quantum gravity, including string theory. It is also useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in cosmological and black holes spacetimes. We discuss the properties of this bi-tensor with the method of point-separation, and derive a regularized expression of the noise-kernel for a scalar field in general curved spacetimes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for Robertson-Walker and Schwarzschild spacetimes.Comment: 22 Pages, RevTeX; version accepted for publication in PR

Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to obtain, for Newtonian and non-Newtonian fluids, heat transfer coefficients, at constant wall temperature as boundary condition, in fully developed laminar flow inside a helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w) and the non-Newtonian fluids aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations 0.1%, 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations 0.1% and 0.2% (w/w). According to the rheological study performed, the polymer solutions had shear thinning behavior and different values of elasticity. The helical coil used has internal diameter, curvature ratio, length and pitch, respectively: 0.004575 m, 0.0263, 5.0 m and 11.34 mm. The Nusselt numbers for the CMC solutions are, on average, slightly higher than those for Newtonian fluids, for identical Prandtl and generalized Dean numbers. As outcome, the viscous component of the shear thinning polymer tends to potentiate the mixing effect of the Dean cells. The Nusselt numbers of the XG solutions are significant lower than those of the Newtonian solutions, for identical Prandtl and generalized Dean numbers. Therefore, the elastic component of the polymer tends to diminish the mixing effect of the Dean cells. A global correlation, for Nusselt number as a function of Péclet, generalized Dean and Weissenberg numbers for all Newtonian and non-Newtonian solutions studied, is presented

Vacuum Energy Density Fluctuations in Minkowski and Casimir States via Smeared Quantum Fields and Point Separation

We present calculations of the variance of fluctuations and of the mean of the energy momentum tensor of a massless scalar field for the Minkowski and Casimir vacua as a function of an intrinsic scale defined by a smeared field or by point separation. We point out that contrary to prior claims, the ratio of variance to mean-squared being of the order unity is not necessarily a good criterion for measuring the invalidity of semiclassical gravity. For the Casimir topology we obtain expressions for the variance to mean-squared ratio as a function of the intrinsic scale (defined by a smeared field) compared to the extrinsic scale (defined by the separation of the plates, or the periodicity of space). Our results make it possible to identify the spatial extent where negative energy density prevails which could be useful for studying quantum field effects in worm holes and baby universe, and for examining the design feasibility of real-life `time-machines'. For the Minkowski vacuum we find that the ratio of the variance to the mean-squared, calculated from the coincidence limit, is identical to the value of the Casimir case at the same limit for spatial point separation while identical to the value of a hot flat space result with a temporal point-separation. We analyze the origin of divergences in the fluctuations of the energy density and discuss choices in formulating a procedure for their removal, thus raising new questions into the uniqueness and even the very meaning of regularization of the energy momentum tensor for quantum fields in curved or even flat spacetimes when spacetime is viewed as having an extended structure.Comment: 41 pages, 2 figure

Investigation of a Multiple-Timescale Turbulence-Transport Coupling Method in the Presence of Random Fluctuations

One route to improved predictive modeling of magnetically confined fusion reactors is to couple transport solvers with direct numerical simulations (DNS) of turbulence, rather than with surrogate models. An additional challenge presented by coupling directly with DNS is that the inherent fluctuations in the turbulence, which limit the convergence achievable in the transport solver. In this article, we investigate the performance of one numerical coupling method in the presence of turbulent fluctuations. To test a particular numerical coupling method for the transport solver, we use an autoregressive-moving-average model to efficiently generate stochastic fluctuations with statistical properties resembling those of a gyrokinetic simulation. These fluctuations are then added to a simple, solvable problem, and we examine the behavior of the coupling method. We find that monitoring the residual as a proxy for the error can be misleading. From a pragmatic point of view, this study aids us in the full problem of transport coupled to DNS by predicting the amount of averaging required to reduce the fluctuation error and obtain a specific level of accuracy.Comment: 18 pages, 9 figure

FLAME PROFILE IN A POROUS RADIANT BURNER USING 1/2” AND 1/4” ALUMINA’S SPHERES

Porous burners are known by their high efficiency and low polluting gases emissions. Their high efficiency is given by the great thermal radiation potential, whereas differently a normal burner, the process of combustion happens in the inner of the porous medium, which is compound by spheres of alumina, and the mix air-fuel goes through the preheating zone, potentializing the combustion. The burners are usually used in the industry, in the process of drying of paper and wood, plastic coating, food cooking and ambient heating. In this article, it was studied the behaviour of the flame in a porous radiant burner with alumina’s sphere of 1/2” and 1/4”, using LPG as fuel, compressed air as oxidizing agent and ceramic wool as thermal insulation. The burner was divided in three essential sections with a type K thermocouple in each one, which are: base, middle and top. The flame profile encountered was a floating one, however it is almost stable, presenting low variations of temperature and according to previously tests, less consuming of fuel