Background independent exact renormalization group for conformally reduced gravity

Within the conformally reduced gravity model, where the metric is parametrised by a function $f(\phi)$ of the conformal factor $\phi$, we keep dependence on both the background and fluctuation fields, to local potential approximation and $\mathcal{O}(\partial^2)$ respectively, making no other approximation. Explicit appearances of the background metric are then dictated by realising a remnant diffeomorphism invariance. The standard non-perturbative Renormalization Group (RG) scale $k$ is inherently background dependent, which we show in general forbids the existence of RG fixed points with respect to $k$. By utilising transformations that follow from combining the flow equations with the modified split Ward identity, we uncover a unique background independent notion of RG scale, $\hat k$. The corresponding RG flow equations are then not only explicitly background independent along the entire RG flow but also explicitly independent of the form of $f$. In general $f(\phi)$ is forced to be scale dependent and needs to be renormalised, but if this is avoided then $k$-fixed points are allowed and furthermore they coincide with $\hat k$-fixed points.Comment: 53 pages, broken reference correcte

Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety

In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of symmetries of the particular choice of renormalisation group equations. This clarifies when Newton’s constant and or the cosmological constant can be considered inessential. We then apply these ideas to the Local Potential Approximation and approximations of a similar spirit such as the f (R) approximation in the asymptotic safety programme in quantum gravity. We show that these approximations can break down if the fixed point does not support a ‘vacuum’ solution in the appropriate domain: all eigenoperators become redundant and the physical space of perturbations collapses to a point. We show that this is the case for the recently discovered lines of fixed points in the f (R) flow equations

Asymptotic safety in the f(R) approximation

In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R>0. We confront these with the requirement that a fixed point solution be smooth and exist for all non-negative R. Singularities induced by cutoff choices force the earlier versions to have no such solutions. However, we show that the most recent version has a number of lines of fixed points, each supporting a continuous spectrum of eigen-perturbations. We uncover and analyse the first five such lines. Sensible fixed point behaviour may be achieved if one consistently incorporates geometry/topology change. As an exploratory example, we analyse the equations analytically continued to R<0, however we now find only partial solutions.We show how these results are always consistent with, and to some extent can be predicted from, a straightforward analysis of the constraints inherent in the equations.Comment: Latex, 66 pages, published version, typos correcte

Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited

The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Gamma_corr of the cross-section correlation function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as function of the parameter under consideration. They, actually, stated that the product of the average number of maxima per unit energy range and Gamma_corr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances

Demonstration of rapid and sensitive module leak certification for Space Station Freedom

A leak detection and quantification demonstration using perflurocarbon tracer (PFT) technology was successfully performed at the NASA Marshall Space Flight Center on January 25, 1991. The real-time Dual Trap Analyzer (DTA) at one-half hour after the start of the first run gave an estimated leak rate of 0.7 mL/min. This has since been refined to be 1.15 (+ or -) 0.09 mL/min. The leak rates in the next three runs were determined to be 9.8 (+ or -) 0.7, -0.4 (+ or -) 0.3, and 76 (+ or -) 6 mL/min, respectively. The theory on leak quantification in the steady-state and time-dependent modes for a single zone test facility was developed and applied to the above determinations. The laboratory PFT analysis system gave a limit-of-detection (LOD) of 0.05 fL for ocPDCH. This is the tracer of choice and is about 100-fold better than that for the DTA. Applied to leak certification, the LOD is about 0.00002 mL/s (0.000075 L/h), a 5 order-of-magnitude improvement over the original leak certification specification. Furthermore, this limit can be attained in a measurement period of 3 to 4 hours instead of days, weeks, or months. A new Leak Certification Facility is also proposed to provide for zonal (three zones) determination of leak rates. The appropriate multizone equations, their solutions, and error analysis have already been derived. A new concept of seal-integrity certification has been demonstrated for a variety of controlled leaks in the range of module leak testing. High structural integrity leaks were shown to have a linear dependence of flow on (Delta)p. The rapid determination of leak rates at different pressures is proposed and is to be determined while subjecting the module to other external force-generating parameters such as vibration, torque, solar intensity, etc

Shatter cones: Diagnostic impact signatures

Uniquely fractured target rocks known as shatter cones are associated with more than one half the world's 120 or so presently known impact structures. Shatter cones are a form of tensile rock failure in which a positive conical plug separates from a negative outer cup or mold and delicate ornaments radiating from an apex are preserved on surfaces of both portions. Although distinct, shatter cones are sometimes confused with other striated geologic features such as ventifacts, stylolites, cone-in-cone, slickensides, and artificial blast plumes. Complete cones or solitary cones are rare, occurrences are usually as swarms in thoroughly fractured rock. Shatter cones may form in a zone where an expanding shock wave propagating through a target decays to form an elastic wave. Near this transition zone, the expanding primary wave may strike a pebble or other inhomogeneity whose contrasting transmission properties produce a scattered secondary wave. Interference between primary and secondary scattered waves produce conical stress fields with axes perpendicular to the plane of an advancing shock front. This model supports mechanism capable of producing such shatter cone properties as orientation, apical clasts, lithic dependence, and shock pressure zonation. Although formational mechanics are still poorly understood, shatter cones have become the simplest geologic field criterion for recognizing astroblemes (ancient terrestrial impact structures)

The local potential approximation in the background field formalism

Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.Comment: 40 pages, version accepted by JHE

The Impact of Stress Shadowing with variations in Cluster Spacing on the Production for Wells Completed in the Marcellus Shale

The design of the well stimulation treatment has significantly changed over the last decade because of the advancement of hydraulic fracturing. The cluster and stage spacing design component of hydraulic fracturing has been a key factor in enhancing the production from the horizontal wells. Recently, the treatment designs are moving towards lower cluster spacing. The reduction of the spacing alters the in-situ stresses in the formation and begin to impact the propagation of next set of future fractures and the properties of previous fractures. These stress alterations from hydraulic fracturing is referred to as stress shadowing. The objective of study was to investigate the impact of the cluster spacing and the completion design on the production from a horizontal shale gas well. The available completion, drilling, and reservoir data from a horizontal shale gas well located at Marcellus Shale Energy and Environment Laboratory (MSEEL) in Morgantown, WV was used to develop the base model for this study using GOHFER 3D fracture modeling software coupled with CMG reservoir simulation software. Subsequently, different the cluster spacings and the completion designs were modeled with GOHFER 3D to evaluate the impact that stress shadowing has on fractures properties. The predicted fractures properties were then imported into CMG reservoir simulation to predict the production performance. The results of the study provided a better understanding of the stress shadowing in shale gas reservoirs relative to the cluster spacing of the completion design

Static axisymmetric spacetimes with non-generic world-line SUSY

The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of solutions admitting Killing-Yano tensors is considered. In particular, it is shown that static, axisymmetric and asymptotically flat vacuum solutions admitting Killing-Yano tensors are only the Schwarzschild solution.Comment: 10 pages (RevTeX), TIT/HEP-253/COSMO-4