Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio

Nitrogen hydrides in interstellar gas: Herschel/HIFI observations towards G10.6-0.4 (W31C)

The HIFI instrument on board the Herschel Space Observatory has been used to observe interstellar nitrogen hydrides along the sight-line towards G10.6−0.4 in order to improve our understanding of the interstellar chemistry of nitrogen. We report observations of absorption in NH N = 1 ← 0, J = 2 ← 1 and ortho-NH_2 1_(1,1) ← 0_(0,0). We also observed ortho-NH_3 1_0 ← 0_0, and 2_0 ← 1_0, para-NH_3 2_1 ← 1_1, and searched unsuccessfully for NH^+. All detections show emission and absorption associated directly with the hot-core source itself as well as absorption by foreground material over a wide range of velocities. All spectra show similar, non-saturated, absorption features, which we attribute to diffuse molecular gas. Total column densities over the velocity range 11−54 km s^(−1) are estimated. The similar profiles suggest fairly uniform abundances relative to hydrogen, approximately 6 × 10^(−9), 3 × 10^(−9), and 3 × 10^(−9) for NH, NH_2, and NH_3, respectively. These abundances are discussed with reference to models of gas-phase and surface chemistry

Interstellar CH absorption in the diffuse interstellar medium along the sight-lines to G10.6–0.4 (W31C), W49N, and W51

We report the detection of the ground state N, J = 1, 3/2 → 1, 1/2 doublet of the methylidyne radical CH at ~532 GHz and ~536 GHz with the Herschel/HIFI instrument along the sight-line to the massive star-forming regions G10.6–0.4 (W31C), W49N, and W51. While the molecular cores associated with these massive star-forming regions show emission lines, clouds in the diffuse interstellar medium are detected in absorption against the strong submillimeter background. The combination of hyperfine structure with emission and absorption results in complex profiles, with overlap of the different hyperfine components. The opacities of most of the CH absorption features are linearly correlated with those of CCH, CN, and HCO^+ in the same velocity intervals. In specific narrow velocity intervals, the opacities of CN and HCO^+ deviate from the mean trends, giving rise to more opaque absorption features. We propose that CCH can be used as another tracer of the molecular gas in the absence of better tracers, with [CCH]/[H_2] ~3.2 ± 1.1 × 10^(−8). The observed [CN]/[CH], [CCH]/[CH] abundance ratios suggest that the bulk of the diffuse matter along the lines of sight has gas densities n_H = n(H) + 2n(H_2) ranging between 100 and 1000 cm^(−3)

The Effect of Negative-Energy Shells on the Schwarzschild Black Hole

We construct Penrose diagrams for Schwarzschild spacetimes joined by massless shells of matter, in the process correcting minor flaws in the similar diagrams drawn by Dray and 't Hooft, and confirming their result that such shells generate a horizon shift. We then consider shells with negative energy density, showing that the horizon shift in this case allows for travel between the heretofore causally separated exterior regions of the Schwarzschild geometry. These drawing techniques are then used to investigate the properties of successive shells, joining multiple Schwarzschild regions. Again, the presence of negative-energy shells leads to a causal connection between the exterior regions, even in (some) cases with two successive shells of equal but opposite total energy.Comment: 12 pages, 10 figure

Rotational 3D Printing of Sensor Devices using Reactive Ink Chemistries

This paper charts progress in three key areas of a project supported by both UK government and UK industry to manufacture novel sensor devices using rotary 3D printing technology and innovative ink chemistries; (1) the development of an STL file slicing algorithm that returns constant Z height 2D contour data at a resolution that matches the given print head setup, allowing digital images to be generated of the correct size without the need for scaling; (2) the development of image transformation algorithms which allow images to be printed at higher resolutions using tilted print heads and; (3) the formulation of multi part reaction inks which combine and react on the substrate to form solid material layers with a finite thickness. A Direct Light Projection (DLP) technique demonstrated the robustness of the slice data by constructing fine detailed three dimensional test pieces which were comparable to identical parts built in an identical way from slice data obtained using commercial software. Material systems currently under investigation include plaster, stiff polyamides and epoxy polymers and conductive metallic’s. Early experimental results show conductivities of silver approaching 1.42x105 Siemens/m.Mechanical Engineerin

Renormalization Group and Universality

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$ scalar field theory. Our equations are superior compared with the usual approach which retains only the contributions that are non-vanishing in the ultraviolet regime. We find an indication for the existence of relevant operators at the infrared fixed point, contrary to common expectations. This result makes the sufficiency of using only renormalizable coupling constants in parametrizing the long distance phenomena questionable.Comment: 32pp in plain tex; revised version to appear in PR

The Near-Infrared Broad Emission Line Region of Active Galactic Nuclei -- I. The Observations

We present high quality (high signal-to-noise ratio and moderate spectral resolution) near-infrared (near-IR) spectroscopic observations of 23 well-known broad-emission line active galactic nuclei (AGN). Additionally, we obtained simultaneous (within two months) optical spectroscopy of similar quality. The near-IR broad emission line spectrum of AGN is dominated by permitted transitions of hydrogen, helium, oxygen, and calcium, and by the rich spectrum of singly-ionized iron. In this paper we present the spectra, line identifications and measurements, and address briefly some of the important issues regarding the physics of AGN broad emission line regions. In particular, we investigate the excitation mechanism of neutral oxygen and confront for the first time theoretical predictions of the near-IR iron emission spectrum with observations.Comment: 45 pages, 17 figures, accepted by ApJ