Topological Defect Lines and Renormalization Group Flows in Two Dimensions

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.Comment: 101 pages, 63 figures, 2 tables; v3: minor changes, added footnotes and references, published versio

Topological Defect Lines in Two Dimensional Fermionic CFTs

We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the worldline of the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. We propose a classification of the rank-2 super fusion categories and explicitly construct all the nontrivial ones. We derive the corresponding spin selection rules that constrain the spectrum of the defect operators. Finally, we discuss a constraint on the renormalization group flow that preserves a q-type TDL.Comment: 38+20 page

Sensitive detection of methane at 3.3 μm using an integrating sphere and interband cascade laser

Detection of methane at 3.3μm using a DFB Interband Cascade Laser and gold coated integrating sphere is performed. A 10cm diameter sphere with effective path length of 54.5cm was adapted for use as a gas cell. A comparison between this system and one using a 25cm path length single-pass gas cell is made using direct TDLS and methane concentrations between 0 and 1000 ppm. Initial investigations suggest a limit of detection of 1.0ppm for the integrating sphere and 2.2ppm for the single pass gas cell. The system has potential applications in challenging or industrial environments subject to high levels of vibration

Influence of incubation temperature on morphology and locomotion performance of Leatherback (<i>Dermochelys coriacea</i>) hatchlings

The journey of Leatherback (Dermochelys coriacea (Vandelli, 1761)) hatchlings from nest to the sea is a vulnerable life-history stage. Studies have shown that nest incubation temperatures influence hatchling morphology and locomotor performance, which may affect hatchling fitness. We obtained incubation temperature profiles from 16 Leatherback nests in Tobago, West Indies, during the 2008 nesting season (March-June). There was significant variation among mean nest incubation temperatures, which had a significant influence on hatchling morphology. Using principal components analysis, we determined the morphological traits that explained the most variation among hatchlings, which allowed investigation of the relationship between hatchling morphology and terrestrial locomotion speed. Hatchlings with a narrower carapace width and longer flipper reach (produced at lower incubation temperatures) had significantly faster terrestrial speed and total run time than those with opposite characteristics (produced at higher incubation temperatures). Our results demonstrate that lower incubation temperatures produce hatchlings with traits that are significantly advantageous to terrestrial locomotion. These findings suggest that nest incubation temperature is important in determining hatchling fitness, as nest incubation temperature significantly influences hatchling morphology and locomotor capabilities. This study supplements related findings in Green Turtles (Chelonia mydas (L., 1758)), but also illustrates some unique features in Leatherbacks

In-situ, real time gas composition measurements for SOFC's using laser spectroscopy

The use of standard gas composition measurement techniques, such as gas chromatography, in large scale solid oxide fuel cells (SOFC's) operating at high temperatures can be both complex and time consuming. One of the main constraints is the necessity to condense out the water vapour present in the gas streams prior to measurement in the Gas Chromatograph (GC). True gas compositions can only be extracted through back-calculation, with each measurement taking in the order of minutes, and a number of measurement points needed to make the final measurement. For system status monitoring such a time delay between condition changes and measurement is a serious disadvantage. One of the main concerns for systems running on natural gas is the risk of methane slippage through the internal reformer, which increases the risk of carbon formation on the SOFC anode, invariably leading to irreversible loss of performance. It is therefore highly advantageous to measure gas stream compositions within the SOFC system in real time, enabling a rapid response to composition deviation outside of acceptable limits. Gas chromatography can never be made to work as a real-time system status monitoring product solution. A suitable, in-situ, solution for measurement is tuneable diode laser spectroscopy, TDLS. Using this technique it is possible to measure both the gas concentration and system pressure simultaneously for a number of different species, without condensing out the water vapour: reducing analysis time considerably and reducing errors associated with back calculation. In this paper, data taken on an operational fuel cell system is presented for methane, and a comparison with results obtained using a GC is made

Calculation of double-lunar swingby trajectories: Part 2: Numerical solutions in the restricted problem of three bodies

The double-lunar swingby trajectory is a method for maintaining alignment of an Earth satellite's line of apsides with the Sun-Earth line. From a Keplerian point of view, successive close encounters with the Moon cause discrete, instantaneous changes in the satellite's eccentricity and semimajor axis. Numerical solutions to the planar, restricted problem of three bodies as double-lunar swingby trajectories are identified. The method of solution is described and the results compared to the Keplerian formulation

Gas cells for tunable diode laser absorption spectroscopy employing optical diffusers. Part 1: single and dual pass cells

New designs for gas cells are presented that incorporate transmissive or reflective optical diffusers. These components offer simple alignment and can disrupt the formation of optical etalons. We analyse the performance-limiting effects in these cells of random laser speckle (both objective and subjective speckle), interferometric speckle and self-mixing interference, and show how designs can be optimised. A simple, single pass transmissive gas cell has been studied using wavelength modulation spectroscopy to measure methane at 1651 nm. We have demonstrated a short-term noise equivalent absorbance (NEA, 1 sigma) of 2x10(-5), but longer term drift of up to 3x10(-4) over 22 hours

Generalized Cardy conditions of topological defect lines

We propose a systematic procedure to work out systems of topological defect lines (TDLs) in minimal models. The only input of this method is the modular invariant partition function. For diagonal and permutation diagonal models, we prove there is a bijection between simple TDLs and primary fields preserving fusion rules. For block-diagonal models, we work out simple TDLs in the $3$-state Potts model as an example. The results agree with those in $3D$ topological field theory methods.Comment: 30 pages, 12 figure