Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function

We review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar ${\cal N} = 4$ supersymmetric Yang-Mills theory. In particular, we highlight the different forms of cluster-algebraic structure that appear in this theory's two-loop MHV amplitudes---considered as functions, symbols, and at the level of their Lie cobracket---and recount how the `nonclassical' part of these amplitudes can be decomposed into specific functions evaluated on the $A_2$ or $A_3$ subalgebras of Gr$(4,n)$. We then extend this line of inquiry by searching for other subalgebras over which these amplitudes can be decomposed. We focus on the case of seven-particle kinematics, where we show that the nonclassical part of the two-loop MHV amplitude is also constructible out of functions evaluated on the $D_5$ and $A_5$ subalgebras of Gr$(4,7)$, and that these decompositions are themselves decomposable in terms of the same $A_4$ function. These nested decompositions take an especially canonical form, which is dictated in each case by constraints arising from the automorphism group of the parent algebra.Comment: 68 pages, 7 figures, 6 table

The host galaxies of luminous radio-quiet quasars

We present the results of a deep K-band imaging study which reveals the host galaxies around a sample of luminous radio-quiet quasars. The K-band images, obtained at UKIRT, are of sufficient quality to allow accurate modelling of the underlying host galaxy. Initially, the basic structure of the hosts is revealed using a modified Clean deconvolution routine optimised for this analysis. 2 of the 14 quasars are shown to have host galaxies with violently disturbed morphologies which cannot be modelled by smooth elliptical profiles. For the remainder of our sample, 2D models of the host and nuclear component are fitted to the images using the chi-squared statistic to determine goodness of fit. Host galaxies are detected around all of the quasars. The reliability of the modelling is extensively tested, and we find the host luminosity to be well constrained for 9 quasars. The derived average K-band absolute K-corrected host galaxy magnitude for these luminous radio-quiet quasars is =-25.15+/-0.04, slightly more luminous than an L* galaxy. The spread of derived host galaxy luminosities is small, although the spread of nuclear-to-host ratios is not. These host luminosities are shown to be comparable to those derived from samples of quasars of lower total luminosity and we conclude that there is no correlation between host and nuclear luminosity for these quasars. Nuclear-to-host ratios break the lower limit previously suggested from studies of lower nuclear luminosity quasars and Seyfert galaxies. Morphologies are less certain but, on the scales probed by these images, some hosts appear to be dominated by spheroids but others appear to have disk-dominated profiles.Comment: 16 pages, 8 figures, revised version to be published in MNRA

Toward gas-phase controlled mass transfer in micro-porous membrane contactors for recovery and concentration of dissolved methane in the gas phase

A micro-porous hollow fibre membrane contactor (HFMC) operated in sweep-gas mode has been studied to enable the recovery of dissolved methane from water in concentrated form. At high sweep-gas flow rates, up to 97% dissolved methane removal efficiency is achievable which is sufficient to achieve carbon neutrality (around 88%). An increase in methane composition of the recovered sweep-gas was achievable through two primary mechanisms: (i) an increase in liquid velocity which improved dissolved methane mass transfer into the gas phase; and (ii) a reduction in gas flow which lowered dilution from the receiving gas phase. It was posited that further refinement of the methane content was provided through counter-diffusion of the nitrogen sweep-gas into the liquid phase. Within the boundary conditions studied, the methane composition of the recovered gas phase exceeded the threshold for use in micro-turbines for electricity production. However, reducing the gas-to-liquid ratio to enhance gas phase methane purity introduced gas-phase controlled mass transfer which constrained removal efficiency. Whilst this reduction in removal efficiency can be compensated for by extending path length (i.e. more than one module in series), it is suggested that the gas-phase controlled conditions encountered were also a product of poor shell-side dispersion rather than an approach toward the limiting theoretical gas-to-liquid ratio. This implies that further optimisation can be ascertained through improved membrane contactor design. Importantly, this study demonstrates that micro-porous hollow fibre membrane contactors provide a compact process for recovery of dissolved methane in sufficient concentration for re-use

Biogas upgrading by chemical absorption using ammonia rich absorbents derived from wastewater

The use of ammonia (NH3) rich wastewaters as an ecological chemical absorption solvent for the selective extraction of carbon dioxide (CO2) during biogas upgrading to ‘biomethane’ has been studied. Aqueous ammonia absorbents of up to 10,000 gNH3 m−3 demonstrated CO2 absorption rates higher than recorded in the literature for packed columns using 20,000–80,000 g NH3 m−3 which can be ascribed to the process intensification provided by the hollow fibre membrane contactor used in this study to support absorption. Centrifuge return liquors (2325 g m−3 ionised ammonium, NH4+) and a regenerant (477 gNH4+ m−3) produced from a cationic ion exchanger used to harvest NH4+ from crude wastewater were also tested. Carbon dioxide fluxes measured for both wastewaters compared reasonably with analogue ammonia absorption solvents of equivalent NH3 concentration. Importantly, this demonstrates that ammonia rich wastewaters can facilitate chemically enhanced CO2 separation which eliminates the need for costly exogenic chemicals or complex chemical handling which are critical barriers to implementation of chemical absorption. When testing NH3 analogues, the potential to recover the reaction product ammonium bicarbonate (NH4HCO3) in crystalline form was also illustrated. This is significant as it suggests a new pathway for ammonia separation which avoids biological nitrification and produces ammonia stabilised into a commercially viable fertiliser (NH4HCO3). However, in real ammonia rich wastewaters, sodium bicarbonate and calcium carbonate were preferentially formed over NH4HCO3 although it is proposed that NH4HCO3 can be preferentially formed by manipulating both ion exchange and absorbent chemistry

Quantifying the loss of methane through secondary gas mass transport (or 'slip') from a micro-porous membrane contactor applied to biogas upgrading

Secondary gas transport during the separation of a binary gas with a micro-porous hollow fibre membrane contactor (HMFC) has been studied for biogas upgrading. In this application, the loss or ‘slip' of the secondary gas (methane) during separation is a known concern, specifically since methane possesses the intrinsic calorific value. Deionised (DI) water was initially used as the physical solvent. Under these conditions, carbon dioxide (CO2) and methane (CH4) absorption were dependent upon liquid velocity (VL). Whilst the highest CO2 flux was recorded at high VL, selectivity towards CO2 declined due to low residence times and a diminished gas-side partial pressure, and resulted in slip of approximately 5.2% of the inlet methane. Sodium hydroxide was subsequently used as a comparative chemical absorption solvent. Under these conditions, CO2 mass transfer increased by increasing gas velocity (VG) which is attributed to the excess of reactive hydroxide ions present in the solvent, and the fast conversion of dissolved CO2 to carbonate species reinitiating the concentration gradient at the gas-liquid interface. At high gas velocities, CH4 slip was reduced to 0.1% under chemical conditions. Methane slip is therefore dependent upon whether the process is gas phase or liquid phase controlled, since methane mass transport can be adequately described by Henry's law within both physical and chemical solvents. The addition of an electrolyte was found to further retard CH4 absorption via the salting out effect. However, their applicability to physical solvents is limited since electrolytic concentration similarly impinges upon the solvents' capacity for CO2. This study illustrates the significance of secondary gas mass transport, and furthermore demonstrates that gas-phase controlled systems are recommended where greater selectivity is required

NICMOS Observations of Low-Redshift Quasar Host Galaxies

We have obtained Near-Infrared Camera and Multi-Object Spectrometer images of 16 radio quiet quasars observed as part of a project to investigate the ``luminosity/host-mass limit.'' The limit results were presented in McLeod, Rieke, & Storrie-Lombardi (1999). In this paper, we present the images themselves, along with 1- and 2-dimensional analyses of the host galaxy properties. We find that our model-independent 1D technique is reliable for use on ground-based data at low redshifts; that many radio-quiet quasars live in deVaucouleurs-law hosts, although some of the techniques used to determine host type are questionable; that complex structure is found in many of the hosts, but that there are some hosts that are very smooth and symmetric; and that the nuclei radiate at ~2-20% of the Eddington rate based on the assumption that all galaxies have central black holes with a constant mass fraction of 0.6%. Despite targeting hard-to-resolve hosts, we have failed to find any that imply super-Eddington accretion rates.Comment: To appear in ApJ, 28 pages including degraded figures. Download the paper with full-resolutio figures from http://www.astro.wellesley.edu/kmcleod/mm.p

An exploration into the client at the heart of therapy : a qualitative perspective

Over 50 years ago Eysenck challenged the existing base of research into psychotherapy. Since that time, a large number of investigations have been conducted to verify the efficacy of therapy. Recently however, an increasing number of studies have cast new doubts on this research base. Instead of therapy being a function of the therapist, it is now becoming ever more apparent that the client plays a prime role in the therapeutic process. The qualitative studies presented in this paper provide some examples of research that demonstrates that clients are actively involved in their therapy, even making counselling work despite their counsellor. These studies suggest that clients may not experience therapy as beneficially as traditional outcome studies indicate. This raises a new challenge to researchers to more fully explore the client's experience of therapy, a challenge to which qualitative methods of inquiry would appear well suited

Practical Bayesian Optimization for Variable Cost Objectives

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to sampling support points, allowing faster construction of the acquisition function. This allows us to achieve optimization with lower overheads than previous approaches and is implemented for a more general class of problem. We show this approach to be effective on synthetic and real world benchmark problems.Comment: 8 pages, 7 figure

Controlling shell-side crystal nucleation in a gas-liquid membrane contactor for simultaneous ammonium bicarbonate recovery and biogas upgrading

A gas–liquid hollow fibre membrane contactor (HFMC) process has been introduced for carbon dioxide (CO2) separation from biogas where aqueous ammonia (NH3) is used to chemically enhance CO2 absorption and initiate heterogeneous nucleation of the reaction product ammonium bicarbonate at the membrane–solvent interface. Aqueous ammonia absorbents (2–7 M) were initially used in single pass for CO2 separation from a synthetic biogas where nucleation of ammonium bicarbonate crystals was observed at the perimeter of the micropores. Recirculation of the aqueous ammonia absorbent encouraged the growth of ammonium bicarbonate crystals on the shell-side of the membrane that measured several microns in diameter. However, at high aqueous NH3 concentrations (3–7 M), lumen side crystallisation occurred and obstructed gas flow through the lumen of the HFMC. The suggested mechanism for lumen-side crystallisation was absorbent breakthrough into the lumen due to pore wetting which was promoted by low absorbent surface tension at high NH3 concentration. Preferential shell-side nucleation can therefore be promoted by (1) raising surface tension of the absorbent and (2) selection of a membrane with a more regulated pore shape than the PTFE membrane used (d/L 0.065) as both actions can diminish solvent ingress into the pore. This was evidenced using 2 M NH3 absorbent where shell-side crystallisation was evidenced without the onset of lumen side crystallisation. Raising surface tension through the inclusion of salt into the chemical absorbent also promoted greater CO2 flux stability. Importantly, this study demonstrates that chemically enhanced HFMC are an attractive prospect for gas–liquid separation applications where reaction product recovery offers further economic value