A parameter robust numerical method for a two dimensional reaction-diffusion problem.

In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximations are almost second order uniformly convergent (in the maximum norm) with respect to the singular perturbation parameter. Some numerical experiments are given that illustrate in practice the theoretical order of convergence established for the numerical method

Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient

In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction–diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter–uniform methods based on piecewise–uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise–uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device

Modification of aftertaste with a menthol mouthwash reduces food wanting, liking, and ad <i>libitum </i>intake of potato crisps

This research investigated the effect of modifying the aftertaste of potato crisps on (1) temporal sensory perception and (2) appetite using three mouthwash conditions (no mouthwash, a water mouthwash, and a menthol mouthwash). For the sensory study, 17 screened female subjects were trained on the Temporal Dominance of Sensations (TDS) methodology. Subjects undertook TDS to monitor all sensory attributes during the mastication of a 2 g crisp until swallowing (at 20s), then conducted the mouthwash, and then continued the TDS task to monitor aftertaste until 90s. For the appetite study, 36 subjects (18 male, 18 female) completed 100 mm Visual Analogue Scales (VAS) for desire, liking, hunger, and thirst, followed by an ad libitum eating task. For the VAS scales testing, subjects chewed and swallowed a 2 g crisp, and then immediately conducted the mouthwash before completing the VAS scales. For the ad libitum task, subjects were given 12 min to consume as many crisps as they desired on a plate (up to 50 g). Every three minutes they were required to conduct a mouthwash. TDS results showed that in comparison with no mouthwash, the water mouthwash significantly reduced aftertaste attributes such as savoury, salty, and fatty mouthcoating, and the menthol mouthwash significantly increased aftertaste attributes of cooling, minty, and tingly. The water mouthwash did not influence desire and liking of crisps, or hunger and thirst. The water mouthwash did not influence ad libitum intake of the crisps over a 12 min period. The menthol mouthwash significantly reduced desire and liking of the crisps, as well as hunger and thirst. Furthermore, the menthol mouthwash significantly reduced ad libitum crisp intake by 29% over the 12 min period

Observational signatures of mass-loading in jets launched by rotating black holes

It is widely believed that relativistic jets in X-ray binaries (XRBs) and active-galactic nuclei are powered by the rotational energy of black holes. This idea is supported by general-relativistic magnetohydrodynamic (GRMHD) simulations of accreting black holes, which demonstrate efficient energy extraction via the Blandford–Znajek mechanism. However, due to uncertainties in the physics of mass loading, and the failure of GRMHD numerical schemes in the highly magnetized funnel region, the matter content of the jet remains poorly constrained. We investigate the observational signatures of mass loading in the funnel by performing general-relativistic radiative transfer calculations on a range of 3D GRMHD simulations of accreting black holes. We find significant observational differences between cases in which the funnel is empty and cases where the funnel is filled with plasma, particularly in the optical and X-ray bands. In the context of Sgr A*, current spectral data constrains the jet filling only if the black hole is rapidly rotating with a gsim 0.9. In this case, the limits on the infrared flux disfavor a strong contribution from material in the funnel. We comment on the implications of our models for interpreting future Event Horizon Telescope observations. We also scale our models to stellar-mass black holes, and discuss their applicability to the low-luminosity state in XRBs

High energy radiation from jets and accretion disks near rotating black holes

We model the low/hard state in X-ray binaries as a magnetically arrested accretion flow, and calculate the resulting radiation using a general-relativistic radiative transport code. Firstly, we investigate the origin of the high-energy emission. We find the following indications of a significant jet contribution at high energies: (i) a pronounced γ-ray peak at ∼ 1023 Hz, (ii) a break in the optical/UV band where the spectrum changes from disk to jet dominated, and (iii) a low-frequency synchrotron peak ≲ 1014 Hz implies that a significant fraction of any observed X-ray and γ-ray emission originates in the jet. Secondly, we investigate the effects of black hole spin on the high-energy emission. We find that the X-ray and γ-ray power depend strongly on spin and inclination angle. Surprisingly, this dependence is not a result of the Blandford-Znajek mechanism, but instead can be understood as a redshift effect. For rapidly rotating black holes, observers with large inclinations see deeper into the hot, dense, highly-magnetized inner regions of the accretion flow. Since the lower frequency emission originates at larger radii, it is not significantly affected by the spin. Therefore, the ratio of the X-ray to near-infrared power is an observational probe of black hole spin

Selection functions of strong lens finding neural networks

Convolution Neural Networks trained for the task of lens finding with similar architecture and training data as is commonly found in the literature are biased classifiers. An understanding of the selection function of lens finding neural networks will be key to fully realising the potential of the large samples of strong gravitational lens systems that will be found in upcoming wide-field surveys. We use three training datasets, representative of those used to train galaxy-galaxy and galaxy-quasar lens finding neural networks. The networks preferentially select systems with larger Einstein radii and larger sources with more concentrated source-light distributions. Increasing the detection significance threshold to 12$\sigma$ from 8$\sigma$ results in 50 per cent of the selected strong lens systems having Einstein radii $\theta_\mathrm{E}$ $\ge$ 1.04 arcsec from $\theta_\mathrm{E}$ $\ge$ 0.879 arcsec, source radii $R_S$ $\ge$ 0.194 arcsec from $R_S$ $\ge$ 0.178 arcsec and source S\'ersic indices $n_{\mathrm{Sc}}^{\mathrm{S}}$ $\ge$ 2.62 from $n_{\mathrm{Sc}}^{\mathrm{S}}$ $\ge$ 2.55. The model trained to find lensed quasars shows a stronger preference for higher lens ellipticities than those trained to find lensed galaxies. The selection function is independent of the slope of the power-law of the mass profiles, hence measurements of this quantity will be unaffected. The lens finder selection function reinforces that of the lensing cross-section, and thus we expect our findings to be a general result for all galaxy-galaxy and galaxy-quasar lens finding neural networks.Comment: Submitted to MNRA

Active stabilisation of single drive dual-parallel Mach-Zehnder modulator for single sideband signal generation

Presented is a study on a single-drive dual-parallel Mach-Zehnder modulator implementation as a single sideband suppressed carrier generator. High values of both extinction ratio and sidemode suppression ratio were obtained at different modulation frequencies over the Cband. In addition, a stabilisation loop had been developed to preserve the single sideband generation over time

The reproductive biology of the exploited razor clam, Ensis siliqua, in the Irish Sea

Knowledge of the reproductive cycle of a species is a prerequisite for sustainable management of a fishery. The infaunal marine bivalve, Ensis siliqua, is a commercially important species in Europe, and is exploited in many countries, including Ireland, where it is sold by wet weight. Seasonal variations in the reproductive cycle of subtidal razor clams from the Skerries region of the Irish Sea, an important fisheries area, were examined between June 2010 and September 2011 while monitoring weight. Histological examination revealed that the E. siliqua sex-ratio was not different from parity, and no hermaphrodites were observed in the samples collected. In the summer months of 2010 all female clams were either spent or in early development, with just a small percentage of males still spawning. The gonads of both sexes developed over the autumn and winter months of 2010, with the first spawning individuals recorded in January 2011. Spawning peaked in March 2011, but unlike in 2010, spawning continued through June and July with all animals spent in August 2011. The earlier and longer spawning period found in this species in 2011 compared to 2010 may have been due to the colder than normal temperature observed during the winter of 2010 plus the relatively warmer temperatures of Spring 2011, which could have affected the gametogenic development of E. siliqua in the Irish Sea. It was noted that wet weight dropped in the summer months of both years, immediately after the spawning period which may impact on the practicality of fishing for this species during this period. Timing of development and spawning is compared with other sites in the Irish Sea and elsewhere in Europe, including the Iberian Peninsula

Autonomic Testing in Functional Gastrointestinal Disorders: Implications of Reproducible Gastrointestinal Complaints during Tilt Table Testing

Background: The pathophysiology of functional abdominal pain (FAP) is unknown. The upright portion of a tilt table test triggers typical symptoms in certain children. Aim: To compare the pathophysiology and treatment response of children with FAP whose gastrointestinal symptoms (GI) were replicated (RGI) by tilt table testing (TTT) to those in whom TTT did not have this effect (NRGI). Methods: An IRB-approved retrospective review of the autonomic laboratory database identified all children tested for GI complaints. We compared results of TTT, Valsalva maneuver, deep breathing and the axon reflex sweat test. Overall treatment response and that specific to fludrocortisone was ranked from 1 to 5, with 1 “much worse,” 3 “neutral,” and 5 “much better.” Results: 32/76 identified children had reproducible symptoms on TTT (RGI) and 44 did not (NRGI). The RGI group was younger, had a shorter duration of symptoms, more postural tachycardia syndrome (POTS) and benefited more from fludrocortisone (73% in RGI vs. 25% in NRGI). Conclusion: Dividing patients with FAP according to the effect of TTT on their symptoms appears to delineate 2 fundamentally different groups, with potentially different pathophysiologies and treatment responses. A prospective study is needed