The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

The propagation mechanism of a vortex on the β plane

The propagation velocity and propagation mechanism for vortices on a β plane are determined for a reduced-gravity model by integrating the momentum equations over the β plane. Isolated vortices, vortices in a background current, and initial vortex propagation from rest are studied. The propagation mechanism for isolated anticyclones as well as cyclones, which has been lacking up to now, is presented. It is shown that, to first order, the vortex moves to generate a Coriolis force on the mass anomaly of the vortex to compensate for the force on the vortex due to the variation of the Coriolis parameter. Only the mass anomaly of the vortex is of importance, because the Coriolis force due to the motion of the bulk of the layer moving with the vortex is almost fully compensated by the Coriolis force on the motion of the exterior flow. Because the mass anomaly of a cyclone is negative the force and acceleration have opposite sign. The role of dipolar structures in steadily moving vortices is discussed, and it is shown that their overall structure is fixed by the steady westward motion of the mass anomaly. Furthermore, it is shown that reduced-gravity vortices are not advected with a background flow. The reason for this behavior is that the background flow changes the ambient vorticity gradient such that the vortex obtains an extra self-propagation term that exactly cancels the advection by the background flow. Last, it is shown that a vortex initially at rest will accelerate equatorward first, after which a westward motion is generated. This result is independent of the sign of the vortex.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Forward modelling to determine the observational signatures of white-light imaging and interplanetary scintillation for the propagation of an interplanetary shock in the ecliptic plane

Recent coordinated observations of interplanetary scintillation (IPS) from the EISCAT, MERLIN, and STELab, and stereoscopic white-light imaging from the two heliospheric imagers (HIs) onboard the twin STEREO spacecraft are significant to continuously track the propagation and evolution of solar eruptions throughout interplanetary space. In order to obtain a better understanding of the observational signatures in these two remote-sensing techniques, the magnetohydrodynamics of the macro-scale interplanetary disturbance and the radio-wave scattering of the micro-scale electron-density fluctuation are coupled and investigated using a newly constructed multi-scale numerical model. This model is then applied to a case of an interplanetary shock propagation within the ecliptic plane. The shock could be nearly invisible to an HI, once entering the Thomson-scattering sphere of the HI. The asymmetry in the optical images between the western and eastern HIs suggests the shock propagation off the Sun–Earth line. Meanwhile, an IPS signal, strongly dependent on the local electron density, is insensitive to the density cavity far downstream of the shock front. When this cavity (or the shock nose) is cut through by an IPS ray-path, a single speed component at the flank (or the nose) of the shock can be recorded; when an IPS ray-path penetrates the sheath between the shock nose and this cavity, two speed components at the sheath and flank can be detected. Moreover, once a shock front touches an IPS ray-path, the derived position and speed at the irregularity source of this IPS signal, together with an assumption of a radial and constant propagation of the shock, can be used to estimate the later appearance of the shock front in the elongation of the HI field of view. The results of synthetic measurements from forward modelling are helpful in inferring the in-situ properties of coronal mass ejection from real observational data via an inverse approach.

A model of net amino acid absorption and utilization by the portal-drained viscera of the lactating dairy cow

A more complete understanding of amino acid ( AA) metabolism by the various tissues of the body is required to improve upon current systems for predicting the use of absorbed AA. The objective of this work was to construct and parameterize a model of net removal of AA by the portal-drained viscera (PDV). Six cows were prepared with arterial, portal, and hepatic catheters and infused abomasally with 0, 200, 400, or 600 g of casein daily. Casein infusion increased milk yield quadratically and tended to increase milk protein yield quadratically. Arterial concentrations of a number of essential AA increased linearly with respect to infusion amount. When infused casein was assumed to have a true digestion coefficient of 0.95, the minimum likely true digestion coefficient for noninfused duodenal protein was found to be 0.80. Net PDV use of AA appeared to be linearly related to total supply (arterial plus absorption), and extraction percentages ranged from 0.5 to 7.25% for essential AA. Prediction errors for portal vein AA concentrations ranged from 4 to 9% of the observed mean concentrations. Removal of AA by PDV represented approximately 33% of total postabsorptive catabolic use, including use during absorption but excluding use for milk protein synthesis, and was apparently adequate to support endogenous N losses in feces of 18.4 g/d. As 69% of this use was from arterial blood, increased PDV catabolism of AA in part represents increased absorption of AA in excess of amounts required by other body tissues. Based on the present model, increased anabolic use of AA in the mammary and other tissues would reduce the catabolic use of AA by the PDV.

Splanchnic metabolism of nitrogenous compounds and urinary nitrogen excretion in steers fed alfalfa under conditions of increased absorption of ammonia and L-arginine supply across the portal-drained viscera

Effects of increased ammonia and/or arginine absorption across the portal-drained viscera (PDV) on net splanchnic (PDV and liver) metabolism of nitrogenous compounds and urinary N excretion were investigated in six cathetenzed Hereford x Angus steers (501 +/- 1 kg BW) fed a 75% alfalfa:25% (as-fed basis) corn-soybean meal diet (0.523 MJ of ME/[kg BW0.15.d]) every 2 h without (27.0 g of N/kg of dietary DM) and with 20 g of urea/kg of dietary DM (35.7 g of N/kg of dietary DM) in a split-plot design. Net splanchnic flux measurements were obtained immediately before beginning and ending a 72-h mesenteric vein infusion of L-arginine (15 mmol/h). For 3 d before and during arginine infusion, daily urine voided was measured and analyzed for N composition. Feeding urea increased PDV absorption (P < 0.01) and hepatic removal (P < 0.01) of ammonia N, accounting for 80% of increased hepatic urea N output (P < 0.01). Numerical increases in net hepatic removal of AA N could account for the remaining portion of increased hepatic urea N output. Arginine infusion increased hepatic arginine removal (P < 0.01) and hepatic urea N output (P < 0.03) and switched hepatic ornithine flux from net uptake to net output (P < 0.01), but numerical changes in net hepatic removal of ammonia and AA N could not account fully for the increase in hepatic urea N output. Increases in urine N excretion equaled quantities of N fed as urea or infused as arginine. Estimated salivary urea N excretion was not changed by either treatment. Urea cycle regulation occurs via a complex interaction of mechanisms and requires N sources other than ammonia, but the effect of increased ammonia absorption on hepatic catabolism of individual AA in the present study was not significant.

Splanchnic metabolism of nutrients and hormones in steers fed alfalfa under conditions of increased absorption of ammonia and L-arginine supply across the portal-drained viscera

Effects of increased ammonia and/or arginine absorption on net splanchnic (portal-drained viscera [PDV] plus liver) metabolism of nonnitrogenous nutrients and hormones in cattle were examined. Six Hereford x Angus steers (501 +/- 1 kg BW) prepared with vascular catheters for measurements of net flux across the splanchnic bed were fed a 75% alfalfa:25% (as-fed basis) corn and soybean meal diet (0.523 MJ of ME/[kg BW(0.75.)d]) every 2 h without (27.0 g of N/kg of DM) and. with 20 g of urea/kg of DM (35.7 g of N/kg of DM) in a split-plot design. Net flux measurements were made immediately before and after a 72-h mesenteric vein infusion Of L-arginine (15 mmol/h). There were no treatment effects on PDV or hepatic 02 consumption. Dietary urea had no effect on splanchnic metabolism of glucose or L-lactate, but arginine infusion decreased net hepatic removal Of L-lactate when urea was fed (P < 0.01). Net PDV appearance of n-butyrate was increased by arginine infusion (P < 0.07), and both dietary urea (P < 0.09) and arginine infusion (P < 0.05) increased net hepatic removal of n-butyrate. Dietary urea also increased total splanchnic acetate output (P < 0.06), tended to increase arterial glucagon concentration (P < 0.11), and decreased arterial ST concentration (P < 0.03). Arginine infusion increased arterial concentration (P < 0.07) and net PDV release (P < 0.10) and tended to increase hepatic removal (P < 0.11) of insulin, as well as arterial concentration (P < 0.01) and total splanchnic output (P < 0.01) of glucagon. Despite changes in splanchnic N metabolism, increased ammonia and arginine absorption had little measurable effect on splanchnic metabolism of glucose and other nonnitrogenous components of splanchnic energy metabolism.

A lightweight supercomputing web portal for inferring phylogenetic trees

In this paper we describe a lightweight Web portal developed for running computational jobs on a IBM JS21 Bladecenter cluster, ThamesBlue, for inferring and analyzing evolutionary histories. We first discuss the need for leveraging HPC as a enabler for molecular phylogenetics research. We go on to describe how the portal is designed to interface with existing open-source software that is typical of a HPC resource configuration, and how by design this portal is generic enough to be portable to other similarly configured compute clusters, and for other applications.

The "freedom to frame questions... worth asking" or three stories and three (other) fragments of research

In our state of centralised control of the curriculum and high-stakes testing an examination subject's assessment objectives have become high profile. Some of the anomalous effects of this profile are shown in the teaching, question-setting, and marking of English literature. Glimpses of earlier times are revealed, all three secondary school key stages are considered, examination performances are discussed, and the views of beginning teachers about teaching to the test are sought.

Disparity with respect to a local reference plane as a dominant cue for stereoscopic depth relief

Earlier studies showed that the disparity with respect to other visible points could not explain stereoacuity performance, nor could various spatial derivatives of disparity [Glennerster, A., McKee, S. P., & Birch, M. D. (2002). Evidence of surface-based processing of binocular disparity. Current Biology, 12:825-828; Petrov, Y., & Glennerster, A. (2004). The role of the local reference in stereoscopic detection of depth relief. Vision Research, 44:367-376.] Two possible cues remain: (i) local changes in disparity gradient or (ii) disparity with respect to an interpolated line drawn through the reference points. Here, we aimed to distinguish between these two cues. Subjects judged.. in a two AFC paradigm, whether a target dot was in front of a plane defined by three reference dots or, in other experiments, in front of a line defined by two reference dots. We tested different slants of the reference line or plane and different locations of the target relative to the reference points. For slanted reference lines or plane, stereoacuity changed little as the target position was varied. For judgments relative to a frontoparallel reference line, stereoacuity did vary with target position, but less than would be predicted by disparity gradient change. This provides evidence that disparity with respect to the reference plane is an important cue. We discuss the potential advantages of this measure in generating a representation of surface relief that is invariant to viewpoint transformations. (c) 2006 Elsevier Ltd. All rights reserved.

Freeze-frame: a new infant inhibition task and its relation to frontal cortex tasks during infancy and early childhood

The current study investigated a new, easily administered, visual inhibition task for infants termed the Freeze-Frame task. In the new task, 9-month-olds were encouraged to inhibit looks to peripheral distractors. This was done by briefly freezing a central animated stimulus when infants looked to the distractors. Half of the trials presented an engaging central stimulus, and the other half presented a repetitive central stimulus. Three measures of inhibitory function were derived from the task and compared with performance on a set of frontal cortex tasks administered at 9 and 24 months of age. As expected, infants' ability to learn to selectively inhibit looks to the distractors at 9 months predicted performance at 24 months. However, performance differences in the two Freeze-Frame trial types early in the experiment also turned out to be an important predictor. The results are discussed in terms of the validity of the Freeze-Frame task as an early measure of different components of inhibitory function. (C) 2007 Elsevier Inc. All rights reserved.