Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Synoptic controls on boundary-layer characteristics

We report the characteristics of the three-dimensional, time evolving, atmospheric boundary layer that develops beneath an idealised, dry, baroclinic weather system. The boundary-layer structure is forced by thermal advection associated with the weather system. Large positive heat fluxes behind the cold front drive a vigorous convective boundary layer, whereas moderate negative heat fluxes in the warm sector between the cold and warm fronts generate shallow, stably stratified or neutral boundary layers. The forcing of the boundary-layer structure is quantified by forming an Eulerian mass budget integrated over the depth of the boundary layer. The mass budget indicates that tropospheric air is entrained into the boundary layer both in the vicinity of the high-pressure centre, and behind the cold front. It is then transported horizontally within the boundary layer and converges towards the cyclone's warm sector, whence it is ventilated out into the troposphere. This cycling of air is likely to be important for the ventilation of pollution out of the boundary layer, and for the transformation of the properties of large-scale air masses.

Controls on boundary layer ventilation: Boundary layer processes and large-scale dynamics

Midlatitude cyclones are important contributors to boundary layer ventilation. However, it is uncertain how efficient such systems are at transporting pollutants out of the boundary layer, and variations between cyclones are unexplained. In this study 15 idealized baroclinic life cycles, with a passive tracer included, are simulated to identify the relative importance of two transport processes: horizontal divergence and convergence within the boundary layer and large-scale advection by the warm conveyor belt. Results show that the amount of ventilation is insensitive to surface drag over a realistic range of values. This indicates that although boundary layer processes are necessary for ventilation they do not control the magnitude of ventilation. A diagnostic for the mass flux out of the boundary layer has been developed to identify the synoptic-scale variables controlling the strength of ascent in the warm conveyor belt. A very high level of correlation (R-2 values exceeding 0.98) is found between the diagnostic and the actual mass flux computed from the simulations. This demonstrates that the large-scale dynamics control the amount of ventilation, and the efficiency of midlatitude cyclones to ventilate the boundary layer can be estimated using the new mass flux diagnostic. We conclude that meteorological analyses, such as ERA-40, are sufficient to quantify boundary layer ventilation by the large-scale dynamics.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Black carbon measurements in the boundary layer over western and northern Europe

Europe is a densely populated region that is a significant global source of black carbon (BC) aerosol, but there is a lack of information regarding the physical properties and spatial/vertical distribution of rBC in the region. We present the first aircraft observations of sub-micron refractory BC (rBC) aerosol concentrations and physical properties measured by a single particle soot photometer (SP2) in the lower troposphere over Europe. The observations spanned a region roughly bounded by 50° to 60° N and from 15° W to 30° E. The measurements, made between April and September 2008, showed that average rBC mass concentrations ranged from about 300 ng m−3 near urban areas to approximately 50 ng m−3 in remote continental regions, lower than previous surface-based measurements. rBC represented between 0.5 and 3% of the sub-micron aerosol mass. Black carbon mass size distributions were log-normally distributed and peaked at approximately 180 nm, but shifted to smaller diameters (~160 nm) near source regions. rBC was correlated with carbon monoxide (CO) but had different ratios to CO depending on location and air mass. Light absorption coefficients were measured by particle soot absorption photometers on two separate aircraft and showed similar geographic patterns to rBC mass measured by the SP2. We summarize the rBC and light absorption measurements as a function of longitude and air mass age and also provide profiles of rBC mass concentrations and size distribution statistics. Our results will help evaluate model-predicted regional rBC concentrations and properties and determine regional and global climate impacts from rBC due to atmospheric heating and surface dimming.

The effects of irrigation, nitrogen fertilizer and grain size on Hagberg falling number, specific weight and blackpoint of winter wheat

The effects of irrigation and nitrogen (N) fertilizer on Hagberg falling number (HFN), specific weight (SW) and blackpoint (BP) of winter wheat (Triticum aestivum L) were investigated. Mains water (+50 and +100 mm month(-1), containing 44 mg NO3- litre(-1) and 28 mg SO42- litre(-1)) was applied with trickle irrigation during winter (17 January-17 March), spring (21 March-20 May) or summer (24 May-23 July). In 1999/2000 these treatments were factorially combined with three N levels (0, 200, 400 kg N ha(-1)), applied to cv Hereward. In 2000/01 the 400 kg N ha(-1) treatment was replaced with cv Malacca given 200 kg N ha(-1). Irrigation increased grain yield, mostly by increasing grain numbers when applied in winter and spring, and by increasing mean grain weight when applied in summer. Nitrogen increased grain numbers and SW, and reduced BP in both years. Nitrogen increased HFN in 1999/2000 and reduced HFN in 2000/01. Effects of irrigation on HFN, SW and BP were smaller and inconsistent over year and nitrogen level. Irrigation interacted with N on mean grain weight: negatively for winter and spring irrigation, and positively for summer irrigation. Ten variables derived from digital image analysis of harvested grain were included with mean grain weight in a principal components analysis. The first principal component ('size') was negatively related to HFN (in two years) and BP (one year), and positively related to SW (two years). Treatment effects on dimensions of harvested grain could not explain all of the effects on HFN, BP and SW but the results were consistent with the hypothesis that water and nutrient availability, even when they were affected early in the season, could influence final grain quality if they influenced grain numbers and size. (C) 2004 Society of Chemical Industry

Chemical composition and fermentation characteristics of grain and different parts of the stover from maize land races harvested at different growing periods in two zones of central Mexico

The objective of this work was to determine the rumen fermentation characteristics of maize land races used as forage in central Mexico. In vitro gas production (ml per 200 mg dry matter (DM)) incubations were carried out, and cumulative gas volumes were fitted to the Krishnamoorthy et al. (1991) model. The trial used a split-plot design with cultivation practices associated with maize colour (COL) as the main plot with three levels: white, yellow and black maize; growing periods (PER) were the split plots where PER1, PER2 and PER3 represented the first, second and third periods, respectively and two contrasting zones (Z1 = valley and Z2 = mountain) were used as blocking factors. The principal effects observed were associated with the maturity of the plants and potential gas production increased (P < 0.05) in stems (PER 1 = 51.8, PER2 = 56.3, PER3 = 58.4 ml per 200 mg DM) and in whole plant (PER 1 = 60.9, PER2 = 60.8, PER3= 70.9 ml per 200 mg DM). An inverse effect was observed with fermentation rates in leaves (P < 0.01) with 0.061, 0.053 and 0.0509 (per h) and in whole plant (P < 0.05) with 0.068, 0.057, 0.050 (per h) in PER1, PER2 and PER3 respectively. The digestibility of the neutral-detergent fibre (NDF) decreased with maturity especially in leaves (P < 0.05) with values of 0.71, 0.67 and 0.66 g/kg; in rachis (P < 0.01) 0.75, 0.72, and 0.65 in PER1, PER2 and PER3 respectively. The NDF content in leaves in leaves (668, 705 and 713 g/kg DM for PER1, PER2 and PER3, respectively), stems (580, 594 and 644 g/kg DM) and, husk (663, 774 and, 808 g/kg DM) increased (P < 0.05) with increasing plant maturity, rachis were significantly different between periods (P < 0.01). The structure with-the best nutritive characteristics was the husk, because it had the lowest fibre contents, especially in acid-detergent lignin, with values of 22.6, 28.6 and 37.6 g/kg DM in PER1, PER2 and PER3, respectively.

Effect of variety, nitrogen fertiliser and various agronomic factors on the nutritive value of husked and naked oats grain

The effect of variety, agronomic and environmental factors on the chemical composition and energy value for ruminants and non-ruminants of husked and naked oats grain was studied. Winter oats were grown as experimental plots in each of 2 years on three sites in England. At each site two conventional husked oat cultivars (Gerald and Image) and two naked cultivars (Kynon and Pendragon) were grown. At each site, crops were sown on two dates and all crops were grown with the application of either zero or optimum fertiliser nitrogen. Variety and factors contained within the site + year effect had the greatest influence on the chemical composition and nutritive value of oats, followed by nitrogen ferfiliser treatment. For example, compared with zero nitrogen, the optimum nitrogen fertiliser treatment resulted in a consistent and significant (P < 0.001) increase in crude protein for all varieties at all sites from an average of 95 to 118 g kg(-1) DM, increased the potassium concentration in all varieties from an average of 4.9 to 5.1 g kg(-1) DM (P < 0.01) and reduced total lipid by a small but significant (P < 0.001) amount. Optimum nitrogen increased (P < 0.001) the NDF concentration in the two husked varieties and in the naked variety Pendragon. Naked cultivars were lower in fibre, had considerably higher energy, total lipid, linoleic acid, protein, starch and essential amino acids than the husked cultivars. Thus nutritionists need to be selective in their choice of naked or husked oat depending on the intended dietary use. (C) 2004 Elsevier B.V. All rights reserved.

Influence of foliar diseases and their control by fungicides on grain yield and quality in wheat

Twenty-eight field experiments on sandy-loam soils in the UK (1982-2003) are reviewed by relating the extension of the green area duration of the flag leaf (GLADF) by fungicides to effects on yield and quality of winter wheat. Over all experiments mean grain yield = 8.85t ha(-1) at 85% DM. With regards quality, mean values were: thousand grain weight (TGW) = 44.5 g; specific weight (SWT) = 76.9 kg hl(-1); crude protein concentration (CP (N x 5.7)) = 12.5 % DM; Hagberg falling number (HFN) = 285 s; and sodium dodecyl sulphate (SDS)-sedimentation volume = 69ml. For each day (d) that fungicides increased GLADF there were associated average increases in yield (0.144 1 ha(-1) d(-1), se 0.0049, df = 333), TGW (0.56 gd(-1), se = 0.017) and SWT (0.22 kg hl(-1) d(-1), se 0.011). Some curvature was evident in all these relationships. When GLADF was delayed beyond 700 degrees Cd after anthesis, as was possible in cool wet seasons, responses were curtailed, or less reliable. Despite this apparent terminal sink limitation, fungicide effects on sink size, eg endosperm cell numbers or maximum water mass per grain, were not prerequisites for large effects on grain yield, TGW or SWT. Fungicide effects on CP were variable. Although the average response of CP was negative (-0.029%DM/d; se = 0.00338), this depended on cultivar and disease controlled. Controlling biotrophs such as rusts, (Puccinia spp.) tended to increase CP, whereas controlling a more necrotrophic pathogen (Septoria tritici) usually reducedCP. Irrespective of pathogen controlled, delaying senescence of the flag leaf was associated with increased nitrogen yields in the grain (averaging 2.24 kg N ha-1 d(-1), se = 0.0848) due to both increased N uptake into the above ground crop, and also more efficient remobilisation of N from leaf laminas. When sulphur availability appeared to be adequate, fungicide x cultivar interactions were similar on S as for CP, although N:S ratios tended to decline (i.e. improve for bread making) when S. tritici was controlled. On average, SDS-sedimentation volume declined (-0. 18 ml/d, se = 0.027) with increased GLADF, broadly commensurate with the average effect on CP. Hagberg falling number decreased as fungicide increased GLADF (-2.73 s/d, se = 0.178), indicating an increase in alpha-amylase activity.