ALBERT

Description: This paper deals with the development of the flow in a curved tube near the inlet. The solution is obtained by the method of matched asymptotic expansions. Two inlet conditions are considered: (i) the condition of constant dynamic pressure at the entrance, which may be of practical interest in applications to blood flow in the aorta; and (ii) a uniform entry condition. It is shown that the geometry and the nature of the entry condition appreciably influence the initial development of the flow. The effect of the secondary flow due to the curvature on the wall shear is discussed and it is shown that the cross-over between shear maxima on the inside and the outside of the tube occurs at a downstream distance which is 1·9 times the radius of the tube for entry condition (i) while in the case of entry condition (ii) it is 0·95 times the radius, which is half the distance required in case (i). It is found that the pressure distribution is not significantly influenced by the secondary flow during the initial development of the motion. The analysis, which is developed for steady motion, can be extended to pulsatile flows, which are of greater physiological interest. © 1974, Cambridge University Press. All rights reserved.

Description: Trials, reflecting the feed needs in dry Mediterranean environments of small-ruminant production systems based on barley, were established at two sites in Syria in 1982. They compared various 2-course rotations of barley with feed legumes, fallow or more barley. This paper summarizes a 14-year sequence of results from an incomplete factorial combination of four rotations (B-V, B-L, B-F, B-B) of barley with vetch (Vicia sativa), lathyrus (Lathyrus sativus), fallow, and barley, with two fertilizer regimes, zero control and biennial NP applied to the barley phase, in terms of long-term mean yields, production stability and yield trends over time.On a 2-year rotational basis, most barley was produced by barley-only rotations, and differences between B-F and B-B were small; but, in terms of total biomass production, feed legume rotations (B-V and B-L) outyielded barley-only rotations by 29% at one site and 19% at the other. Responses to biennial fertilization were large but did not interact significantly with rotation treatment. The crude protein status (%N) of barley grain and straw was strongly determined by seasonal rainfall, but that of the grain could be enhanced, irrespective of rainfall, by a preceding feed-legume crop; and, altogether, the total mean crop nitrogen output of legume-based rotations exceeded that of barley-only rotations by 80% and 64% at the two sites. The inclusion of legumes thus enhances both quantity and quality of feed production.Annual yield fluctuations, attributable mainly to rainfall difference, were greater at the drier site. No consistent effect from fertilizer was observed, but at the wetter site rotation differences were appreciable, with B-F rotation giving the most stable yields. A number of time trends in yield values were tentatively identified. On a relative basis, some widening over time of the gap between fertilized and unfertilized treatments was observed in feed-legume yields at both sites and barley yields at the wetter site; over 14 years, yields in unfertilized plots had apparently declined relative to those receiving biennial NP. But, apart from a probable decline in lathyrus productivity compared to that of common vetch, changes in relative yield performance between rotations were difficult to detect. Regression models developed to describe absolute yield trends indicated a real decline over time in barley grain yields in continuous barley (B-B) at both sites and in unfertilized plots of all four rotations at the wetter site.

Description: Results from monocropped barley treatments in long-term rotation (RTN) and continuous barley (CB) trials at two sites were examined for fertilizer effects on yield means and long-term yield trends. In RTN trials, mean responses to fertilizer (N[ratio ]P2O5) applied annually at rates of 20[ratio ]60 at the drier and 40[ratio ]60 at the wetter site were almost double those from biennial application, confirming the need for annual fertilization in monocropped barley systems. In CB trials, with N and P applied annually in nine factorial combinations, at rates up to 120[ratio ]90, responses to each nutrient were curvilinear and dependent on the presence of the other nutrient. Trend analysis showed a decline in grain yields over time where NP fertilizer had not been applied or applied only at low annual rates (〈 60[ratio ]45 or 〈 60[ratio ]90, according to site); but straw yields, at worst, remained approximately stable in the absence of fertilizer and generally increased strongly with higher NP rates. Uncertainties in the interpretation of trend-analysis results indicate the need for methodology improvements, to include (i) additional single-value parameters of the growth environment, to improve the model's ability to account for seasonal variability, and (ii) a more flexible, non-linear function for time.It was concluded that barley monocropping is not necessarily non-sustainable in the medium term, provided adequate annual fertilization is maintained; but risks of pest or disease build-up, in addition to the superiority of legume-barley systems in biomass and crude protein output demonstrated in preceding papers, undoubtedly favour the introduction of some forage legumes into long-term barley sequences. The most practicable (and acceptable) systems may well be ones in which continuous barley is interrupted by a legume, or even a bare fallow, every third or fourth year. Above all, farmers should be helped to experiment with different forage legumes, barley–legume sequences, and modes of legume harvest, to optimize outputs in relation to their evolving and individual enterprise needs.

Description: Rotations of barley with feed legumes produce more biomass and crude protein than barley-fallow and continuous barley sequences, but scope remains to improve the potential value to farmers of feed legume-based systems. This paper summarizes 6-year results from two sites from 2-year rotations of barley with: narbon vetch (Vicia narbonensis) and lathyrus (Lathyrus sativus), each harvested mature; and common vetch (Vicia sativa), harvested by simulated green-grazing and mature, all in factorial combination with four NP fertilizer regimes applied biennially to the barley.Mean yield differences between rotations were quite small, but at the drier site the narbon vetch rotation was significantly superior in both total biomass and crop total nitrogen. Other results implied yield compensation between barley and legume phases: barley performance was relatively depressed at the wetter site after high-yielding narbon vetch but was relatively enhanced at both sites after green-grazed common vetch. Evidence from year-round soil-water monitoring suggests that the benefit following green grazing may have arisen, in part, from a small carry-over of profile moisture between crops not much inferior to that residual from a fallow year. Both crop phases responded strongly to biennial P fertilizer; and barley responded strongly to three rates of N-fertilizer, but a sometimes significant curvilinear component to this response reflected a tendency for grain yields to be depressed by added nitrogen in the driest years. But interactions between N-rates and rotations were not significant.It was concluded that narbon vetch may have greater potential than common vetch and lathyrus for mature harvest in drier areas, but its unsuitability for grazing green is a limitation. Flexibility of utilization is important, to accommodate the needs of different farmers and the exigencies of different seasons. The green-graze option has major potential where there is a demand for high-quality spring grazing; and indications that barley may be as productive after green-grazed vetch as after a year of fallow suggest an alternative approach for farmers who have previously avoided legumes in order to maximize barley production.

Description: Incomplete block (IB) analysis of lentil yield trials in lattice block designs substantially reduced experimental error variability compared to randomized complete block (RCB) analysis. Spatial variability, which may exist in two dimensions in the field, can be modelled using various alternative covariance structures for the plot errors. To investigate the adequacy of the incomplete block analysis, we fitted a first order autocorrelation error structure (AR1) in both the column direction and the row direction after allowing for the variance model of the lattice design. We also considered random splines in columns. The best model was selected on the basis of the residual deviance of each of the 53 trials we examined. Gains in efficiency (over RCB) for pair-wise comparison of genotypes and selection gains were obtained for the selected models and for the lattice blocks (considered as a control model). Spatial models where the plot error was modelled as AR1 in columns or as AR1×AR1 in rows and columns after allowing for random effects of lattice blocks were most frequently selected. Models with spatial errors were found best in 74% of the trials when used with random effects of lattice block and in the remaining trials when used without lattice blocks. The average gain in efficiency over RCB analysis by using the best models at the analysis stage was around 50%. The best models were also, on average, more efficient than the lattice model. Expected average genetic gain due to selection of the top five lines was approximately 20% for the best models. The predicted genotype means showed less change in rank when comparing RCB with lattice analysis than when comparing RCB with the best method. Use of spatial models resulted in different genotypes being selected, giving a higher genetic advance. Since the use of spatial models requires only a change in computation together with knowledge of the field layout, the use of spatial methods together with good experimental design is recommended as a cost-effective method for achieving improved genetic progress.

Description: Crop rotation serves as a mechanism for developing sustainable crop production systems. Crop-rotation trials are used to identify agronomic input factors suitable for use in a cropping system. In crop-rotation trials, experimental errors within the same plot over time are correlated. The form of the covariance structure of the plot errors may be specific to the data from a rotation trial, but is unknown and is generally assumed. Statistical analyses are usually based on the assumption that plot errors are independent, or have constant covariance. An experiment was conducted using wheat-based, three-course rotations containing tillage treatment subplots over 12 years at ICARDA's experimental station at Tel Hadya, a moderately dry area in northern Syria. This study examined several covariance structures for temporal errors arising over the rotation plots and tillage subplots, in order to model wheat yield data. Eighteen covariance structures were examined, and the best pair was selected using the Akaike Information Criterion. The best pair comprised first-order autocorrelation and homogeneous variance for temporal errors in rotation plots, and uniform correlation with heterogeneous variances for temporal errors in tillage subplots. Using the 12 years of data obtained for wheat yield and the best pair of covariance structures, the tillage and rotation effects were found to be statistically significant and to have significant interactions with the cycle of rotation. The precision of the means calculated differed from those calculated using a control structure based on homogeneous error variances and constant correlation. The cumulative yield build-up over time differed significantly over the rotations and the tillage methods. An increasing yield trend was observed for the bread wheat rotation, while a yield decline was observed in durum wheat when the rotation was repeated. When evaluating the effects of input factors in crop rotations, we therefore recommend that the covariance structures be examined and that a suitably chosen structure be used.