The limit to wheat water-use efficiency in eastern Australia. I. Gradients in the radiation environment and atmospheric demand

In the wheatbelt of eastern Australia, rainfall shifts from winter dominated in the south (South Australia, Victoria) to summer dominated in the north (northern New South Wales, southern Queensland). The seasonality of rainfall, together with frost risk, drives the choice of cultivar and sowing date, resulting in a flowering time between October in the south and August in the north. In eastern Australia, crops are therefore exposed to contrasting climatic conditions during the critical period around flowering, which may affect yield potential, and the efficiency in the use of water (WUE) and radiation (RUE). In this work we analysed empirical and simulated data, to identify key climatic drivers of potential water- and radiation-use efficiency, derive a simple climatic index of environmental potentiality, and provide an example of how a simple climatic index could be used to quantify the spatial and temporal variability in resource-use efficiency and potential yield in eastern Australia. Around anthesis, from Horsham to Emerald, median vapour pressure deficit (VPD) increased from 0.92 to 1.28 kPa, average temperature increased from 12.9 to 15.2°C, and the fraction of diffuse radiation (FDR) decreased from 0.61 to 0.41. These spatial gradients in climatic drivers accounted for significant gradients in modelled efficiencies: median transpiration WUE (WUEB/T) increased southwards at a rate of 2.6% per degree latitude and median RUE increased southwards at a rate of 1.1% per degree latitude. Modelled and empirical data confirmed previously established relationships between WUEB/T and VPD, and between RUE and photosynthetically active radiation (PAR) and FDR. Our analysis also revealed a non-causal inverse relationship between VPD and radiation-use efficiency, and a previously unnoticed causal positive relationship between FDR and water-use efficiency. Grain yield (range 1-7 t/ha) measured in field experiments across South Australia, New South Wales, and Queensland (n = 55) was unrelated to the photothermal quotient (Pq = PAR/T) around anthesis, but was significantly associated (r2 = 0.41, P < 0.0001) with newly developed climatic index: a normalised photothermal quotient (NPq = Pq . FDR/VPD). This highlights the importance of diffuse radiation and vapour pressure deficit as sources of variation in yield in eastern Australia. Specific experiments designed to uncouple VPD and FDR and more mechanistic crop models might be required to further disentangle the relationships between efficiencies and climate drivers.

The limit to wheat water-use efficiency in eastern Australia. II. Influence of rainfall patterns

We investigated the influence of rainfall patterns on the water-use efficiency of wheat in a transect between Horsham (36°S) and Emerald (23°S) in eastern Australia. Water-use efficiency was defined in terms of biomass and transpiration, WUEB/T, and grain yield and evapotranspiration, WUEY/ET. Our working hypothesis is that latitudinal trends in WUEY/ET of water-limited crops are the complex result of southward increasing WUEB/T and soil evaporation, and season-dependent trends in harvest index. Our approach included: (a) analysis of long-term records to establish latitudinal gradients of amount, seasonality, and size-structure of rainfall; and (b) modelling wheat development, growth, yield, water budget components, and derived variables including WUEB/T and WUEY/ET. Annual median rainfall declined from around 600 mm in northern locations to 380 mm in the south. Median seasonal rain (from sowing to harvest) doubled between Emerald and Horsham, whereas median off-season rainfall (harvest to sowing) ranged from 460 mm at Emerald to 156 mm at Horsham. The contribution of small events (≤ 5 mm) to seasonal rainfall was negligible at Emerald (median 15 mm) and substantial at Horsham (105 mm). Power law coefficients (τ), i.e. the slopes of the regression between size and number of events in a log-log scale, captured the latitudinal gradient characterised by an increasing dominance of small events from north to south during the growing season. Median modelled WUEB/T increased from 46 kg/ha.mm at Emerald to 73 kg/ha.mm at Horsham, in response to decreasing atmospheric demand. Median modelled soil evaporation during the growing season increased from 70 mm at Emerald to 172 mm at Horsham. This was explained by the size-structure of rainfall characterised with parameter τ, rather than by the total amount of rainfall. Median modelled harvest index ranged from 0.25 to 0.34 across locations, and had a season-dependent latitudinal pattern, i.e. it was greater in northern locations in dry seasons in association with wetter soil profiles at sowing. There was a season-dependent latitudinal pattern in modelled WUEY/ET. In drier seasons, high soil evaporation driven by a very strong dominance of small events, and lower harvest index override the putative advantage of low atmospheric demand and associated higher WUEB/T in southern locations, hence the significant southwards decrease in WUEY/ET. In wetter seasons, when large events contribute a significant proportion of seasonal rain, higher WUEB/T in southern locations may translate into high WUEY/ET. Linear boundary functions (French-Schultz type models) accounting for latitudinal gradients in its parameters, slope, and x-intercept, were fitted to scatter-plots of modelled yield v. evapotranspiration. The x-intercept of the model is re-interpreted in terms of rainfall size structure, and the slope or efficiency multiplier is described in terms of the radiation, temperature, and air humidity properties of the environment. Implications for crop management and breeding are discussed.

Gas properties as a limit to gas turbine performance

Although increasing the turbine inlet temperature has traditionally proved the surest way to increase cycle efficiency, recent work suggests that the performance of future gas turbines may be limited by increased cooling flows and losses. Another limiting scenario concerns the effect on cycle performance of real gas properties at high temperatures. Cycle calculations of uncooled gas turbines show that when gas properties are modelled accurately, the variation of cycle efficiency with turbine inlet temperature at constant pressure ratio exhibits a maximum at temperatures well below the stoichiometric limit. Furthermore, the temperature at the maximum decreases with increasing compressor and turbine polytropic efficiency. This behaviour is examined in the context of a two-component model of the working fluid. The dominant influences come from the change of composition of the combustion products with varying air/fuel ratio (particularly the contribution from the water vapour) together with the temperature variation of the specific heat capacity of air. There are implications for future industrial development programmes, particularly in the context of advanced mixed gas-steam cycles.

Temperature sensitivity of the low-moisture-content limit to negative seed longevity-moisture content relationships in hermetic storage

Background and Aims The negative logarithmic relationship between orthodox seed longevity and moisture content in hermetic storage is subject to a low-moisture-content limit (m(c)), but is m(c) affected by temperature? Methods Red clover (Trifolium pratense) and alfalfa (Medicago sativa) seeds were stored hermetically at 12 moisture contents (2-15 %) and five temperatures (-20, 30, 40, 50 and 65 degrees C) for up to 14.5 years, and loss in viability was estimated. Key Results Viability did not change during 14.5 years hermetic storage at -20 degrees C with moisture contents from 2.2 to 14.9 % for red clover, or 2.0 to 12.0 % for alfalfa. Negative logarithmic relationships between longevity and moisture contents > m(c) were detected at 30-65 degrees C, with discontinuities at low moisture contents; m(c) varied between 4.0 and 5.4 % (red clover) or 4.2 and 5.5 % (alfalfa), depending upon storage temperature. Within the ranges investigated, a reduction in moisture content below m(c) at any one temperature had no effect on longevity. Estimates of m(c) were greater the cooler the temperature, the relationship (P < 0.01) being curvilinear. Above m(c), the estimates of C-H and C-Q (i.e. the temperature term of the seed viability equation) did not differ (P > 0.10) between species, whereas those of K-E and C-W did (P < 0.001). Conclusions The low-moisture-content limit to negative logarithmic relationships between seed longevity and moisture content in hermetic storage increased the cooler the storage temperature, by approx. 1.5 % over 35 degrees C (4.0-4.2 % at 65 degrees C to 5.4-5.5 % at 30-40 degrees C) in these species. Further reduction in moisture content was not damaging. The variation in m(c) implies greater sensitivity of longevity to temperature above, compared with below, m(c). This was confirmed (P < 0.005).

A temporal limit to the association between flag leaf life extension by fungicides and wheat yields

Three field experiments, each repeated over two or three seasons, on winter wheat investigated a possible limit to the association between grain yield and flag leaf life, as extended by fungicide application. The experiments involved up to six cultivars and different application rates, timings and frequencies of the strobilurin azoxystrobin and the triazole epoxiconazole. In the 2000/01 and 2001/02 seasons, the relationships between the thermal time to 37 % green flag leaf area (m) and yield deviated from linearity. 'Broken stick' models were fitted to cultivar x experiment combinations within each season and the limit to the benefit to yield associated with extending flag leaf life was 700 degrees C days (S.E. = 20.7) and 725 degrees C days (S.E. = 9.33) after anthesis in 2000/01 and 2001/02, respectively. In 2002/03, the relationship between yield and in did not deviate significantly (P > 0.05) from linearity, but in this latter year the fungicide application failed to increase In past 700 degrees C days. (c) 2004 Elsevier B.V. All rights reserved.

A preliminary assessment of the impact of lowering the illegal per se limit to 0.08 in five states.

National Highway Traffic Safety Administration, Washington, D.C.

¿Qué caracteriza el conocimiento del profesor de matemáticas en la planificación del concepto de límite al infinito de una función para su enseñanza?

Se reportan avances de una investigación que se interesa por determinar las características del conocimiento matemático para la enseñanza del concepto de límite al infinito de una función que pone en acción el profesor en la planificación del tópico. El estudio se fundamenta en el modelo Conocimiento Matemático para la Enseñanza (MKT). En el estudio participan dos profesores de matemáticas de España y uno de México. Los datos se obtienen mediante una entrevista semiestructurada que involucró aspectos sobre los datos personales, el aula de clases, la planificación del profesor y del investigador sobre el tópico. El análisis de los daros se realiza en tres fases: generación de las unidades de análisis, agrupamiento en categorías de dichas unidades y determinación de las características del conocimiento del profesor. Los resultados evidencian que el profesor pone en acción los subdominios del MKT cuando planifica la enseñanza del concepto de límite al infinito de una función.

Some central limit theorems for doubly restricted partitions

Let P_{K, L}(N) be the number of unordered partitions of a positive integer N into K or fewer positive integer parts, each part not exceeding L. A distribution of the form

Ʃ/N≤x P_K,L(N)

is considered first. For any fixed K, this distribution approaches a piecewise polynomial function as L increases to infinity. As both K and L approach infinity, this distribution is asymptotically normal. These results are proved by studying the convergence of the characteristic function.

The main result is the asymptotic behavior of P_K,K(N) itself, for certain large K and N. This is obtained by studying a contour integral of the generating function taken along the unit circle. The bulk of the estimate comes from integrating along a small arc near the point 1. Diophantine approximation is used to show that the integral along the rest of the circle is much smaller.

A path integral approach to the full Dicke model with dipole-dipole interaction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Path integral approach to the full Dicke model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.