High frequency scattering by convex curvilinear polygons

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.

Anharmonic force constant calculations

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an / tensor, which is a straightforward generalization of the / matrix used in the customary description of harmonic force constant calculations. General formulae for the / tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.

Redundant coordinates in harmonic force-field calculations

Redundancy relations between vibrational coordinates may be linear (as for rectilinear coordinates used in deriving a G matrix), or non-linear (as for curvilinear coordinates used in formulating model force fields). It is shown that geometrically defined internal coordinates are necessarily curvilinear. Hence it is shown that linear force constants can occur in model force field calculations involving redundant coordinates, in disagreement with the recent proposal of Gussoni and Zerbi.

Potential surfaces from vibration-rotation data

The problems of inverting experimental information obtained from vibration-rotation spectroscopy to determine the potential energy surface of a molecule are discussed, both in relation to semi-rigid molecules like HCN, NO2, H2CO, etc., and in relation to non-rigid or floppy molecules with large amplitude vibrations like HCNO, C3O2, and small ring molecules. Although standard methods exist for making the necessary calculations in the former case, they are complex, and they require an abundance of precise data on the spectrum that is rarely available. In the case of floppy molecules there are often data available over many excited states of the large amplitude vibration, but there are difficulties in knowing the precise form of the large amplitude coordinate(s), and in allowing for the vibrational averaging effects of the other modes. In both cases difficulties arise from the curvilinear nature of the vibrational paths which are not adequately handled by our present theories.

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).

Environmental control for layers

Light patterns have less effect on numbers of eggs laid by current stocks than on those of forty years ago, but the principles have not changed. Ovarian activity is stimulated by increasing photoperiods and suppressed by decreasing photoperiods. The light pattern used during rearing can still have large effects on age at 50% lay, even for modern stocks. Early sexual maturity maximises egg numbers but gives smaller eggs. Late maturity maximises egg size at the expense of numbers. The relationship between egg output (g/hen d) and age at first egg is curvilinear, with maximum yield occurring in flocks maturing in about the centre of their potential range. Fancy patterns of increasing daylength after maturity are probably not justified. A flock held on a constant 14h day will lay as many eggs as one given step up lighting. Intermittent lighting saves about 5% of feed consumption with no loss of output, provided that the feed has adequate amino acid content to allow for the reduced feed intake. Producers with light-proof laying houses should be taking advantage of intermittent lighting. The recommended light intensity for laying houses is still 10 lx, although the physiological threshold for response to changes in photoperiod is closer to 2 lx. Very dim (0.05 lx) light filtering into blacked out houses will not stimulate the hypothalamic receptors responsible for photo-sexual responses, but may affect the bird's biological clock, which can alter its response to a constant short photoperiod. Feed intake shows a curvilinear dependence on environmental temperature. At temperatures below the panting threshold, performance can be maintained by adjusting the feed so as to maintain an adequate intake of critical amino acids. Above the panting threshold, the hen is unable to take in enough energy to maintain normal output. There is no dietary modification which can effectively offset this problem. Diurnally cycling temperatures result in feed intake and egg production equivalent to that observed under a constant temperature equal to the mean of the cycle. When the poultry house is cooler at night than by day, it helps to provide light so that the birds can feed during the cooler part of the cycle.

Differential effects of temperature on fruit development and bean quality of contrasting genotypes of cacao (Theobroma cacao)

The effects of temperature and light integral on fruit growth and development of five cacao genotypes (Amelonado, AMAZ 15/15, SCA 6, SPEC 54/1 and UF 676) were studied in semi-controlled environment glasshouses in which the thermal regimes of cacao-growing regions of Brazil, Ghana and Malaysia were simulated. Fruit losses because of physiological will (cherelle will) were greater at higher temperatures and also differed significantly between genotypes, reflecting genetic differences in competition for assimilates between vegetative and reproductive components. Short-term measurements of fruit growth indicated faster growth rates at higher temperatures. In addition, a significant negative linear relationship between temperature and development time was observed. There was an effect of genotype on this relationship, such that time to fruit maturation at a given temperature was greatest for the clone UF 676 and least for AMAZ 15/15. Analysis of base temperatures, derived from these relationships indicated genetic variability in sensitivity of cacao fruit growth to temperature (base temperatures ranged from 7.5 degrees C for Amelonado and AMAZ 15/15 to 12.9 for SPEC 54/1). Final fruit size was a positive function of beam number for all genotypes and a positive function of light integral for Amelonado in the Malaysia simulated environment (where the temperature was almost constant). In simulated environments where temperature was the main variable (Brazil and Ghana) increases in temperature resulted in a significant decrease in final pod size for one genotype (Amelonado) in Brazil and for two genotypes (SPEC 54/1 and UF 676) in Ghana. It was hypothesised that pod growth duration (mediated by temperature), assimilation and beam number are all determinants of final pod size but that under specific conditions one of these factors may override the others. There was variability between genotypes in the response of beam size and beam lipid content to temperature. Negative relationships between temperature and bean size were found for Amelonado and UF 676. Lipid concentration was a curvilinear function of temperature for Amelonado and UF 676, with optimal temperatures of 23 degrees C and 24 degrees C, respectively. The variability observed here of different cacao genotypes to temperature highlights the need and opportunities for appropriate matching of planting material with local environments.

UV irradiance as a major influence on growth, development and secondary products of commercial importance in Lollo Rosso lettuce 'Revolution' grown under polyethylene films

The growth and production of anthocyanin, flavonoid and phenolic compounds were evaluated in Lollo Rosso lettuce 'Revolution' grown continuously under films varying in their ability to transmit LTV radiation (completely transparent to IN, transparent above 320, 350, 370 and 3 80 nm and completely opaque to LTV radiation). Plants were grown from seed under UV transparent and UV blocking films and destructively harvested 3-4 weeks after transplanting. Plants under a complete UV blocking film (UV400) produced up to 2.2 times more total above ground dry weight than plants under the UV transparent film. In contrast, anthocyanin content in plants under the UV blocking film was approximately eight times lower than in plants under a UV transparent film. Furthermore, there was a curvilinear relationship between the anthocyanin content and LTV wavelength cutoff such that above 370 run there was no further reduction in anthocyanin content. Fluorescence measurements indicated that photosynthetic performance index was 15% higher under the presence of UVB and UVA (UV280) than under the presence of UVA (UV320) and 53% higher than in the absence of UV radiation suggesting protection of the photosynthetic apparatus possibly by phenolic compounds. These findings are of particular importance as the potential of UV transmitting films to increase secondary compounds may offer the opportunity to produce plants commercially with increased health benefits compared to those grown under conventional films.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications