Biaxial-load effects on isopachics for a crack at the interface of dissimilar media

The plane problem of two dissimilar materials, bonded together and containing a crack along their common interface, which were subjected to a biaxial load at infinity, is examined by giving a closed-form expression for the first stress invariant of the normal stresses, which is equally valid everywhere, near to, and far from, the crack-tip region. This exact expression for the first-stress invariant is compared by constructing the respective isopachic-fringe patterns, to the approximate expression with non-singular terms, due to the biaxiality factor, for the same quantity. Significant differences between respective isopachic-patterns were found and their dependence on the elastic properties of both materials and the applied loads was demonstrated. The relative errors between the computedK I - andK II -components by using the approximate expression for the first stress-invariant and the accurate one, derived from closed-form solution along either isopachic-fringes or along circles and radii from the crack-tip have been given, indicating in some cases large discrepancies between exact and approximate solutions.

On the propagation of a multi-dimensional shock of arbitrary strength

In this paper the kinematics of a curved shock of arbitrary strength has been discussed using the theory of generalised functions. This is the extension of Moslov’s work where he has considered isentropic flow even across the shock. The condition for a nontrivial jump in the flow variables gives the shock manifold equation (sme). An equation for the rate of change of shock strength along the shock rays (defined as the characteristics of the sme) has been obtained. This exact result is then compared with the approximate result of shock dynamics derived by Whitham. The comparison shows that the approximate equations of shock dynamics deviate considerably from the exact equations derived here. In the last section we have derived the conservation form of our shock dynamic equations. These conservation forms would be very useful in numerical computations as it would allow us to derive difference schemes for which it would not be necessary to fit the shock-shock explicitly.

Phosphorus in agricultural soils of Finland - characterization of reserves and retention in mineral soil profiles

An overwhelming majority of all the research on soil phosphorus (P) has been carried out with soil samples taken from the surface soils only, and our understanding of the forms and the reactions of P at a soil profile scale is based on few observations. In Finland, the interest in studying the P in complete soil profiles has been particularly small because of the lack of tradition in studying soil genesis, morphology, or classification. In this thesis, the P reserves and the retention of orthophosphate phosphorus (PO4-P) were examined in four cultivated mineral soil profiles in Finland (three Inceptisols and one Spodosol). The soils were classified according to the U.S. Soil Taxonomy and soil samples were taken from the genetic horizons in the profiles. The samples were analyzed for total P concentration, Chang and Jackson P fractions, P sorption properties, concentrations of water-extractable P, and for concentrations of oxalate-extractable Al and Fe. Theoretical P sorption capacities and degrees of P saturation were calculated with the data from the oxalate-extractions and the P fractionations. The studied profiles can be divided into sections with clearly differing P characteristics by their master horizons Ap, B and C. The C (or transitional BC) horizons below an approximate depth of 70 cm were dominated by, assumingly apatitic, H2SO4-soluble P. The concentration of total P in the C horizons ranged from 729 to 810 mg kg-1. In the B horizons between the depths of 30 and 70 cm, a significant part of the primary acid-soluble P has been weathered and transformed to secondary P forms. A mean weathering rate of the primary P in the soils was estimated to vary between 230 and 290 g ha-1 year-1. The degrees of P saturation in the B and C horizons were smaller than 7%, and the solubility of PO4-P was negligible. The P conditions in the Ap horizons differed drastically from those in the subsurface horizons. The high concentrations of total P (689-1870 mg kg-1) in the Ap horizons are most likely attributable to long-term cultivation with positive P balances. A significant proportion of the P in the Ap horizons occurred in the NH4F- and NaOH-extractable forms and as organic P. These three P pools, together with the concentrations of oxalate-extractable Al and Fe, seem to control the dynamics of PO4-P in the soils. The degrees of P saturation in the Ap horizons were greater (8-36%) than in the subsurface horizons. This was also reflected in the sorption experiments: Only the Ap horizons were able to maintain elevated PO4-P concentrations in the solution phase − all the subsoil horizons acted as sinks for PO4-P. Most of the available sorption capacity in the soils is located in the B horizons. The results suggest that this capacity could be utilized in reducing the losses of soluble P from excessively fertilized soils by mixing highly sorptive material from the B horizons with the P-enriched surface soil. The drastic differences in the P characteristics observed between adjoining horizons have to be taken into consideration when conducting soil sampling. Sampling of subsoils has to be made according to the genetic horizons or at small depth increments. Otherwise, contrasting materials are likely to be mixed in the same sample; and the results of such samples are not representative of any material present in the studied profile. Air-drying of soil samples was found to alter the results of the sorption experiments and the water extractions. This indicates that the studies on the most labile P forms in soil should be carried out with moist samples.

Tuotantotekniikan ja säilytysajan vaikutus kasvihuonekurkkujen ja -tomaattien aistittavaan laatuun.

Finland has moved from growing vegetables by natural light to year-round greenhouse production using artificial lighting. Determination of sensory effects on greenhouse-grown vegetables is important as sensory evaluation provides information which chemical methods can not. It can tell us about the quality of samples which affects the consumers' behaviour. There are different opinions on how the quality of vegetables should be determined. The consumers are dissatisfied with the quality of vegetables and fruits, although the variety of products is larger than ever. The aim of this study was to find out how artificial lighting contributes to the sensory quality of greenhouse tomatoes and cucumbers compared to traditional natural lighting, and how storage affects the sensory attributes of the samples. In this study there were two sets of tomatoes and two sets of cucumbers, representing two different harvest seasons. Sensory evaluation involved two steps. The first step was to sort the samples and the second step was to generate a profile using descriptive analysis. Sorting was found to give some approximate information on differences between tomato and cucumber samples. MDS-maps dimensions were presented by age and lighting technique. The reliability of sorting results was quite good. The quality of the natural products was inconsistent. Production technology had more of an effect on cucumber samples than tomato samples. Natural light cucumbers were, for example sweeter and softer than artificial light cucumbers. Age had an especially large effect on cucumber appearance characteristics. There were less differences between tomato samples than cucumber samples. Production technology had less of an effect on tomato samples than age, e.g. hardness decreased during storage. In this study, it was found that artificial lighting has little effect on the sensory quality of Finnish greenhouse tomatoes compared with tomatoes grown under natural light.

A note on the period of oscillation of non-linear systems

This paper deals with two approximate methods of finding the period of oscillations of non-linear conservative systems excited by step functions. The first method is an extension of the analysis presented by Jonckheere [4] and the second one is based on a weighted bilinear approximation of the non-linear characteristic. An example is presented and the approximate results are compared with the exact results

Morphological changes in the conjunctiva, episclera and sclera following short-term miniscleral contact lens wear in rigid lens neophytes

PURPOSE To quantify the influence of short-term wear of miniscleral contact lenses on the morphology of the corneo-scleral limbus, the conjunctiva, episclera and sclera. METHODS OCT images of the anterior eye were captured before, immediately following 3h of wear and then 3h after removal of a miniscleral contact lens for 10 young (27±5 years) healthy participants (neophyte rigid lens wearers). The region of analysis encompassed 1mm anterior, to 3.5mm posterior to the scleral spur. Natural diurnal variations in thickness were measured on a separate day and compensated for in subsequent analyses. RESULTS Following 3h of lens wear, statistically significant tissue thinning was observed across all quadrants, with a mean decrease in thickness of -24.1±3.6μm (p<0.001), which diminished, but did not return to baseline 3h after lens removal (-16.9±1.9μm, p<0.001). The largest tissue compression was observed in the superior quadrant (-49.9±8.5μm, p<0.01) and in the annular zone 1.5mm from the scleral spur (-48.2±5.7μm), corresponding to the approximate edge of the lens landing zone. Compression of the conjunctiva/episclera accounted for about 70% of the changes. CONCLUSIONS Optimal fitting miniscleral contact lenses worn for three hours resulted in significant tissue compression in young healthy eyes, with the greatest thinning observed superiorly, potentially due to the additional force of the eyelid, with a partial recovery of compression 3h after lens removal. Most of the morphological changes occur in the conjunctiva/episclera layers.

Crystallization Kinetics and Electrical Relaxation of BaO-0.5Li(2)O-4.5B(2)O(3) Glasses

Transparent glasses in the composition BaO-0.5Li(2)O-4.5B(2)O(3) (BLBO) were fabricated via the conventional melt-quenching technique. X-ray powder diffraction combined with differential scanning calorimetric (DSC) studies carried out on the as-quenched samples confirmed their amorphous and glassy nature, respectively. The crystallization behavior of these glasses has been studied by isothermal and nonisothermal methods using DSC. Crystallization kinetic parameters were evaluated from the Johnson-Mehl-Avrami equation. The value of the Avrami exponent (n) was found to be 3.6 +/- 0.1, suggesting that the process involves three-dimensional bulk crystallization. The average value of activation energy associated with the crystallization of BLBO glasses was 317 +/- 10 kJ/mol. Transparent glass-ceramics were fabricated by controlled heat-treatment of the as-quenched glasses at 845 K/40 min. The dielectric constants for BLBO glasses and glass-ceramics in the 100 Hz-10 MHz frequency range were measured as a function of the temperature (300-925 K). The electrical relaxation and dc conductivity characteristics were rationalized using electric modulus formalism. The imaginary part of the electric modulus spectra was modeled using an approximate solution of the Kohlrausch-Williams-Watts relation. The temperature-dependent behavior of stretched exponent (beta) was discussed for the as-quenched and heat-treated BLBO glasses.

Inelastic Postbuckling of Columns of Variable Flexural Rigidity

Effects of large deformation and inelasticity are considered in formulating the behavior of columns of variable cross section subjected to an axial compressive load. Simple, approximate methods are used to obtain numerical results. The combined effect of the nonlinearities is shown to be of a hardening type for small column deflections

High-anthocyanin strawberries through cultivar selection

BACKGROUND: Diets high in fruit and vegetables are known to have significant health benefits. This is in part due to the presence of phytochemicals, which possess potential protective health benefits. This study focuses on the ability of strawberries to be bred for higher anthocyanin content. This is a major contributor to the characteristic colour and nutritional value of ripe strawberries, together with phenolic acids, ascorbic acid and total antioxidant capacity. RESULTS: Anthocyanins in five commercial strawberry cultivars and three breeding lines were assessed. This led to the discovery of one breeding line (BL 2006-221) as an exceptional source of anthocyanins (approximate to 1 g kg1 fresh weight), with approximately double the levels of current commercial cultivars. Temperature was shown to influence anthocyanin extraction, with 40 degrees C being the best extraction temperature using the accelerated solvent extraction (ASE) method. Hue angle and anthocyanin concentration showed a good correlation (r2 = 0.69). CONCLUSION: The new breeding line BL 2006-221 has the potential to be used in the development of phytochemically rich strawberry cultivars. Using hue angle as a screening tool for total anthocyanin concentration and extraction of anthocyanins from strawberries by ASE at 40 degrees C would support such cultivar development. (c) 2012 Commonwealth of Australia

Deriving optimal fishing effort for managing Australia's Moreton Bay multispecies trawl fishery with aggregated effort data

Deriving an estimate of optimal fishing effort or even an approximate estimate is very valuable for managing fisheries with multiple target species. The most challenging task associated with this is allocating effort to individual species when only the total effort is recorded. Spatial information on the distribution of each species within a fishery can be used to justify the allocations, but often such information is not available. To determine the long-term overall effort required to achieve maximum sustainable yield (MSY) and maximum economic yield (MEY), we consider three methods for allocating effort: (i) optimal allocation, which optimally allocates effort among target species; (ii) fixed proportions, which chooses proportions based on past catch data; and (iii) economic allocation, which splits effort based on the expected catch value of each species. Determining the overall fishing effort required to achieve these management objectives is a maximizing problem subject to constraints due to economic and social considerations. We illustrated the approaches using a case study of the Moreton Bay Prawn Trawl Fishery in Queensland (Australia). The results were consistent across the three methods. Importantly, our analysis demonstrated the optimal total effort was very sensitive to daily fishing costs—the effort ranged from 9500–11 500 to 6000–7000, 4000 and 2500 boat-days, using daily cost estimates of $0, $500, $750, and $950, respectively. The zero daily cost corresponds to the MSY, while a daily cost of $750 most closely represents the actual present fishing cost. Given the recent debate on which costs should be factored into the analyses for deriving MEY, our findings highlight the importance of including an appropriate cost function for practical management advice. The approaches developed here could be applied to other multispecies fisheries where only aggregated fishing effort data are recorded, as the literature on this type of modelling is sparse.

Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Geological factors affecting on after-use of Finnish cut-over peatlands : with implications on the carbon accumulation

In Finland, peat harvesting sites are utilized down almost to the mineral soil. In this situation the properties of mineral subsoil are likely to have considerable influence on the suitability for the various after-use forms. The aims of this study were to recognize the chemical and physical properties of mineral subsoils possibly limiting the after-use of cut-over peatlands, to define a minimum practice for mineral subsoil studies and to describe the role of different geological areas. The future percentages of the different after-use forms were predicted, which made it possible to predict also carbon accumulation in this future situation. Mineral subsoils of 54 different peat production areas were studied. Their general features and grain size distribution was analysed. Other general items studied were pH, electrical conductivity, organic matter, water soluble nutrients (P, NO3-N, NH4-N, S and Fe) and exchangeable nutrients (Ca, Mg and K). In some cases also other elements were analysed. In an additional case study carbon accumulation effectiveness before the intervention was evaluated on three sites in Oulu area (representing sites typically considered for peat production). Areas with relatively sulphur rich mineral subsoil and pool-forming areas with very fine and compact mineral subsoil together covered approximately 1/5 of all areas. These areas were unsuitable for commercial use. They were recommended for example for mire regeneration. Another approximate 1/5 of the areas included very coarse or very fine sediments. Commercial use of these areas would demand special techniques - like using the remaining peat layer for compensating properties missing from the mineral subsoil. One after-use form was seldom suitable for one whole released peat production area. Three typical distribution patterns (models) of different mineral subsoils within individual peatlands were found. 57 % of studied cut-over peatlands were well suited for forestry. In a conservative calculation 26% of the areas were clearly suitable for agriculture, horticulture or energy crop production. If till without large boulders was included, the percentage of areas suitable to field crop production would be 42 %. 9-14 % of all areas were well suitable for mire regeneration or bird sanctuaries, but all areas were considered possible for mire regeneration with correct techniques. Also another 11 % was recommended for mire regeneration to avoid disturbing the mineral subsoil, so total 20-25 % of the areas would be used for rewetting. High sulphur concentrations and acidity were typical to the areas below the highest shoreline of the ancient Litorina sea and Lake Ladoga Bothnian Bay zone. Also differences related to nutrition were detected. In coarse sediments natural nutrient concentration was clearly higher in Lake Ladoga Bothnian Bay zone and in the areas of Svecokarelian schists and gneisses, than in Granitoid area of central Finland and in Archaean gneiss areas. Based on this study the recommended minimum analysis for after-use planning was for pH, sulphur content and fine material (<0.06 mm) percentage. Nutrition capacity could be analysed using the natural concentrations of calcium, magnesium and potassium. Carbon accumulation scenarios were developed based on the land-use predictions. These scenarios were calculated for areas in peat production and the areas released from peat production (59300 ha + 15 671 ha). Carbon accumulation of the scenarios varied between 0.074 and 0.152 million t C a-1. In the three peatlands considered for peat production the long term carbon accumulation rates varied between 13 and 24 g C m-2 a-1. The natural annual carbon accumulation had been decreasing towards the time of possible intervention.

Mathematical model of an arterial stenosis, allowing for tethering

Closed-form solutions are presented for approximate equations governing the pulsatile flow of blood through models of mild axisymmetric arterial stenosis, taking into account the effect of arterial distensibility. Results indicate the existence of back-flow regions and the phenomenon of flow-reversal in the cross-sections. The effects of pulsatility of flow and elasticity of vessel wall for arterial blood flow through stenosed vessels are determined.

Prediction of Intrinsic kinetics in diffusion disguised immobilized enzyme systems

When immobilized enzyme kinetics are disguised by inter- and intraparticle diffusion effects, an approximate mathematical procedure is indicated whereby experimental data obtained in the limiting ranges of first- and zeroth-order Michaelis-Menten kinetics could be used for the prediction of the kinetic constants.

Bayesian synthetic likelihood

Having the ability to work with complex models can be highly beneficial, but the computational cost of doing so is often large. Complex models often have intractable likelihoods, so methods that directly use the likelihood function are infeasible. In these situations, the benefits of working with likelihood-free methods become apparent. Likelihood-free methods, such as parametric Bayesian indirect likelihood that uses the likelihood of an alternative parametric auxiliary model, have been explored throughout the literature as a good alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which assumes a multivariate normal approximation to the likelihood of a summary statistic of interest. This paper explores the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. We relate BSL to pseudo-marginal methods and propose to use an alternative SL that uses an unbiased estimator of the exact working normal likelihood when the summary statistic has a multivariate normal distribution. Several applications of varying complexity are considered to illustrate the findings of this paper.