The determination of the form of a probability density function (PDF3) of diameters for nodular particles by using a probability density function (PDF2), which form is empirically estimated from cross-sections of these nodules in a metallographic specimen, can be regarded as a special case of Wicksell's corpuscle problem (WCP). The estimation of the PDF3 for the nodular particles provides information about the kinetics of these particles nucleation, and so about the kinetics of their growth. This information is essential for building more accurate mathematical models of the alloy crystallization. In the paper there are presented two derivations of the methods used for the estimation of the PDF3 form. The first method bases on diameters received from a planar cross-section. The second one uses also data from the planar cross-section but not the diameters only chords. Both methods provide practical rules for the analysis of the empirical diameters’ and chord’s size distribution and allow to estimate the mean value of the external surface area of the particles.
The paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF3) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.
Hornsund and Kongsfjorden are two similar-sized Arctic fjords on the West coast of Spitsbergen. They are influenced by cold coastal Arctic water (Hornsund) and warmer Atlantic water (Kongsfjorden). Environmental conditions affect the timing, quantity, spatial distribution (horizontal and vertical) of spring and summer blooms of protists as well as the taxonomic composition of those assemblages. Here, we compile published data and unpublished own measurement from the past two decades to compare the environmental factors and primary production in two fjord systems. Kongsfjorden is characterized by a deeper euphotic zone, higher biomass and greater proportion of autotrophic species. Hornsund seems to obtain more nutrients due to the extensive seabird colonies and exhibits higher turbidity compared to Kongsfjorden. The annual primary production in the analysed fjords ranges from 48 g C m-2 y-1 in Kongsfjorden to 216 g C m-2 y-1 in Hornsund, with a dominant component of microplankton (90%) followed by macrophytes and microphytobenthos.