The form of the z log z estimator is derived for both Pareto and K distributed clutter plus noise. When noise is included, numerical zero finding is required to obtain the shape parameter from the estimator, but it still provides a robust and accurate method that is relatively quick to compute. It is compared with two other methods. The method of moments is the simplest and fastest to compute, but less accurate than other methods if the clutter shape parameter is small. A constrained maximumlikelihood (ML) estimator is constructed by maximising the log likelihood function in one dimension to find the shape parameter, while holding the mean power and clutter to noise ratio constant. This estimator is robust and accurate, but relatively slow because numerical integration is required to calculate the likelihood function, along with numerical optimisation to find the maximum. If the noise power is unknown, it can be obtained using the first two intensity moments in combination with either the constrained ML or z log z estimator. These combinations provide more robust and accurate estimates than the third intensity moment.
The distinctive Mossbauer spectra of fine-particle goethite (a-FeOOH) have been attributed by many authors to superparamagnetism.However, measurements of the magnetic anisotropy energy and particle volume show that the superparamagnetic blocking temperature for most samples is much greater than the Neel temperature. A model involving magnetic ordering of clusters created by high concentrations of vacancy defects is proposed, in which the cluster moments slowly relax, thus producing a Boltzmann distribution in the z component of the magnetization. The model provides excellent fits to the temperature-dependent hyperfine-field distributions observed in the Mossbauer spectra, and may have wider applicability to other diamagnetically substituted iron oxide materials. A linear relation is observed between Tn and the inverse mean crystallite dimension in the [111]direction of -1060 (130) K nm, and it is shown that goethite particles must have a volume of less than 1000 nm' in order to show superparamagnetic Mossbauer spectra at room temperature.
This paper is concerned with the characterisation of Doppler spectra from high range resolution X-band radar sea clutter observed from an airborne platform over the range of grazing angles, 15° to 45°. It is observed that when looking up or down wind there is a strong correlation between mean Doppler shift and local spectrum intensity. When combined with random fluctuations of spectrum width, these characteristics give the spectra a temporal and spatial variability. This behaviour has previously been observed in low grazing angle data and these results confirm the wider applicability of the models developed using that data. The modelling method is also extended here to capture the bimodal behaviour observed with high intensity returns from breaking waves looking up or down-wind.
The distinctive Mössbauer spectra of goethite cannot be explained on the basis of superparamagnetism. Consideration of superparamagnetic fluctuations in only the transverse components of the sublattice magnetization ('mode superparamagnetism', proposed by Coey et al), or of possible interactions between superparamagnetic particles, does not alter this conclusion.
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