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  • 1
    Electronic Resource
    Electronic Resource
    Scale Effect on Principal Component Analysis for Vector Random Functions (1999)
    Springer
    Mathematical geology 31 (1999), S. 701-722 
    Details
    ISSN: 1573-8868
    Keywords: dispersion covariances ; spatial support ; Pearson correlation ; spatial scales of variability ; PCA ; matrix variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Principal component analysis (PCA) is commonly applied without looking at the “spatial support” (size and shape, of the samples and the field), and the cross-covariance structure of the explored attributes. This paper shows that PCA can depend on such spatial features. If the spatial random functions for attributes correspond to largely dissimilar variograms and cross-variograms, the scale effect will increase as well. On the other hand, under conditions of proportional shape of the variograms and cross-variograms (i.e., intrinsic coregionalization), no scale effect may occur. The theoretical analysis leads to eigenvalue and eigenvector functions of the size of the domain and sample supports. We termed this analysis “growing scale PCA,” where spatial (or time) scale refers to the size and shape of the domain and samples. An example of silt, sand, and clay attributes for a second-order stationary vector random function shows the correlation matrix asymptotically approaches constants at two or three times the largest range of the spherical variogram used in the nested model. This is contrary to the common belief that the correlation structure between attributes become constant at the range value. Results of growing scale PCA illustrate the rotation of the orthogonal space of the eigenvectors as the size of the domain grows. PCA results are strongly controlled by the multivariate matrix variogram model. This approach is useful for exploratory data analysis of spatially autocorrelated vector random functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007532527596
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  • 2
    Electronic Resource
    Electronic Resource
    Studies on microemulsions (1982)
    Springer
    Colloid & polymer science 260 (1982), S. 96-107 
    Details
    ISSN: 1435-1536
    Keywords: microemulsions ; light scattering ; neutron scattering ; particle interactions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The microemulsions formed in the 4-component system water-potassium oleate-hexanol-dodecane have been investigated by time-average light scattering and small angle neutron scattering. A constant volume fraction ratio water: potassium oleate of 1.44 was used and at this constant composition, which gave a pseudo 3-component system, a wide region of the microemulsion domain was examined. In order to interpret the scattering data at finite volume fractions of the dispersed phase, water, allowance had to be made for interactions between the water-in-oil microemulsion droplets. This was carried out using a hard sphere model for the interaction. It is shown that using this model self-consistent results are obtained by light scattering and neutron scattering and an estimate can be made of the size of the particles in concentrated colloidal dispersions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01447682
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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