Spatial analysis structure

Stevens, P.M., A genetic analysis of the pea crabs (Decapoda Pinnotheridae) of New Zealand. II. Patterns and intensity of spatial population structure in Pinnotheres atrinicola, Mar. Biol., 108, 403, 1990. 

After the CASSCF calculation with the above choice of orbitals, in order to perform an efficient VB analysis, it is better in this case to resort to an overcomplete non-orthogonal hybrid set. The five active orbitals, in fact, can be split into ten hybrids, in term of which the VB transcription of the wavefunction turns out to be the simplest and the most compact. Such kinds of overcomplete basis sets are commonly used in constructing the so called non-paired spatial orbital structures (NPSO, see for example [35]), but it should be remarked that their use is restricted to gradient methods of wavefunction optimization, such as steepest descent, because other methods, which need to invert the hessian matrix (like Newton--Raphson) clearly have problems with singularities. 

S. Hanan, The Design and analysis of spatial data structures, Addison-Wesley, 1990. 

The spatial structure of the turbulent field is contained in the eigenvectors. We see that the eigenvectors are expanded as a Fourier series in the directions of flow homogeneity, x and y. The rate of convergence of the sequence of eigenvalues is a sensitive indicator of the presence and relative importance of coherent structures. EOF analysis provides not only an objective measure of the existence of dominant, spatially-extensive structure but, with minimal additional assumptions, allows us to deduce the 3-dimensional structure of the dominant eddies in their mature phase. 

Brenner (1980) has explored the subject of solute dispersion in spatially periodic porous media in considerable detail. Brenner s analysis makes use of the method of moments developed by Aris (1956) and later extended by Horn (1971). Carbonell and Whitaker (1983) and Koch et al. (1989) have addressed the same problem using the method of volume averaging, whereby mesoscopic transport coefficients are derived by averaging the basic conservation equations over a single unit cell. Numerical simulations of solute dispersion, based on lattice scale calculations of the Navier-Stokes velocity fields in spatially periodic structures, have also been performed (Eidsath et al., 1983 Edwards et al., 1991 Salles et al., 1993). These simulations are discussed in detail in the Emerging Areas section. 

For simulation studies, some progress on this subject has been achieved through development of theoretical techniques to analyze the angular and spatial local structure of water in a systematic way [115,120,129]. A particular application of this orientation-dependent microstructural analysis to supercritical water [65,112,130] was used to dispute the claims on the disappearance of HB by Postorino et al. [121]. 

K. Jacobs, R. Seemann, and K. Mecke, Dynamics of structure formation in thin films a special spatial analysis. In eds., K. R. Mecke and D. Stoyan, Statistical Physics and Spatial Statistics. Vol. 554. Lecture Notes in Physics, Berlin Springer. 72-91 (2000). ISBN 3-540-67750-X. 

Schwartz, G., and E. Klucas. 1998. Spatial Analysis and Social Structure at Tell al-Raqa i. In Espace natural, espace habite en Syrie du Nord (10 -2 millenaires av. J.-C.),... 

A linear stability analysis of (A3.3.57) can provide some insight into the structure of solutions to model B. The linear approximation to (A3.3.57) can be easily solved by taking a spatial Fourier transfomi. The result for the Ml Fourier mode is... 

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