Cluster pattern

V.K. Vanag, L.F. Yang, M. Dolnik, A.M. Zhabotinsky, and l.R. Epstein. Oscillatory cluster patterns in a homogeneous chemical system with global feedback. Nature, 406(6794) 389-391, 2000. 

Thin Sections or pieces of the rock about 1 mm in size or less can be also analyzed with this instrument at glancing incident irradiation, if the site to be analyzed is close to the surface of the section or the edge of a fraction. However in this mode of operation, mass resolution is severely reduced. Nevertheless ions can be identified because of their low mass numbers and the very low background in the spectra, by known cluster patterns or by comparison with reference spectra obtained with reduced laser irradiation. The spectra have shown to be highly reproducible. For more precise bulk. sample analysis, other instruments such as the LAMMA 1000 are more suited. Their lateral resolution is 1-3 pm in diameter and the depth of analysis is typically 0.1 pm. 

The compound Mo MogFe contains linear polymers of cluster spheres in which 6 out of the 30 Fe positions in Mo72Fe30 are replaced by effectively diamagnetic Mo positions.41 The relative positioning of these Mo sites can take on a variety of scenarios from a purely statistical distribution, with the six nonmagnetic positions evenly distributed over the icosidodecahedral sites, to a clustering pattern, where all six positions are situated adjacent to each other on one spot of the icosidodecahedron. 

Brown DE, Huntley CL (1992) A practical application of simulated annealing to clustering. Pattern Recog 25 401-412... 

A large parameter range in which cluster patterns dominated the spatiotemporal dynamics was also observed for the oscillatory oxidation of H2 in the presence of electrosorbing cations and anions [175], Characteristically, the cluster-type patterns were found at lower concentrations of Cu2+ ions compared with the pulse-type motions shown in Fig. 56. Examples of two-phase and three-phase clusters are depicted in Fig. 63. In these figures the homogeneously oscillating mode has been subtracted. 

Fig. 61. Cluster pattern observed during the electrodissolution of a Fe ring electrode in the active/passive transition region under potentiostatic conditions. The RE was located in the plane of the WE. (a) and (b) Snapshots taken during two successive oscillations of the total current, (c) Spatiotemporal plot of the azimuthal intensity. (Reproduced with permission from B. J. Green and J. L. Hudson, Phys. Rev. E 63 (2001) 026214, (2001) by the American Physical Society).

For the linear chain, any connected cluster (/x, v) is simply a set of consecutive sites n, n + 1,... n + m. Numerical results for ansatze using connected-cluster patterns involving up to M = 4 sites, for alternate chains, and up to M = 5 sites, for regular chains, have been obtained so far. The hierarchy of patterns have been defined as... 

Numerical results for such ansatze with connected-cluster patterns involving up to M = 5 bonds have been treated so far. The hierarchy of patterns have been defined as... 

Fig. 6.7 A cluster pattern in a set of composition diagrams of five adjacent springs. The pattern indicates one type of water is involved. The more parameters that are checked, the higher is the confidence of the conclusion.

Brown, D. and Huntley, C. (1992). A Practical Application of Simulated Annealing to Clustering, Pattern Recognition 25, 401-412. 

These relative weights depend on such factors as ease of assay and cost. The latter is directly related by the prevalence to the reliability of the results (e.g., cost of treatment of false positives versus benefits). Prevalence may, however, be less constant than commonly assumed and clustering (epidemics genetic predisposition) may occur. Clustering patterns are recognized with the Poisson distribution (e.g., time, space Section S.4.3.2). 

Figure 1. Morphology, size and clustering pattern of Sp powders basic crystallites.

If more than one chlorine atom or bromine atom is present in a molecule, distinctive isotope cluster patterns are seen in the mass spectrum. Figure 10.8 gives a graphical... 

Figure 10.9 A mass spectrum of trichloroethylene, C2HCI3, showing the typical isotope cluster pattern for a compound containing 3 Cl atoms.

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