Anderson distribution

A comparative study of the alumina-supported catalysts prepared from [H2FeOs3(CO)i3], [H20s3Rh(acac)(CO)io], and [Rli4(CO)i2] was performed and each catalyst was found to be active in the conversion of CO -I- H2. The major product observed in each experiment was methane and the hydrocarbon products were formed in approximately a Schulz-Flory-Anderson distribution. The heterogeneous [Os3Rh] catalyst was two orders of magnitude more active at 543 K than the [FeOs3] catalyst, but showed a lower selectivity for ether formation. ... 

Keck J 1960 Variational theory of chemical reaction rates applied to three-body recombinations J. Chem. Phys. 32 1035 Anderson J B 1973 Statistical theories of chemical reactions. Distributions in the transition region J. Chem. Phys. 58 4684... 

The Fischer-Tropsch process can be considered as a one-carbon polymerization reaction of a monomer derived from CO. The polymerization affords a distribution of polymer molecular weights that foUows the Anderson-Shulz-Flory model. The distribution is described by a linear relationship between the logarithm of product yield vs carbon number. The objective of much of the development work on the FT synthesis has been to circumvent the theoretical distribution so as to increase the yields of gasoline range hydrocarbons. 

The FTS mechanism could be considered a simple polymerization reaction, the monomer being a Ci species derived from carbon monoxide. This polymerization follows an Anderson-Schulz-Flory distribution of molecular weights. This distribution gives a linear plot of the logarithm of yield of product (in moles) versus carbon number. Under the assumptions of this model, the entire product distribution is determined by one parameter, a, the probability of the addition of a carbon atom to a chain (Figure 4-7). ... 

Anderson (A2) has derived a formula relating the bubble-radius probability density function (B3) to the contact-time density function on the assumption that the bubble-rise velocity is independent of position. Bankoff (B3) has developed bubble-radius distribution functions that relate the contacttime density function to the radial and axial positions of bubbles as obtained from resistivity-probe measurements. Soo (S10) has recently considered a particle-size distribution function for solid particles in a free stream ... 

The first approach developed by Hsu (1962) is widely used to determine ONE in conventional size channels and in micro-channels (Sato and Matsumura 1964 Davis and Anderson 1966 Celata et al. 1997 Qu and Mudawar 2002 Ghiaasiaan and Chedester 2002 Li and Cheng 2004 Liu et al. 2005). These models consider the behavior of a single bubble by solving the one-dimensional heat conduction equation with constant wall temperature as a boundary condition. The temperature distribution inside the surrounding liquid is the same as in the undisturbed near-wall flow, and the temperature of the embryo tip corresponds to the saturation temperature in the bubble 7s,b- The vapor temperature in the bubble can be determined from the Young-Laplace equation and the Clausius-Clapeyron equation (assuming a spherical bubble) ... 

By application of first-order, kinetic equations, B. Anderson and Degn claimed that an equilibrated (25°) aqueous solution of D-fructose contains 31.56% of jS-D-fructofuranose and 68.44% of -D-fructopyranose. N.m.r. studies, however, showed that, at equilibrium, a solution of D-fructose contains /3-D-fructopyranose, -D-fructofuranose, a-D-fructofuranose, and a trace of a-D-fructopyranose the distribution of these isomers was shown by gas-liquid chromatography to be 76,19.5, and 4%, respectively. Based on Anderson and Degn s result, Shallenberger reasoned that, as 0.68 X 1.8 = 1.22 (which approximates the reported sweetness of mutarotated D-fructose ), the furanose form(s) must possess very little sweetness. 

The STM postulated tunneling matrix element distribution P(A) oc 1 /A implies a weakly (logarithmically) time-dependent heat capacity. This was pointed out early on by Anderson et al. [8], while the first specific estimate appeared soon afterwards [93]. The heat capacity did indeed turn out time dependent however, its experimental measures are indirect, and so a detailed comparison with theory is difficult. Reviews on the subject can be found in Nittke et al. [99] and Pohl [95]. Here we discuss the A distribution dictated by the present theory, in the semiclassical limit, and evaluate the resulting time dependence of the specific heat. While this limit is adequate at long times, quantum effects are important at short times (this concerns the heat condictivity as well). The latter are discussed in Section VA. 

The chain lengths of the hydrocarbons obey a statistical distribution named after Anderson, Schulz, and Flory, given by... 

Orientational disorder and packing irregularities in terms of a modified Anderson-Hubbard Hamiltonian [63,64] will lead to a distribution of the on-site Coulomb interaction as well as of the interaction of electrons on different (at least neighboring) sites as it was explicitly pointed out by Cuevas et al. [65]. Compared to the Coulomb-gap model of Efros and Sklovskii [66], they took into account three different states of charge of the mesoscopic particles, i.e. neutral, positively and negatively charged. The VRH behavior, which dominates the electrical properties at low temperatures, can conclusively be explained with this model. 

Bacon MP, Anderson RF (1982) Distribution of thorium isotopes between dissolved and particulate forms in the deep sea. J Geophys Res 87 2045-2056... 

Efforts to apply Equations (6) and (7) to distributions of Th isotopes in the oceans showed that the situation was more complex. For example. Bacon and Anderson (1982) measured vertical distributions of Th in the deep sea and found that both the particulate and dissolved fractions increased linearly with depth. While the former observation is predictable from Equation (7) if sinking particles continue to scavenge Th during their descent, the latter is inconsistent with Equation (6). Bacon and Anderson (1982) suggested that the data could best be explained by a reversible scavenging equilibrium maintained between dissolved and particulate Th. Thus Equation (6) must be modified to ... 

Bacon MP, Spencer DW, Brewer PG (1976) Pb-210/Ra-226 and Po-210/Pb-210 disequilibria in seawater and snspended particulate matter. Earth Planet Sci Lett 32 277-296 Bacon MP, Anderson RF (1982) Distribution of thorium isotopes between dissolved and particulate forms in the deep sea. J Geophys Res 87 2045-2056... 

Nozaki Y, Zhang J, Takeda A (1997) °Pb and °Po in the equatorial Pacific and Bering Sea the effects of biological productivity and boundary scavenging. Deep-Sea Res II 44 2203-2220 Nozaki Y, Dobashi F, Kato Y, Yamamoto Y (1998) Distribution of Ra isotopes and the °Pb and °Po balance in surface waters of the mid Northern Hemisphere. Deep-Sea Res. 145 1263-1284 Pates JM, Cook GT, MacKenzie AB, Anderson R, Bury SJ (1996) Determination of Th-234 in marine samples by liquid scintillation spectrometry. Anal Chem 68 3783-3788... 

Shimmield GB, Murray JW, Thomson J, Bacon MP, Anderson RF, Price NB (1986) The distribution and behaviour of °Th and Pa at an ocean margin, Baja California, Mexico. Geochim Cosmochim Acta 50 2499-2507... 

Hegele, R. A., Anderson, C., Young, T. K. Connelly, P. W. (1999). G-protein beta3 subunit gene splice variant and body fat distribution in Nunavut Inuit. Genome Res., 9, 972-7. 

Anderson, Flavia. The ancient secret fire from the sun. 3rd ed ed. Wellingborough Research into Lost Knowledge Organisation distributed by Thorsons, 1987. 288p. 

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