Herbert model

Sumeria, V.H., J.A. Rovnak, I. Heitner, RJ. Herbert, Model to Predict Transient Consequences of a Heat Exchanger Tube Rupture, Proceedings-Refining Department, Vol. 55, American Petroleum Institute, Washington, D.C., 1976, p.63... 

The VSEPR model was first explored by the British chemists Nevil Sidgwick and Herbert Powell and has been developed by the Canadian chemist Ronald Gillespie. 

Herbert JM, Dol E Bemat A, Falotico R, Lale A, Savi P The antiaggregating and antithrombotic activity of clopidogrel is potentiated by aspirin in several experimental models in the rabbit. Thromb Haemost 1998 80 512-518. 

Another model that is also used widely in rats and mice is a model of systemic thrombosis or disseminated intravascular coagulation (DIC), which is induced by tissue factor, endotoxin (lipopolysaccharide), or FXa (Herbert et al. 1996 Yamazaki et al. 1994 Sato et al. 1998). After systemic administration of the thrombogenic stimulus, this model can be performed with or without mechanical vena caval stasis. When stasis is used, the major parameter is the thrombus mass, but when stasis is not used, the readouts are... 

Herbert Hauptman, a mathematician turned crystallographer and chemistry Nobel laureate for 1985, has devoted a lot of attention to close packing of spheres in the icosahedron. Figure 9-31 shows one of his beautiful stained-glass models. 

Figure 9-31. Herbert Hauptman (photograph by the authors) and one of his stained-glass models—an icosahedron—with densely packed spheres (photograph courtesy of Herbert Hauptman, Buffalo, New York).

We seek to write differential equations for this model, and begin by considering just one organism growing in the chemostat. (A more complete derivation can be found elsewhere see e.g. Herbert, Elsworth, and Telling [HET].) The rate of change of the nutrient can be expressed as... 

Herbert Hauptman with one of his polyhedral packing models (courtesy of Herbert Hauptman). 

More extensive discussions of the theoretical aspects of chemostat culture have been published elsewhere (e.g. Herbert et al, 1956 Pirt, 1975 Bailey Ollis, 1977). Many of the theoretical principles apphed to microbial chemostat cultures can be applied successfully to animal cell cultures, although there are a number of instances where the behaviour of animal cells has been reported to deviate from the models used to describe microbial growth kinetics (Tovey, 1980 Boraston et al, 1984 Miller et al., 1988). 

The most basic model is the toxic unit model which involves determining the toxic strength of an individual compound, expressed as a "toxic unit." The toxicity of the mixture is determined by summing the strengths of the individual compounds (Herbert and Vandyke 1964) using the following model ... 

ML is a subfield of artificial intelligence that is concerned with the design and development of algorithms that allow computers (machines) to improve their performance over time (or learn) based on data. A major focus of ML research is to automatically produce models. Many researchers quote Herbert Simon in describing ML (23) ... 

The modeling results show that a large amount of iron and aluminum hydroxide will be precipitated. Coprecipitation with iron and aluminum hydroxide is commonly found and is a significant natural attenuation process (Herbert, 1996 National Research Council, 2000 Zhu et al, 1993). 

Fig. 16. Comparison of Monod s model with data of Herbert et al. (HIO) on growth of Aerobacter cloacae. Solid line calculated from Monod s model with /a = 0.85 hr , K = 0.0123 g/liter, C,f = 2.5 g/liter, and a = 1.89 g/g. Replotted from J. Gen. Microbiol. 14, 601-622 (1956), by permission of Cambridge University Press.

Experimental results of Herbert et al. are compared with predictions of Monod s model in Fig. 16. At long holding times, agreement of the model with experiment is good this is not the case at holding times near the critical, where there is a definite trend not predicted by the model. Thus, it appears that the maximum specific growth rate (//) is faster than that determined from batch experiments also the stoichiometric coefficient a changes as 6 approaches the critical. 

Herbert attributes part of the discrepancy to the occurrence of endogenous metabolism, not accounted for in Monod s model. In other words, cells not only convert substrate into protoplasm, but they also carry on reactions... 

Work concerned with other aspects of biomass conversion normally start with equations (3-74) and (3-75). For example, a number of models for maintenance have been proposed. [(D. Herbert, Proc. Symp. Continuous Cultivation of Micro-organisms, (I. Malek, ed.), Czech. Academy of Sciences, Prague, (1958)] suggested that the source of energy for maintenance was oxidation of the cell... 

Does the chronic medical condition concept make sense Again, it does for some of the people in our example. Certainly, the disease model examples (Raymond, Fred, Cheryl) appear to have chronic medical conditions. However, Raymond (nausea-treatment alcoholic) did not have any continuing care after treatment, yet he remained sober. Herbert (maintenance drinker) certainly had a chronic problem with alcohol. But, he never had any formal treatment intervention for his drinking and was able to stop drinking and never start again without any assistance. 

Lange, A. W., and Herbert, J. M. (2010). Polarizable continuum reaction-field solvation models affording smooth potential energy surfaces, J. Phys. Chem. Lett. 1, pp. 556-561. 

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