Schumann model

In addition to the Burke and Schumann model (34) and the Displacement Distance theory, a comprehensive laminar diffusion flame theory can be written using the equations of conservation of species, energy, and momentum, including diffusion, heat transfer, and chemical reaction. 

Schumann Model. This is the simplest and the least accurate of all models. The two equations are given as... 

Besides the strictly kinetic properties of the system, the idealized flame structure represented by the Burke-Schumann model is also often disturbed by other processes disregarded by this model. Most often, this disturbance is caused by turbulence of gas flows. Such flames are called turbulent. (For turbulence effects on the reaction rate see e.g. [434]). 

Evaporation and burning of Hquid droplets are of particular interest in furnace and propulsion appHcations and by applying a part of the Burke and Schumann approach it is possible to obtain a simple model for diffusion flames. 

Schumann W, Turner P (1978) Membrane model of the human oral mucosa as derived from buccal absorption performance and physicochemical properties of the beta-blocking drugs atenolol and propranolol. J Pham Pharmacol 30 137-147... 

Reitz, R.H., McDougal. J.N.. Himmelstein, M.W., Nolan, R.J. Schumann, A.M. (1988) Physiologically based phannacokinetic modeling with methylchloroform implications for interspecies, high dose/low dose, and dose route extrapolations. Toxicol, appl. Pharmacol., 95, 185-199... 

In full-scale Are modeling, a diffusion flame structure is usually assumed. However, in many fire situations, such as underventilated fires, premixed or partially premixed flame theory may be more appropriate. The Burke-Schumann description of the diffusion flames can be used to conveniently represent the transport of gaseous species by a single scalar quantity called mixture fraction. For a simple one-step reaction ... 

A number of authors, however, have represented forest or urban canopy layers by porous regions of distributed force (or drag) [206, 213, 217, 318, 320, 576, 662], The advantage of such an approach is that it permits inclusion of a canopy sublayer without the use of excessive and costly grid resolution. Yamada [662] and Shaw and Schumann [576] introduced the approach in order to add vegetation to meso-scale models of complex terrain. Jeram et al. [320] used the concept in 2d calculations for inviscid flow and constant eddy diffusivity flow estimates of the up and downwind penetration of flow within simple urban areas. 

Schumann U (1975) Subgrid Scale Model for Einite Difference Simulations of Turbulent Flows in Plane Channels and Annuli. J Comput Phys 18 376-404... 

The determination of the O2 photodissociation frequency in the Schumann-Runge bands is obtained from a computation including the complex rotational structure of the band system. A major difficulty in the calculation of Schumann-Runge band photolysis in the middle atmosphere, in addition to requirements for high spectral resolution, arises from the temperature dependence of absorption cross sections. Polynomial expressions have been derived to reproduce the temperature variation provided by the line-by-line calculations (Minschwaner et al., 1992) this kind of approach, however, is generally not feasible to be implemented in detailed middle atmosphere models, but can be used to develop more efficient broad-band parameterizations (see Section 4.7.3). 

Since a detailed treatment of radiative transfer in the Schumann-Runge bands is often computationally prohibitive when applied to photochemical models, the effective O2 cross section atmospheric transmission are often pre-calculated through detailed... 

Gijs, A., A. Koppers, and D.P. Murtagh, Model studies of the influence of O2 photodissociation parameterizations in the Schumann-Runge bands on ozone related photolysis in the upper atmosphere. Ann Geophys If, 68, 1997. 

Sass, G., Heinlein, S., Agli, A., Bang, R., Schumann, J. and Tiegs, G. Cytokine expression in three mouse models of experimental hepatitis. Cytokine 19 (2002) 115-120. 

Freude S, Hettich MM, Schumann C, Stohr O, Koch L, Kohler C, Udelhoven M, Leeser U, Muller M, Kubota N, Kadowaki T, Krone W, Schroder H, Bruning JC, Schubert M (2009a) Neuronal IGF-1 resistance reduces Abeta accumulation and protects against premature death in a model of Alzheimer s disease. FASEB J 23 3315-3324... 

Pickering, K., H. Huntrieser and U. Schumann (2009) Lightning and NOx production in global models. In Betz et al. (2009), pp. 551-572 Pidwirny, M. (2006) The hydrologic cycle. Fundamentals of physical geography, 2" Edition. 

U. Schumann. Realizability of Reynolds-stress turbulence models. Physics of Fluids, 20 721-725, 1977. 

Escudero LF, Galindo E, Garcia G et al (1999) Schumann, a modeling framework for supply chain management under uncertainty. Eur J Oper Res 119(l) 14—34... 

Schumann H. et al., 2010, Concurrent Systems Engineering in Aerospace From Excel-based to Model Driven Design, 8th Conference on Systems Engineering Research, Hoboken NJ. 

Schumann H., A. Berres, 2011, Modellbasierter Syste-ment wurf mit dem PrEMISE-Modell, Tag des System sengineering2011 Hamburg. 

Schumann, D., Novgorodov, A.F., Misiak, R., Wunderlich, G. Model Studies for the separation and identification of element 107 (Bohrium, Bh) ion exchange and precipitation experiments with Tc, Re, Nb and Ta nuclides from HNO3/HF containing aqueous solution. 

Sandler SI (1999) Chemictil and engineering thermodynamics, 3rd edn. Wiley, New York Schlichting H, Gersten K (2000) Boundary-layer theory. Springer, Berlin Schumann U (1975) Subgrid settle model for finite difference simulations of turbulent flows in plane channels and annuli. J Comput Phys 18 376-404... 

Schumann U (1989) Laige-eddy simulation of the turbulent diffusion with chemical reactions in the convective boundary layer. Atmos Environ 23(8) 1713-1727 Schumann U (1992) Simulations and parameterizations of laige eddies in convective atmospheric boundary layers. In Proceedings of a workshop held at the European Centre for Medium-Range Weather Forecasts (ECMWF) on Fine Scale Modelling and the Development of Parameterization Schemes, 16-18 September 1991, ECMWF Shames IH (1962) Mechemics of fluids. McGraw-Hill, New York... 

A59. Steil, B. Briihl, C. Cmtzen, P.J. Dameris, M. Ponater, M. Sausen, R. Roeckner, E. Schlese, U. Roelofs, G.J., 1994 A Chemistry Model for Use in Comprehensive Climate Models , in Schumann, U. Wurzel, D. (Eds.) Proceedings of an International Scientific Colloquium on Impact of Emissions from Aircraft and Spacecraft upon the Atmosphere, Koln, Germany, April 18-20, 1994, DLR-Mitteilung 94-06, 235-240. 

ATP synthesis as well as light induced ATPase activity. This means that photll drives enzymatic activity of CF1 without showing a correlation with nucleotide exchange as found with PMS mediated electron transport through photl (J.Schumann, H.Strotmann, 1981). We conclude from this that protons from the water splitting system are not the regulative ones discussed in our model. 

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