Compromise mechanism, description

Representation of Atmospheric Chemistry Through Chemical Mechanisms. A complete description of atmospheric chemistry within an air quaUty model would require tracking the kinetics of many hundreds of compounds through thousands of chemical reactions. Fortunately, in modeling the dynamics of reactive compounds such as peroxyacetyl nitrate [2278-22-0] (PAN), C2H2NO, O, and NO2, it is not necessary to foUow every compound. Instead, a compact representation of the atmospheric chemistry is used. Chemical mechanisms represent a compromise between an exhaustive description of the chemistry and computational tractabiUty. The level of chemical detail is balanced against computational time, which increases as the number of species and reactions increases. Instead of the hundreds of species present in the atmosphere, chemical mechanisms include on the order of 50 species and 100 reactions. 

Another challenge to the "variational" multi-scale CFD lies in the computing scheme, in the sense that the "dominant mechanisms" as well as their "compromise" in terms of certain stability conditions may relate with scales different from those of CFD computation. A clear example for that situation can be found in gas-solid fluidization (Li et al., 2004 Zhang et al., 2005), where locally the two dominant mechanisms for particles (e = min) and gas (Wst = min) can be realized alternately with respect to time and space, with the term for characterizing stability condition fluctuating intensively, while their compromise leads to the stability condition (Nst = min) at the meso-scale. When CFD computation is performed at a scale smaller than that, how to incorporate the larger scale stability condition into the CFD description of hydrodynamics will be a hard topic. 

In fact, extremum tendencies expressing the dominant mechanisms in systems like turbulent pipe flow (Li et al, 1999), gas-liquid-solid flow (Liu et al, 2001), granular flow, emulsions, foam drainages, and multiphase micro-/nanoflows also follow similar scenarios of compromising as in gas-solid and gas-liquid systems (Ge et al., 2007), and therefore, stability conditions established on this basis also lead to reasonable descriptions of the meso-scale structures in these systems. We believe that such an EMMS-based methodology accords with the structure of the problems being solved, and hence realize the similarity of the structures between the physical model and the problems. That is the fundamental reason why the EMMS-based multi-scale CFD improves the... 

MD simulations require the description of the interactions between the particles (potential function, or a force field) of a molecular system [27]. The potential function can be defined on various levels. The most conunonly adopted potential functions in chemistry and biology are based on molecular mechanics (MM), with a classical treatment of particle-particle interactions. With well-chosen parameter sets, these potential functions can reproduce structural and conformational changes in systems, except chemical reactions. The analytic forms of the potential functions, which involve low computational cost, make it possible for MD simulations to include a huge number of atoms. When potentials based on quantum mechanics (QM) are adopted, MD simulations can give finer levels of detail, such as chemical reactions and electronic structures, but expensive computational costs are involved simultaneously. As a compromise, hybrid QM/MM approaches are... 

In this chapter we examine more carefully the formation of the covalent bond. The description of molecules by quantum mechanics can become exceedingly complicated. The best compromise between simplicity and accuracy is probably the molecular orbital (MO) theory, developed about 1932 by Friedrich Hund, Robert Mulliken, Erich Hiickel, and John Lennard-Jones,... 

The coupling of quantiun mechanical approaches and molecular mechanics with accurate force fields adjusted from quantum chenucal calculations is a strategy that is increasingly used to study condensed phases and clusters. A detailed quantiun description of a subsystem in which important changes in electronic distribution occur is performed taking into account the effect of the environment. Finding a compromise between accuracy and the simplicity of the description of the quantum subsystem and of the enviromnent inter-... 

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