Model, box

Identification of the material properties as an estimation of transfer function (TF) for the black box model. In this case the problem of identification is solving according to the results of the input (IN) and output (OUT) actions. There is a transfer of notion of mathematical description of TF on characterization of the material. This logical substitution gives us an opportunity to formalize testing procedure and describe the material as a set of formulae, which can be used for quantitative and qualitative characterization of the materials. 

The above partiele in a box model for motion in two dimensions ean obviously be extended to three dimensions or to one. 

For two and three dimensions, it provides a erude but useful pieture for eleetronie states on surfaees or in erystals, respeetively. Free motion within a spherieal volume gives rise to eigenfunetions that are used in nuelear physies to deseribe the motions of neutrons and protons in nuelei. In the so-ealled shell model of nuelei, the neutrons and protons fill separate s, p, d, ete orbitals with eaeh type of nueleon foreed to obey the Pauli prineiple. These orbitals are not the same in their radial shapes as the s, p, d, ete orbitals of atoms beeause, in atoms, there is an additional radial potential V(r) = -Ze /r present. However, their angular shapes are the same as in atomie strueture beeause, in both eases, the potential is independent of 0 and (j). This same spherieal box model has been used to deseribe the orbitals of valenee eleetrons in elusters of mono-valent metal atoms sueh as Csn, Cun, Nan and their positive and negative ions. Beeause of the metallie nature of these speeies, their valenee eleetrons are suffieiently deloealized to render this simple model rather effeetive (see T. P. Martin, T. Bergmann, H. Gohlieh, and T. Lange, J. Phys. Chem. 6421 (1991)). 

This simple partiele-in-a-box model does not yield orbital energies that relate to ionization energies unless the potential inside the box is speeified. Choosing the value of this potential Vq sueh that Vq + ti2 h2/2m [ 52/E2] is equal to minus the lowest ionization energy of the 1,3,5,7-nonatetraene radieal, gives energy levels (as E = Vq + ti2 h2/2m [ n2/E2]) whieh then are approximations to ionization energies. 

Euleria.n Models. Of the Eulerian models, the box model is the easiest to conceptualize. The atmosphere over the modeling region is envisioned as a well-mixed box, and the evolution of pollutants in the box is calculated following conservation-of-mass principles including emissions, deposition, chemical reactions, and atmospheric mixing. 

This forms a basis for an urban photochemical box model (6) discussed later in this chapter. 

Schere, K. L., and Demerjian, K. L., A photochemical box model for urban air quality simulation, in "Proceedings of the Fourth Joint Conference on Sensing of Environmental Pollutants." American Chemical Society, Washington, DC, 1978, pp. 427-433. 

Demerjian, K. L., and Schere, K. L., Application of a photochemical box model for O3 air quality in Houston, TX, in "Proceedings of Ozone/Oxidants Interactions with the Total Environment II." Air Pollution Control Association, Pittsburgh, 1979, pp. 329-352. 

What is the steady-state concentrahon derived from the box model for a 10-km city with average emissions of 2 x 10" g m s when the mixing height is 500 m and the wind speed is 4 m s ... 

PBM (Photochemical Box Model) is a simple stationary single-cell model with a variable height lid designed to provide volume-integrated hour averages of ozone and otlier photochemical smog pollutants for an urban area for a single day of simulation. 

We can also use the Boltzmann formula to interpret the increase in entropy of a substance as its temperature is raised (Eq. 2 and Table 7.2). We use the same par-ticle-in-a-box model of a gas, but this reasoning also applies to liquids and solids, even though their energy levels are much more complicated. At low temperatures, the molecules of a gas can occupy only a few of the energy levels so W is small and the entropy is low. As the temperature is raised, the molecules have access to larger numbers of energy levels (Fig. 7.10) so W rises and the entropy increases, too. 

Research should be conducted to understand how the oceans have operated under past climates. This would involve paleoclimatic studies including analysis of sediment and ice core records coupled with tracer-style ocean models or box models. 

This chapter focuses on types of models used to describe the functioning of biogeochemical cycles, i.e., reservoir or box models. Certain fundamental concepts are introduced and some examples are given of applications to biogeochemical cycles. Further examples can be found in the chapters devoted to the various cycles. The chapter also contains a brief discussion of the nature and mathematical description of exchange and transport processes that occur in the oceans and in the atmosphere. This chapter assumes familiarity with the definitions and basic concepts listed in Section 1.5 of the introduction such as reservoir, flux, cycle, etc. 

Let us define a two-box model for a steady-stafe ocean as shown in Fig. 10-22. The two well mixed reservoirs correspond to the surface ocean and deep oceans. We assume that rivers are the only source and sediments are the only sink. Elements are also removed from the surface box by biogenic particles (B). We also assume there is mixing between the two boxes that can be expressed as a velocity Vmix = 2 m/yr and that rivers input water to the surface box at a rate of Vnv = 0.1 m/yr. The resulting ratio of F mix/V riv is 20. 

There is some debate about what controls the magnesium concentration in seawater. The main input is rivers. The main removal is by hydrothermal processes (the concentration of Mg in hot vent solutions is essentially zero). First, calculate the residence time of water in the ocean due to (1) river input and (2) hydro-thermal circulation. Second, calculate the residence time of magnesium in seawater with respect to these two processes. Third, draw a sketch to show this box model calculation schematically. You can assume that uncertainties in river input and hydrothermal circulation are 5% and 10%, respectively. What does this tell you about controls on the magnesium concentration Do these calculations support the input/removal balance proposed above Do any questions come to mind Volume of ocean = 1.4 x 10 L River input = 3.2 x lO L/yr Hydrothermal circulation = 1.0 x 10 L/yr Mg concentration in river water = 1.7 X 10 M Mg concentration in seawater = 0.053 M. 

Box models have a long tradition (Craig, 1957b Revelle and Suess, 1957 Bolin and Eriksson, 1959) and still receive a lot of attention. Most work is concerned with the atmospheric CO2 increase, with the main goal of predicting global CO2 levels during the next hundred years. This is accomplished with models that reproduce carbon fluxes between the atmosphere and other reservoirs on time... 

Simple three-box models with the atmosphere assumed to be one well-mixed reservoir and the oceans described by a surface layer and a deep-sea reservoir have been used extensively. Keeling (1973) has discussed this type of model in detail. The two-box ocean model is refined by including a second surface box, simulating an "outcropping" (deep-water forming) polar sea (e.g.. Keeling and Bolin, 1967, 1968), and to include a better resolution of the main thermo-cline (e.g., Bjorkstrom, 1979). The terrestrial biota are included in a simple manner (e.g., Bolin and Eriksson, 1959) in some studies Fig. 11-18 shows a model used by Machta (1972) where the role of biota is simulated by one reservoir connected to the atmosphere with a time lag of 20 years. 

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