Closed box model

Closed box" model for the mass of the galaxy and the distribution of mass between stars and gas as a function of time. The mass of gas is constrained to match the currently observed value of -10%. 

This question can be examined further by studying metallicity as a function of gas fraction. In the context of the simple, closed box, chemical evolution, Edmunds (1990) derived a few simple theorems that show that outflows of gas and inflows of metal-poor gas cause galactic systems to deviate from the closed box model in similar ways. Specifically, defining the effective yield yef f... 

In a closed box or leaky-box chemical evolution model the most metal-poor stars would have formed before the majority of the Type la SN or the AGB stars... 

In models alc-a2c the predicted stellar distributions are almost indistinguishable (see Figure 1), except for the absence of stars with [Fe/H]< —3.0 in the case with Pop III stars. The reason for this resides in the fact that the Pop III phase is very short and at the same time the star formation rate is small at early stages. In the closed-box cases (models bl and b2) the difference is more noticeable since at the beginning the star formation is quite high. In both models, in fact, no stars with metallicity lower than -3.0 and -2.0, respectively, are predicted. The distribution of stars with metallicity, in turn, influences the calculation of [< Mg/H > ] and [< Fe/H > ]. For the ale and a2c models there is very little difference in these average values, whereas for bl and b2 model the [< Mg/Fe > ] varies from... 

Pop III stars in classic monolithic models for ellipticals (closed-box) produce larger, although still acceptable, [< Mg/Fe > ] ratios. However, the predicted integrated colors are too red. As a consequence these models should be rejected. 

One important issue concerning fire prevention is the early detection of overheated wire insulation, a common source of smoldering fires. Therefore model experiments were performed to examine how far early indications of overheated insulation could be recognized by the gradient microarray and its simple sampling arrangement. The tests were carried out in a closed box with KAMINA placed next to a cable overheated by a current overload. The experiments were performed... 

A closed-system 3-box model with concentrations as the variables... 

To assess the relative importance of the volatilisation removal process of APs from estuarine water, Van Ry et al. constructed a box model to estimate the input and removal fluxes for the Hudson estuary. Inputs of NPs to the bay are advection by the Hudson river and air-water exchange (atmospheric deposition, absorption). Removal processes are advection out, volatilisation, sedimentation and biodegradation. Most of these processes could be estimated only the biodegradation rate was obtained indirectly by closing the mass balance. The calculations reveal that volatilisation is the most important removal process from the estuary, accounting for 37% of the removal. Degradation and advection out of the estuary account for 24 and 29% of the total removal. However, the actual importance of degradation is quite uncertain, as no real environmental data were used to quantify this process. The residence time of NP in the Hudson estuary, as calculated from the box model, is 9 days, while the residence time of the water in the estuary is 35 days [16]. 

The box model is closely related to the more complex airshed models described below in that it is based on the conservation of mass equation and includes chemical submodels that represent the chemistry more accurately than many plume models, for example. However, it is less complex and hence requires less computation time. It has the additional advantage that it does not require the detailed emissions, meteorological, and air quality data needed for input and validation of the airshed models. However, the resulting predictions are... 

Fig. 1. Two-compartment model to describe the metabolism of oxygen-derived free radicals in myocardial tissue. This figure depicts the progressive reduction of intracellular oxygen during the cycle of ischemia and reperfusion. Inhibitors of radical metabolism are shown in dashed boxes. Radical spin traps are shown in closed boxes.

This is the case, for example, for Mg. For Ca, the 4s and 4p orbitals overlap. There is a continuous energy band, but a band that is fiUed by only two electrons per atom. Mg and Ca are, therefore, metals. This case corresponds closely to the classical Drude model when electrons may take on any energy value. To make the simplest possible quantum mechanical model, we only need to treat the electrons as in the box model. We have to observe the Pauli principle and occupy the orbitals with two electrons until the actual total number has been reached. This is essentially the FEM for metals. 

In the present paper a more systematic procedure is proposed. The key idea of this procedure is to exploit the close connection between ODE models and SDE models to develop a methodology for determining the proper structure of the functional relations directly from the experimental data. The new procedure more specifically allows important trends and dependencies to be visually determined without making any prior assumptions and in turn allows appropriate parametric expressions to be inferred. The proposed procedure is a tailored application of the grey-box modelling approach to process model development proposed by Kristensen et al. (2002b), within which specific model deficiencies can be pinpointed and their structural origin uncovered to improve the model. 

---