General Model Characteristics

Due to the fact that multiple products with different processing requirements share production equipment and internally produced intermediates have to be included in the analysis, a multiple-product model is required. 

As discussed in Chapter 2.3.4 specialty chemicals companies operate global production networks. Additionally, tariffs often constitute a higher share of total costs than transportation costs. Thus, a model that explicitly considers international trade is required. 

As argued in Chapter 2.1.2 this work focuses on production network design. Demand is assumed to be independent of production network design decisions and the cost structure achieved. Also, unlimited quantities of raw materials are assumed to be available. An extensions to include make-or-buy decisions (and possibly vendor selection) is provided to accommodate application cases where sourcing decisions have to be included. 

The number of production levels that have to be modeled explicitly depends on the type of value chain considered and the level of vertical integration pursued by the company. Consequently, the model does not structurally limit the number of levels. However, from a computational point of view limits might still apply. 

In theory, a company should be able to finance any investment that earns a return exceeding the cost of capital and hence no budget constraints would be required. Additionally, Melo et al. (2005, p. 201) observed that budget restrictions can lead to increased calculation time. Primarily for the first reason the proposed model does not contain a restriction on the investment budget. If required a budget restriction can easily be added to reflect the fact that in practice investment budgets are often limited. 

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The next and very important step is to make a decision about the descriptors we shall use to represent the molecular structures. In general, modeling means assignment of an abstract mathematical object to a real-world physical system and subsequent revelation of some relationship between the characteristics of the object on the one side, and the properties of the system on the other. 

There are at least as many variants of the basic CA algorithm as there are ways of generalizing the characteristics of a typical CA system. Here are a few general models ... 

In what follows we briefly review some of the previous attempts to analyze the available spectra of plutonium (6). In addition, we estimate energy level parameters that identify at least the gross features characteristic of the spectra of plutonium in various valence states in the lower energy range where in most cases, several isolated absorption bands can be discerned. The method used was based on our interpretation of trivalent actinide and lanthanide spectra, and the generalized model referred to earlier in the discussion of free-ion spectra. 

Spatial accommodation of the guest evidently allows disordering of the guest molecule, another characteristic feature of true clathrates. This structure may serve as a general model for other possible inclusion compounds of 1 with apolar guests and also, in lack of the structure of the free host 1 (cf. Sect. 4.1), it may help to imagine a probable steric arrangement for that case... 

The specific problem characteristics are modeled most appropriately by a combination of concepts from various general modeling frameworks leading to a mixed-integer nonlinear programming (MINLP) model. 

The SNP model contains all relevant locations, i.e., production plants and distribution centers, in the supply network. The cross-locational sourcing aspect of the planning scenario is handled within the master planning process. SNP determines which of the plants produces which quantities of which products in which time periods. On a rough level, SNP also determines which production alternative is used at a specific plant, for instance with regard to ingredients and general process characteristics. 

Krt < k scalar spectral transport time scale defined in terms of the velocity spectrum (e.g., rst). 

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

Intramolecular dynamics and chemical reactions have been studied for a long time in terms of classical models. However, many of the early studies were restricted by the complexities resulting from classical chaos, Tlie application of the new dynamical systems theory to classical models of reactions has very recently revealed the existence of general bifurcation scenarios at the origin of chaos. Moreover, it can be shown that the infinite number of classical periodic orbits characteristic of chaos are topological combinations of a finite number of fundamental periodic orbits as determined by a symbolic dynamics. These properties appear to be very general and characteristic of typical classical reaction dynamics. 

Pressure solution can cause major alterations in carbonate rock structures on megascopic to microscopic scales. Numerous papers and reviews deal with this topic (e.g., Bathurst, 1975 Choquette and James, 1987). We feel that one of the best attempts to bring an orderly picture out of the many complex features that are observed was that by Wanless (1979), who also emphasized the importance of pressure solution for subsurface dolomitization (see next section). Figure 8.12 presents his general model for the characteristics and controls on pressure solution types in limestones. The primary variables that Wanless considered were the clay content of the limestone, the concentration of structurally resistant elements, and variations between different units or beds. Temperature, pressure and fluid composition are also likely to play an important role in determining the timing and extent of pressure solution. 

Global reactions models are those where the reactants and products are defined by available analytical separation schemes. They generally represent the interconversion of lumps or pseudocomponents, i.e., aggregates of many molecules with common attributes. In general, the characteristics which assemble given sets of molecules into a lump will not be reactivity. For example, perhaps the two most commonly found globally lumped models are based on boiling point or solubility characteristics. 

Most characteristic sizes of organic particles of marine aerosols do not exceed 10 pm. Data on organic aerosol are rather inadequate and do not even permit one to draw, in general terms, a reliable pattern of its optical properties. No doubt much effort is required before real possibilities appear to consider this component in a general model of aerosol. 

Likewise, animal models characteristically discern three types of activity activity against electrically induced convulsions correlates with activity again.st generalized tonic-clonic and partial seizures, and activity against penty-Icnetetrazole (PTZ)-induced. seizures correlates with antiabsence activity. Of late, a fourth model, activity against pilocarpine and kainic acid seizures, is said to predict protection against temporal lobe epilep.sy (a complex partial seizure). 

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