Recipe Representations

Very similar to the STN is the state sequence network (SSN) that was proposed by Majozi and Zhu (2001). The fundamental, and perhaps subtle, distinction between the SSN and the STN is that the tasks are not explicitly declared in the SSN, but indirectly inferred by the changes in states. A change from one state to another, which is simply represented by an arc, implies the existence of a task. Consequently, the mathematical formulation that is founded on this recipe representation involves only states and not tasks. The strength of the SSN lies in its ability to utilize information pertaining to tasks and even the capacity of the units in which the tasks are conducted by simply tracking the flow of states within the network. Since this representation and its concomitant mathematical formulation constitute the cornerstone of this textbook, it is presented in detail in the next chapter. 

Chapter 2 introduces the reader to the basis of all the mathematical techniques presented in this textbook. The mathematical techniques are founded on a recipe representation known as the state sequence network (SSN), which allows the use of states to dominate the analysis thereby reducing the binary dimension. 

The use of Grafcet/SFC for recipe representation has been studied by Johnsson and Arzen [17]. They have used and extended version called grafchart, where Grafcet is extended with high level Petri Nets ideas and object oriented programming concepts, for its application in batch control, recipe execution and resource allocation [18]. 

The above applications require plant models at different levels of detail. Long term capacity analysis requires the least detail in recipe representation. Typically, the recipe of a batch process is represented with a small number of activities occupying key equipment that is likely to limit production. Long term planning utilizes models with a detail similar to those of capacity analysis. Short term planning and scheduling require more detailed models that account for the ntihzation of all main equipment and the critical auxiliary equipment (i.e., those with high utilization that... 

If a batch process is already modeled in SuperPro Designer, its recipe can be exported to SchedulePro via a recipe database. The same is possible with batch process automation and manufacturing execution systems that foUow the ISA S-88 standards for batch recipe representation. Alternatively, recipes can be created by users directly in SchedulePro. 

Another important aspect of batch plants relates to the representation of the recipe which is invariably the underlying feature of the resultant mathematical formulation. The most common representation of recipe in the published literature is the state task network (STN) that was proposed by Kondili et al. (1993), which comprises of 2 types of nodes, viz. state nodes and task nodes. The state nodes represent all the materials that are processed within the plant. These are broadly categorized into feeds, intermediates and final products. On the other hand, task nodes represent unit operations or tasks that are conducted in various equipment units within the process. 

The plant is used to produce two chemically different EPS -types A and B in five grain size fractions each from raw materials FI, F2, F3. The polymerization reactions exhibit a selectivity of less than 100% with respect to the grain size fractions Besides one main fraction, they yield significant amounts of the other four fractions as by-products. The production processes are defined by recipes which specify the EPS-type (A or B) and the grain size distribution. For each EPS-type, five recipes are available with the grain size distributions shown in Figure 7.2 (bottom). The recipes exhibit the same structure as shown in Figure 7.2 (top) in state-task-network-representation (states in circles, tasks in squares). They differ in the parameters, e.g., the amounts of raw materials, and in the temperature profiles of the polymerization reactions. 

The recipe for constructing a second quantization representation of a one-electron operator is thus to use Eq. (2.2) with the integrals of Eq. (2.4). 

One must agree that the precise recipe implied by Van Vleck s and Sherman s language is daunting. The use of characters of the irreducible representations in dealing with spin state-antisymmetrization problems does not appear to lead to any very useful results. Prom today s perspective, however, it is known that some irreducible representation matrix elements (not just the characters) are fairly simple, and when applications are written for large computers, the systematization provided by the group methods is useful. 

Fig. 2 Schematic representation of the calculation recipe in Td point group - VCI4...

Some domain ontologies have been developed, which so far cover only a small portion of the chemical engineering domain They enable the representation of material properties, experiments and process recipes, as well as the structural description of mathematical models. In parallel, an ontology for the modeling of work processes and decisions has been built. Yet the representation of work processes is confined to deterministic guidelines, the input/output information of activities cannot be modeled, and the acting persons are not... 

The problem of the searching for the optimal one-electron representation is one of the oldest in the theory of multielectron atoms. Three decades ago, Davidson had pointed the principal disadvantages of the traditional representation based on the self-consistent field approach and suggested the optimal natural orbitals representation. Nevertheless, there remain insurmountable calculational difficulties in the realization of the Davidson program (see, e.g. Ref. [12]). One of the simplified recipes represents, for example, the DPT method [18,19]. Unfortunately, this method does not provide a regular refinement procedure in the case of the complicated atom with few quasiparticles (electrons or vacancies above a core of the closed electronic shells). For simplicity, let us consider now the one-quasiparticle atomic system (i.e., atomic system with one electron or vacancy above a core of the closed electronic shells). The multi-quasiparticle case does not contain principally new moments. In the lowest second order of the QED PT for the A , there is the only one-quasiparticle Feynman diagram a (Fig. 12.1), contributing the ImAZ (the radiation decay width). 

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