Goal and Task Formulation

The following principles have been formulated based on the stated goals and tasks of modeling and on the analysis of the existing approaches in this area. 

During system analysis, the goals and the requirements of the model are formulated, the boundaries of the system are determined and the system is put into context with its environment. The primary task of a model is not to give the best possible representation of reality, but to provide answers to questions. The formulation of a clear goal is not a trivial task. The list of requirements is a suimnary of conditions and constraints that should be met. As mentioned before, the definition phase is the most important phase. Feedback does not happen until the evaluation phase. Then it will become clear whether the goals are met. 

These difficulties have led to a revival of work on internal coordinate approaches, and to date several such techniques have been reported based on methods of rigid-body dynamics [8,19,34-37] and the Lagrange-Hamilton formalism [38-42]. These methods often have little in common in their analytical formulations, but they all may be reasonably referred to as internal coordinate molecular dynamics (ICMD) to underline their main distinction from conventional MD They all consider molecular motion in the space of generalized internal coordinates rather than in the usual Cartesian coordinate space. Their main goal is to compute long-duration macromolecular trajectories with acceptable accuracy but at a lower cost than Cartesian coordinate MD with bond length constraints. This task mrned out to be more complicated than it seemed initially. 

A process-synthesis problem can be formulated as a combination of tasks whose goal is the optimization of an economic objective function subject to constraints. Two types of mathematical techniques are the most used mixed-integer linear programming (MILP), and mixed-integer nonlinear programming (MINLP). 

Cognitive task analysis deals with how operators respond to tasks delegated to them either by the system or by their supervisors. Tasks is used here to designate the operations undertaken to achieve certain goals under a set of conditions created by the work system (Leplat 1990). CTA looks at several mental activities or processes that operators rely upon in order to assess the current situation, make decisions, and formulate plans of actions. CTA can include several stages ... 

The interaction task includes the set of lower-level interactions that are performed by the human and product to accomphsh the apphcation task that may also be at different levels. For example, the application-level goal of reviewing a medical record may involve the interaction-level task of retrieving the record from an electronic database. The retrieval task, in turn, entails lower-level interaction tasks of search that involves the still lower-level task of formulating a proper search query. Each level of tasks may impose cognitive demands. 

These equations require the enthalpy and entropy of the system and its various streams. The problem, then is how to calculate the properties of mixture. The properties of pure substance are functions of pressure and temperature. For mixtures, in addition to pressure and temperature we must consider composition. The goal in this chapter is to formulate equations for the properties of mixtures as a function of pressure, temperature and composition. Essentially, the task will be to incorporate composition as a new independent variable. We will express composition in terms of moles of each component, therefore, when we refer to composition as an independent variable we will understand not a single variable but a set of variables. First we will develop formal mathematical expressions for properties, their differentials and their partial derivatives in terms of the independent variables, temperature, pressure and moles of component i. Next we will show how we can use equations of state to calculate the volume, enthalpy and entropy of mixtures. The mathematical formulation is based on the material developed in Chapter r. A review of that chapter is recommended, as we will make frequent references to results obtained there. 

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