Problem specification

When operated for extended periods, the two junctions showed different behavior [48). Thus, the Nb/Pb type exhibited both an initial stabilization period (five to six months) of the main electrical parameters and then after about three years a progressive deterioration of the Pb film as a consequence of adsorbed ambient humidity. In contrast, the Nb/(Pb-In) junction possessed superior stability of the top electrode against degradation induced by humidity, and its electrical performance was of a higher standard. 

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Thus the optimal reflux ratio for an appropriately integrated distillation column will be problem-specific and is likely to be quite different from that for a stand-alone column. 

The properties linked to storage and distribution do not directly affect the performance of engines and burners, but they are important in avoiding upstream incidents that could sometimes be very serious. We will examine in turn the problems specific to gasoline, diesel fuel, jet fuel and heavy fuel. 

Because the Navier-Stokes equations are first-order in pressure and second-order in velocity, their solution requires one pressure bound-aiy condition and two velocity boundaiy conditions (for each velocity component) to completely specify the solution. The no sBp condition, whicn requires that the fluid velocity equal the velocity or any bounding solid surface, occurs in most problems. Specification of velocity is a type of boundary condition sometimes called a Dirichlet condition. Often boundary conditions involve stresses, and thus velocity gradients, rather than the velocities themselves. Specification of velocity derivatives is a Neumann boundary condition. For example, at the boundary between a viscous liquid and a gas, it is often assumed that the liquid shear stresses are zero. In numerical solution of the Navier-... 

Moisture content is another common and controllable flow factor. Most materials can safely absorb moisture up to a certain point further addition of moisture can cause significant flow problems. Specifications can control the amount of moisture content present in purchased raw materials. Moisture content can be lowered in the plant by including a drying operation in the process line. The costs incurred in drying may be offset by more efficient flow, lower shipping cost, and control of deterioration losses. 

Adjuncts include antifoams and defoamers, some problem-specific polymers, and alkalinity boosters. 

Problem-specific polymers include terpolymers, used for iron dispersion, iron transport, and silica control. 

Anodic inhibitor programs are not employed for steam boilers operating at over 15 psig. Above this pressure, more comprehensive and problem-specific programs are employed. 

Stabilizers, transport agents, or problem-specific polymers to... 

This list is by no means exhaustive. Many other amines have been employed from time to time, and novel materials are occasionally tested under high temperature conditions to control problems specific to critical units, especially in PWR secondary cycles and other power applications. 

Apart from physically cleaning tanks periodically, dispersants that promote homogeneity are employed. These often take the form of dispersant packages, which are polymer blends containing asphaltene and wax dispersants and other problem-specific additives. In addition, low-priced general-purpose dispersants, microbiocides, and antioxidants form part of the package. 

Problem-specific polymer, function of all-organics 443 Problem-specific polymers, as adjuncts 389... 

Finding differences is one aspect of the problem, the second is to integrate problem-specific chemical know-how with statistics ... 

Figure 8 depicts our view of an ideal structure for an applications program. The boxes with the heavy borders represent those functions that are problem specific, while the light-border boxes represent those functions that can be relegated to problem-independent software. This structure is well-suited to problems that are mathematically either systems of nonlinear algebraic equations, ordinary differential equation initial or boundary value problems, or parabolic partial differential equations. In these cases the problem-independent mathematical software is usually written in the form of a subroutine that in turn calls a user-supplied subroutine to define the system of equations. Of course, the user must write the subroutine that defines his particular system of equations. However, that subroutine should be able to make calls to problem-independent software to return many of the components that are needed to assemble the governing equations. Specifically, such software could be called to return in-... 

Figure 8. Schematic representation of an ideal applications program. The boxes with the heavy borders represent those functions that are problem specific, while the light-border boxes represent those functions that can be relegated to problem-independent software.

To solve the problems of representation and control, we will employ the framework of the branch-and-bound algorithm, which has been used to solve many types of combinatorial optimization problems, in chemical engineering, other domains of engineering, and a broad range of management problems. Specifically, we will use the framework proposed by Ibaraki (1978), which is characterized by the following features ... 

We can thus think of our predicates as falling into two classes (1) the formulation-specific, and (2) the problem-specific. The implications fall into three classes (1) those that interconnect the general concepts of the formulation, (2) those that connect the general concepts of the formulation to the specific details of the problem, and finally (3) those that enable reasoning about the specific details of the problem. We have already described the predicates necessary for reasoning within the flowshop problem thus the rest of this section will focus on the general predicates and their interconnection with the specific problem details. 

Fouling of the reactor and other equipment is another problem specific for homogeneous catalysis. 

The same problem specification has been used in earlier examples to illustrate the shortcut design methods. 

The characteristics of the network also enter into the considerations in selecting the problem formulation. If the network is acyclic, are the formulations involving cycle equations still appropriate Epp and Fowler (E2) suggested that if the pressures at two connected vertices are given, a cycle equation can always be written for a pseudo-loop which contains a fictitious edge linking these two vertices. In this way formulation D may be modified to accommodate networks that are not completely cyclic. However, for other types of specifications, formulations A and C are clearly more appropriate. The choice of a formulation is thus closely intertwined with the nature of problem specification which is the next topic of our discussion. 

In Section II,C we have deliberately chosen a simple set of problem specifications for our steady-state pipeline network formulation. The specification of the pressure at one vertex and a consistent set of inputs and outputs (satisfying the overall material balance) to the network seems intuitively reasonable. However, such a choice may not correspond to the engineering requirements in many applications. For instance, in analyzing an existing network we may wish to determine certain input and output flow rates from a knowledge of pressure distribution in the network, or to compute the parameters in the network element models on the basis of flow and pressure measurements. Clearly, the specified and the unknown variables will be different in these cases. For any pipeline network how many variables must be specified And what constitutes an admissible set of specifications in... 

Let us consider the problem specification discussed in Section II,C. For a network with M external flows (inputs and outputs), the specification introduces the following additional equations ... 

More recently, Cheng (C7) showed that to apply tearing effectively one must take into consideration the topology of the network and the nature of problem specifications. For instance, if the network consists of a number of cyclic subnetworks imbedded in an acyclic framework and if all the external flows and one reference pressure are specified, the flows and the pressures external to the cyclic subnetworks may be computed sequentially and only... 

Although selection of the appropriate analysis techniques is often very problem specific, the basic elements of human health risk analysis are few, as presented in Figure 1. The figure shows that the aggregate risk to human health from exposure to an airborne pollutant results from two factors (1) the spread of the primary agent (and/or its... 

Note that in Fig. 2.8, product 2 is produced almost 1 h prior to the completion of separation in accordance with problem specification in Table 2.4. 

In both the above solutions a change in the length of the time horizon will affect the resulting solution. It is very possible that an increase in the length of the time horizon will allow for the production of less effluent, whilst, a decrease in the time horizon could result in an increase in the amount of effluent produced. It is impossible to say if there is a specific trend as the time horizon increases. It is assumed that the time horizon in each problem is fixed during problem specification. The impact of the time horizon on the wastewater reuse opportunities fell outside the scope of the investigation. 

Secondly, the network layout showed in Fig. 12.7 shows that 12.5 t of water should be supplied to Process 3, instead of 25 t stipulated in the problem specification. This can only be true if this process does not have flowrate constraints, but has a fixed mass load. The assumption of fixed mass loads was never mentioned in the analysis. This variation of flowrate is contrary to the assumption made in targeting. During targeting it was implicitly assumed that the flowrates were fixed as shown by the calculation of water demand in each of the time subintervals. 

Fig. 12.8 Graphical representation of the problem specification, with x set to 0.1 kg salt/kg water... 

To accommodate completely batch operations, the procedure is easily modified by recognizing that water is required or available in discrete amounts, only at the beginning and end of both concentration and time intervals. The unknown concentrations (x) in the problem specification can be handled by repeating the calculations for a series of successively lower values for x, and selecting the lowest value that does not cause the overall water demand to increase. 

The same hypothetical example was used to illustrate the targeting procedure for a case where concentration is treated as a primary constraints. The problem specification still remains the same as that used Section 12.2.2 (Table 12.2). 

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