Capacity interacting

Mazzola JB (1989) Generalized assignment with nonlinear capacity interaction. Management Science 35 923-941... 

The stirred tank heater of Example 4.4 is characterized by its capacity to store mass and energy. It is easy to show that these two capacities interact when the inlet flowrate changes. Thus, a change in the inlet flowrate affects the liquid level in the tank, which in turn affects the temperature of the liquid. Consequently, the temperature response to an inlet flowrate change exhibits second-order overdamped characteristics. The reader should note that the two capacities do not interact when the inlet temperature changes. Therefore, the temperature response to inlet temperature changes exhibits first-order characteristics. 

It is easy to show that the three capacities interact. 

Distillation and gas absorption columns are very often encountered in chemical processes for the separation of a mixture into its components. Both systems have a number of trays. Each tray has material and heat capacities. Therefore, each column with N trays can be considered as a system with 2 N capacities in series. From the physics of distillation and absorption it is easy to see that the 2N capacities interact. 

In an ideal binary distillation column the dynamics of each tray can be described by first-order systems. Are these capacities interacting or not What general types of responses would you expect for the overhead and bottoms compositions to a step change in the feed composition ... 

A drum boiler (Figure PII. 10) has a capacity to store material and thermal energy. Are these capacities interacting or not ... 

This chapter begins with an overview of these three components of the Project De-sign approach. Representation is described as modeling of sociotechnical characteristics include scope, teams, complexity, distribution, coordination as activity, and con-current and mutual dependence. Next, agent-based simulation of the engineering project is described which analyzes realistic outcomes including limits due to technical complexity, human priorities, capacities, interactions, and mistakes. These models and analytics are then shown as they are used in collaborative workshops. Two industrial cases are discussed, followed by a comparison with contemporary approaches and discussion of the benefits of Project Design. 

An important point to grasp is that interaetion makes control easier. Recall that the proportional band required to regulate a two-eapacity process varies with t, Vijvith the most difficult case being t = ti. Where capacities interact, however, it is impossible to make rj = ri. The ratio of two equal interacting time constants is 0.382 - 2.0)18 = 0.146. By this standard the noninteracting process is nearly seven times more difficult to control ... 

But where the principal flow passes through coupled capacities, interaction is manifest. This is thr case iii the lower pair of tanks in Fig. 2.1. If each of these tanks has a volume 1 and a discharge flow coetficient k, the response of level in the second tank to variations >n don- in the first will be characterized by a steady-state gain of 1 k and time constants of 2.()1817 fc nd 0.3821 /FA . I t may be recalled that the time constant of the individual tanks was V/Fk. The steady-state level in the second tank equals /,/A . The steady-state level in the first tank would be 2/,/fc... 

As an example, the lo-capacity interacting process of Fig. 2.2 has an effective dead time of about 0.15 of the total lag. Since the balance is the dominant time constant, the ratio t /ti = 0.1a/0.8o = 0.18. The proportional band needed for I -ampIitude damping of this process can be found by referring to Fig. 1.26. 

Aguilar M A and Olivares del Valle F J 1989 Solute-solvent interactions. A simple procedure for constructing the solvent capacity for retaining a molecular solute Ohem. Rhys. 129 439-50... 

Nevertheless, the examination of the applicability of the crude BO approximation can start now because we have worked out basic methods to compute the matrix elements. With the advances in the capacity of computers, the test of these methods can be done in lower and lower cost. In this work, we have obtained the formulas and shown their applications for the simple cases, but workers interested in using these matrix elements in their work would find that it is not difficult to extend our results to higher order derivatives of Coulomb interaction, or the cases of more-than-two-atom molecules. 

The second important influence of the solvent on Lewis acid - Lewis base equilibria concerns the interactions with the Lewis base. Consequently the Lewis addity and, for hard Lewis bases, especially the hydrogen bond donor capacity of tire solvent are important parameters. The electron pair acceptor capacities, quantified by the acceptor number AN, together with the hydrogen bond donor addities. O, of some selected solvents are listed in Table 1.5. Water is among the solvents with the highest AN and, accordingly, interacts strongly witli Lewis bases. This seriously hampers die efficiency of Lewis-acid catalysis in water. 

Salt Effects. The definition of a capacity factor k in hydrophobic interaction chromatography is analogous to the distribution coefficient, in gel permeation chromatography ... 

Although the chiral recognition mechanism of these cyclodexttin-based phases is not entirely understood, thermodynamic and column capacity studies indicate that the analytes may interact with the functionalized cyclodextrins by either associating with the outside or mouth of the cyclodextrin, or by forming a more traditional inclusion complex with the cyclodextrin (122). As in the case of the metal-complex chiral stationary phase, configuration assignment is generally not possible in the absence of pure chiral standards. 

The principle of specific chemical recognition is common to ligand—macromolecule interactions, but this alone does not suffice to define a receptor in the pharmacologic sense. Rather, it is the combination of chemical specificity or recognition and the capacity to initiate biological response or transduction that define the pharmacologic receptor (1,10,11). 

Molecular Interactions. Various polysaccharides readily associate with other substances, including bile acids and cholesterol, proteins, small organic molecules, inorganic salts, and ions. Anionic polysaccharides form salts and chelate complexes with cations some neutral polysaccharides form complexes with inorganic salts and some interactions are stmcture specific. Starch amylose and the linear branches of amylopectin form inclusion complexes with several classes of polar molecules, including fatty acids, glycerides, alcohols, esters, ketones, and iodine/iodide. The absorbed molecule occupies the cavity of the amylose helix, which has the capacity to expand somewhat to accommodate larger molecules. The starch—Hpid complex is important in food systems. Whether similar inclusion complexes can form with any of the dietary fiber components is not known. 

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