Critical variation

Similarly, the layer compressibility constant, B, exhibits a critical variation in the vicinity of the transition. This pretransitional behavior above AN has been recognized by de Vries [32], who, by X-ray diffraction experiments, has shown the existence of small domains with a smectic... 

In order to test the economic performance of the project to variations in the base case estimates for the input data, sensitivity analysis is performed. This shows how robust the project is to variations in one or more parameters, and also highlights which of the inputs the project economics is more sensitive to. These inputs can then be addressed more specifically. For example if the project economics is highly sensitive to a delay in first production, then the scheduling should be more critically reviewed. 

Figure 4.15 Geometrical representation of the temperature variation of the actual volume (solid line) and the occupied volume (broken line). The shaded difference indicates the free volume which decreases to a critical value at T .

We noted above that the presence of monomer with a functionality greater than 2 results in branched polymer chains. This in turn produces a three-dimensional network of polymer under certain circumstances. The solubility and mechanical behavior of such materials depend critically on whether the extent of polymerization is above or below the threshold for the formation of this network. The threshold is described as the gel point, since the reaction mixture sets up or gels at this point. We have previously introduced the term thermosetting to describe these cross-linked polymeric materials. Because their mechanical properties are largely unaffected by temperature variations-in contrast to thermoplastic materials which become more fluid on heating-step-growth polymers that exceed the gel point are widely used as engineering materials. 

The processes used commercially for the manufacture of film and sheeting materials are generaUy similar in basic concept, but variations in equipment or process conditions are used to optimize output for each type of film or sheeting material. The nature of the polymer to be used, its formulation with plasticizers (qv), fillers (qv), flow modifiers, stabilizers, and other modifiers, as weU as its molecular weight and distribution are aU critical to the... 

Volumetric heat generation increases with temperature as a single or multiple S-shaped curves, whereas surface heat removal increases linearly. The shapes of these heat-generation curves and the slopes of the heat-removal lines depend on reaction kinetics, activation energies, reactant concentrations, flow rates, and the initial temperatures of reactants and coolants (70). The intersections of the heat-generation curves and heat-removal lines represent possible steady-state operations called stationary states (Fig. 15). Multiple stationary states are possible. Control is introduced to estabHsh the desired steady-state operation, produce products at targeted rates, and provide safe start-up and shutdown. Control methods can affect overall performance by their way of adjusting temperature and concentration variations and upsets, and by the closeness to which critical variables are operated near their limits. 

Milling not only provides intimate mixing, but also eliminates variation in ribbon thickness and cmshes lumpy materials, eg, overdried soap, which might impact finished bar texture. Milling is also used for the formation of the proper bar soap crystalline phase, which plays a critical role in both the performance properties of the soap bar and the handling characteristics of the in-process soap. For example, too hot a milling temperature can create sticky soap that is difficult to process further. 

Polyphase Alloys. The two-phase alloys have a rather wide range of properties resulting from variations within the stmcture. If the second phase is distributed in critical depression, the hardness and strength are at a maximum and the ductility is at a moderate level. Tensile strength may be 415—825 MPa (60,000—120,000 psi) yield strength, 170—585 MPa (25,000—85,000 psi) and elongation, 10—40%. 

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