Complex systems, characterization

Fig. 2.21 shows a few examples of very complex systems characterized by the formation of several (point and solution range) intermediate phases often involved in a number of different formation and decomposition reactions. The crowded sequence of intermediate compounds of interrelated structures is noteworthy in the Au-rich region of the Au-Mn system. A similar situation (however, not yet well defined) may... 

Swiss Cheese Model of Accident Causation (Introduction) A metaphorical, visual representation of the nature of emerging risks in complex systems characterized by vulnerabilities as well as defenses. 

The design of adhesive mortars was based on binders of either hydrate lime-metakaolin or natural hydraulie lime, with the aim of formulating a complex system characterized by the highest compatibility. Nowadays, both hydrate lime-metakaolin and natural hydraulic lime mortars are widely used in the field of restoration and conservation of architectural monuments, due to their capability to enhance the chemical, physical, structural and mechanical compatibility with historical building materials (stones, bricks and mortars) (Rosario 2009). This compatibility is a very critical prerequisite for the optimum performance of conservation mortars, considering the damage caused to historic monuments dming the past decades, due to the extensive use of cement-based composites. 

This level of simplicity is not the usual case in the systems that are of interest to chemical engineers. The complexity we will encounter will be much higher and will involve more detailed issues on the right-hand side of the equations we work with. Instead of a constant or some explicit function of time, the function will be an explicit function of one or more key characterizing variables of the system and implicit in time. The reason for this is that of cause. Time in and of itself is never a physical or chemical cause—it is simply the independent variable. When we need to deal with the analysis of more complex systems the mechanism that causes the change we are modeling becomes all important. Therefore we look for descriptions that will be dependent on the mechanism of change. In fact, we can learn about the mechanism of... 

In the systems characterized by more complex surface structure, consisting of patches of different size and different magnitude of the boundary field, the properties of adsorption isotherms have been found to depend on the... 

A similar shift of peak between the two forms occurs in modes 7 and 8 (in the 0 form, peak 7 is quite strong while peak 8 is weak these intensities are reversed for the 180 form). These mode. are characterized by motion of several hydrogen nuclei. They could be used for further discussion of normal modes in this more complex system. 

It is one thing to describe as we have done informally above, even qualitatively, what a complex system is, and to conjure up myriad examples of complex systems. It is quite another to quantify the notion of complexity itself, to describe the relationship between complexity and information, and/or to understand the role that complexity plays in various physical and/or computational contexts. Each of these difficult problems in fact remains very much open. While we may find it easy enough to distinguish a complex object from a less complex object, it is far from trivial to furnish anything that goes beyond a vague characterization as to how we have done so. Some recent attempts at quantifying the notion of complexity are sketched below. 

However, we have to criticize more specifically the paper by Lown et al. (1984), who characterized alkanediazonium ions, as well as (E)- and (Z)-alkanediazoate ions, by 15N NMR spectroscopy. They also report NMR data on the (E)- and (Z)-benzenediazohydroxides as reference compounds, describing the way they obtained these compounds in only three lines. Obviously the authors are not familiar with the work on the complex system of acid-base equilibria which led 30 years earlier to the conclusion that the maximum equilibrium concentration of benzenediazohydroxide is less than 1 % of the stoichiometric concentration in water (see Ch. 5). The method of Lown et al. consists in adding 10% (v/v) water to a mixture of benzenediazonium chloride and KOH in dimethylsulfoxide. In the opinion of the present author it is unlikely that this procedure yields the (Z)- and CE>benzenediazohydroxides. Such a claim needs more detailed experimental evidence. 

The simplest solid—solid reactions are those involving two solid reactants and a single barrier product phase. The principles used in interpreting the results of kinetic studies on such systems, and which have been described above, can be modified for application to more complex systems. Many of these complex systems have been resolved into a series of interconnected binary reactions and some of the more fully characterized examples have already been mentioned. While certain of these rate processes are of considerable technological importance, e.g. to the cement industry [1], the difficulties of investigation are such that few quantitative kinetic studies have been attempted. Attention has more frequently been restricted to the qualitative identifications of intermediate and product phases, or, at best, empirical rate measurements for technological purposes. 

Most of the existing tools to improve process operations fail to provide a. systematic and formal process of handling complex systems, or do so in ways that do not fulfill the preceding set of requests. In this paragraph we provide a more formal characterization of a complex system and its several... 

An unusual pH dependence has been reported for the Gd111 complex of a tetraamide-based ligand with extended noncoordinating phosphonate side chains (Scheme 12).169,170 The relaxivity increases from pH 4 to 6, followed by a decrease until pH 8.5, then from pH 10.5 it increases again. The system, as well as isostructural lanthanide complexes, was characterized by various techniques such as 31P and 170 NMR and fluorescence measurements. The pH dependence could be attributed to protonation equilibria of the noncoordinating phosphonate groups, which can... 

In complex systems, fA is not a unique parameter for following the course of a reaction, unlike in simple systems. For both kinetics and reactor considerations (Chapter 18), this means that rate laws and design equations cannot be uniquely expressed in terms of /A, and are usually written in terms of molar concentrations, or molar flow rates or extents of reaction. Nevertheless, fA may still be used to characterize the overall reaction extent with respect to reactant A. 

A sample may be characterized by the determination of a number of different analytes. For example, a hydrocarbon mixture can be analysed by use of a series of UV absorption peaks. Alternatively, in a sediment sample a range of trace metals may be determined. Collectively, these data represent patterns characteristic of the samples, and similar samples will have similar patterns. Results may be compared by vectorial presentation of the variables, when the variables for similar samples will form clusters. Hence the term cluster analysis. Where only two variables are studied, clusters are readily recognized in a two-dimensional graphical presentation. For more complex systems with more variables, i.e. //, the clusters will be in -dimensional space. Principal component analysis (PCA) explores the interdependence of pairs of variables in order to reduce the number to certain principal components. A practical example could be drawn from the sediment analysis mentioned above. Trace metals are often attached to sediment particles by sorption on to the hydrous oxides of Al, Fe and Mn that are present. The Al content could be a principal component to which the other metal contents are related. Factor analysis is a more sophisticated form of principal component analysis. 

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