Process systems engineering (PSE), as the name suggests, emphasizes an approach to understanding the behavior of systems as a whole with a view to improving decision-making for optimization and control of processes. The discipline emphasizes the application of mathematical techniques in this effort, and a plausible claim has been made that is at the very core of the discipline of chemical engineering. Being a generalized approach to process systems in general, it finds wide application to many areas in chemical engineering. This work reviews the application of PSE to the area of reaction engineering, which is also at the core of chemical engineering. We highlight the impactful applications of PSE in reaction engineering and discuss aspects of model building and analysis, reactor control, optimization, chemometrics, and chemoinformatics.
Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximising algebraic connectivity both local and globally over all simple, undirected, unweighted graphs with a given number of vertices and edges. We pursue this optimization by equivalently minimizing the largest eigenvalue of the Laplacian of the 'complement graph'. We establish that the union of complete subgraphs are largest eigenvalue local minimizer graphs. Further, under sufficient conditions satisfied by the edge/vertex counts we prove that this union of complete components graphs are, in fact, Laplacian largest eigenvalue global maximizers; these results generalize the ones in the literature that are for just two components. These sufficient conditions can be viewed as quantifying situations where the component sizes are either 'quite homogeneous' or some of them are relatively 'negligibly small', and thus generalize known results of homogeneity of components. We finally relate this optimization with the Discrete Fourier Transform (DFT) and circulant graphs/matrices.
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