Plenary Lecture

Applying Linear Algebra for Semi-Empirical Modeling in Physical and Economic Systems by Means of Dimensional Analysis

Professor Fragiskos Batzias
Laboratory of Simulation of Industrial Processes
Department of Industrial Management and Technology
University of Piraeus

Abstract: Linear Algebra application under the form of Dimensional Analysis was initially used early in the last century by scientists and engineers for expressing the behaviour of a physical system in terms of the minimum number of independent/explanatory variables/parameters/coefficients (VPCs) and in a mathematical mode that is unaffected by changes in the magnitude of the units of measurement. The first attempt to a similar approach in Economics was made by Allais (1943, 1953), who presented a systematic treatment of the theory of dimensions and its foundations. Later, some researchers, among them the presenter (Batzias et al., 2009), contributed to the diffusion of this scientific topic either for systems analysis by using special Linear Algebra techniques or for checking simulation models by using a properly designed algorithm.
In the present work, a Linear Algebra methodology is introduced under the form of a flow chart, including 24 activity stages and 6 decision nodes, to develop a cyclic/iterative inductive/deductive procedure for modelling physical and economic systems. This methodology, although it produces empirical relations, especially useful to facilitate scale-up/down in chemical engineering and economic growth, uses dimensionless groups expressing ratios with some kind of scientific/economic meaning. As a matter of fact, such relations (if properly selected/synthesized) may serve as knowledge carriers, capable to bridge the gap between an empirical and a corresponding theoretical model; in this sense, the relations, including dimensionless groups, are rather ‘grey’ than ‘black’ boxes. The functionality of the methodology presented herein is proved by making reference to three case studies, thoroughly analyzed and discussed within the framework of Linear Algebra and Group Theory.

Brief Biography of the Speaker: Prof. Fragiskos Batzias holds a 5years Diploma and a PhD degree in Chemical Engineering, and a BSc in Economics. He has also studied Mathematics and Philosophy. He is Director of the Laboratory of Simulation of Industrial Processes and Head of the Research Group on Systems Analysis at the Department of Industrial Management and Technology of the University of Piraeus, Greece. He is teaching at the interdepartmental postgraduate courses (i) Systems of Energy Management and Protection of the Environment, running by the University of Piraeus in cooperation with the Chem. Eng. Dept. of the Nat. Tech. Univ. of Athens, and (ii) Techno-Economic Systems, running by the Electr. & Comp. Eng. Dept. of the Nat. Tech. Univ. of Athens in cooperation with the University of Athens and the University of Piraeus. His research interests are in chemical engineering systems analysis and knowledge based decision making. He has >100 publications in highly ranked journals and conference proceedings, including 29 research monographs in collective volumes, with 171 citations and an h-index of 8 (for the period 2004-2012, source: ISI Web of Science, Thompson Scientific; self-citations have been excluded).
He has participated (and chaired after invitation from the organizers) in prestigious international conferences, such as those organized periodically by the IEEE, the European Federation of Chemical Engineering (EFCE), the DECHEMA, CHISA, WSEAS Organizations. He organizes the annual Symposium on Industrial and Environmental Case Studies running successfully since 2004 within the International Conference of Computational Methods in Sciences and Engineering (ICCMSE).

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