Abstract
Phenomena in the physical sciences are described with quantities that have a numerical value and a dimension, i.e., a physical unit. Dimensional analysis is a powerful aspect of modeling and simulation. Characteristic quantities formed by a combination of model parameters can give new insights without detailed analytic or numerical calculations. Dimensional requirements lead to Buckingham’s Π theorem—a general mathematical structure of all models in physics. These aspects are illustrated with many examples of modeling, e.g., an elastic beam on supports, wave propagation on a liquid surface, the Lennard-Jones potential for the interaction between atoms, the Lindemann melting rule, and saturation phenomena in electrical and thermal conduction.
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Grimvall, G. (2008). Characteristic quantities and dimensional analysis. In: Yip, S., de la Rubia, T.D. (eds) Scientific Modeling and Simulations. Lecture Notes in Computational Science and Engineering, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9741-6_4
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DOI: https://doi.org/10.1007/978-1-4020-9741-6_4
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