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Characteristic quantities and dimensional analysis

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Scientific Modeling and Simulation SMNS

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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  1. Theoretical Physics, Royal Institute of Technology, AlbaNova University Center, 106 91, Stockholm, Sweden

    Göran Grimvall

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  1. Göran Grimvall
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Correspondence to Göran Grimvall.

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Grimvall, G. Characteristic quantities and dimensional analysis. Sci Model Simul 15, 21–39 (2008). https://doi.org/10.1007/s10820-008-9102-4

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  • DOI: https://doi.org/10.1007/s10820-008-9102-4

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