Characteristic quantities and dimensional analysis
2009 (English)In: Scientific Modeling and Simulations, Springer Netherlands, 2009, 21-39 p.Chapter in book (Refereed)
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.
Place, publisher, year, edition, pages
Springer Netherlands, 2009. 21-39 p.
, Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 68
Buckingham's theorem, Characteristic quantity, Dimensional analysis, Lennard-Jones interaction, Scaling, Elastic beam, Lennard-Jones potential, Lindemann melting, Liquid surface, Mathematical structure, Model parameters, Modeling and simulation, Numerical calculation, Numerical values, Physical science, Thermal conduction, Computer simulation, Mathematical techniques
IdentifiersURN: urn:nbn:se:kth:diva-152429DOI: 10.1007/978-1-4020-9741-6_4ScopusID: 2-s2.0-78651549758ISBN: 978-140209740-9OAI: oai:DiVA.org:kth-152429DiVA: diva2:755300
QC 201410142014-10-142014-09-262014-10-14Bibliographically approved